diff options
| author | David Hook <dgh@cryptoworkshop.com> | 2022-08-08 17:37:50 +1000 |
|---|---|---|
| committer | David Hook <dgh@cryptoworkshop.com> | 2022-08-08 17:37:50 +1000 |
| commit | 2c6872aad29f8187ddc6535c5c4702e2a0238ecc (patch) | |
| tree | ab1d02cd6e820c877a86bdbce700f7f00db812d8 | |
| parent | move KEMExtractor to KemExtractor (diff) | |
| download | BouncyCastle.NET-ed25519-2c6872aad29f8187ddc6535c5c4702e2a0238ecc.tar.xz | |
Initial Falcon implementation
25 files changed, 12649 insertions, 0 deletions
diff --git a/crypto/src/pqc/crypto/falcon/FPREngine.cs b/crypto/src/pqc/crypto/falcon/FPREngine.cs new file mode 100644 index 000000000..d92c23235 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FPREngine.cs @@ -0,0 +1,1311 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FPREngine + { + internal FalconFPR FPR(double v) + { + return new FalconFPR(v); + } + + /* + * License from the reference C code (the code was copied then modified + * to function in C#): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + + internal FalconFPR fpr_of(long i) + { + return FPR((double)i); + } + + + + internal long fpr_rint(FalconFPR x) + { + /* + * We do not want to use llrint() since it might be not + * constant-time. + * + * Suppose that x >= 0. If x >= 2^52, then it is already an + * integer. Otherwise, if x < 2^52, then computing x+2^52 will + * yield a value that will be rounded to the nearest integer + * with exactly the right rules (round-to-nearest-even). + * + * In order to have constant-time processing, we must do the + * computation for both x >= 0 and x < 0 cases, and use a + * cast to an integer to access the sign and select the proper + * value. Such casts also allow us to find out if |x| < 2^52. + */ + long sx, tx, rp, rn, m; + uint ub; + + sx = (long)(x.v - 1.0); + tx = (long)x.v; + rp = (long)(x.v + 4503599627370496.0) - 4503599627370496; + rn = (long)(x.v - 4503599627370496.0) + 4503599627370496; + + /* + * If tx >= 2^52 or tx < -2^52, then result is tx. + * Otherwise, if sx >= 0, then result is rp. + * Otherwise, result is rn. We use the fact that when x is + * close to 0 (|x| <= 0.25) then both rp and rn are correct; + * and if x is not close to 0, then trunc(x-1.0) yields the + * appropriate sign. + */ + + /* + * Clamp rp to zero if tx < 0. + * Clamp rn to zero if tx >= 0. + */ + m = sx >> 63; + rn &= m; + rp &= ~m; + + /* + * Get the 12 upper bits of tx; if they are not all zeros or + * all ones, then tx >= 2^52 or tx < -2^52, and we clamp both + * rp and rn to zero. Otherwise, we clamp tx to zero. + */ + ub = (uint)((ulong)tx >> 52); + m = -(long)((((ub + 1) & 0xFFF) - 2) >> 31); + rp &= m; + rn &= m; + tx &= ~m; + + /* + * Only one of tx, rn or rp (at most) can be non-zero at this + * point. + */ + return tx | rn | rp; + } + + internal long fpr_floor(FalconFPR x) + { + long r; + + /* + * The cast performs a trunc() (rounding toward 0) and thus is + * wrong by 1 for most negative values. The correction below is + * constant-time as long as the compiler turns the + * floating-point conversion result into a 0/1 integer without a + * conditional branch or another non-constant-time construction. + * This should hold on all modern architectures with an FPU (and + * if it is false on a given arch, then chances are that the FPU + * itself is not constant-time, making the point moot). + */ + r = (long)x.v; + return r - ((x.v < (double)r) ? 1 : 0); + } + + internal long fpr_trunc(FalconFPR x) + { + return (long)x.v; + } + + internal FalconFPR fpr_add(FalconFPR x, FalconFPR y) + { + return FPR(x.v + y.v); + } + + internal FalconFPR fpr_sub(FalconFPR x, FalconFPR y) + { + return FPR(x.v - y.v); + } + + internal FalconFPR fpr_neg(FalconFPR x) + { + return FPR(-x.v); + } + + internal FalconFPR fpr_half(FalconFPR x) + { + return FPR(x.v * 0.5); + } + + internal FalconFPR fpr_double(FalconFPR x) + { + return FPR(x.v + x.v); + } + + internal FalconFPR fpr_mul(FalconFPR x, FalconFPR y) + { + return FPR(x.v * y.v); + } + + internal FalconFPR fpr_sqr(FalconFPR x) + { + return FPR(x.v * x.v); + } + + internal FalconFPR fpr_inv(FalconFPR x) + { + return FPR(1.0 / x.v); + } + + internal FalconFPR fpr_div(FalconFPR x, FalconFPR y) + { + return FPR(x.v / y.v); + } + + + internal FalconFPR fpr_sqrt(FalconFPR x) + { + return FPR(System.Math.Sqrt(x.v)); + } + + internal bool fpr_lt(FalconFPR x, FalconFPR y) + { + return x.v < y.v; + } + + internal ulong fpr_expm_p63(FalconFPR x, FalconFPR ccs) + { + /* + * Polynomial approximation of exp(-x) is taken from FACCT: + * https://eprint.iacr.org/2018/1234 + * Specifically, values are extracted from the implementation + * referenced from the FACCT article, and available at: + * https://github.com/raykzhao/gaussian + * Tests over more than 24 billions of random inputs in the + * 0..log(2) range have never shown a deviation larger than + * 2^(-50) from the true mathematical value. + */ + + + /* + * Normal implementation uses Horner's method, which minimizes + * the number of operations. + */ + + double d, y; + + d = x.v; + y = 0.000000002073772366009083061987; + y = 0.000000025299506379442070029551 - y * d; + y = 0.000000275607356160477811864927 - y * d; + y = 0.000002755586350219122514855659 - y * d; + y = 0.000024801566833585381209939524 - y * d; + y = 0.000198412739277311890541063977 - y * d; + y = 0.001388888894063186997887560103 - y * d; + y = 0.008333333327800835146903501993 - y * d; + y = 0.041666666666110491190622155955 - y * d; + y = 0.166666666666984014666397229121 - y * d; + y = 0.500000000000019206858326015208 - y * d; + y = 0.999999999999994892974086724280 - y * d; + y = 1.000000000000000000000000000000 - y * d; + y *= ccs.v; + return (ulong)(y * fpr_ptwo63.v); + + } + + internal FalconFPR[] fpr_gm_tab = { + new FalconFPR(0), new FalconFPR(0), /* unused */ + new FalconFPR(-0.000000000000000000000000000), new FalconFPR( 1.000000000000000000000000000), + new FalconFPR( 0.707106781186547524400844362), new FalconFPR( 0.707106781186547524400844362), + new FalconFPR(-0.707106781186547524400844362), new FalconFPR( 0.707106781186547524400844362), + new FalconFPR( 0.923879532511286756128183189), new FalconFPR( 0.382683432365089771728459984), + new FalconFPR(-0.382683432365089771728459984), new FalconFPR( 0.923879532511286756128183189), + new FalconFPR( 0.382683432365089771728459984), new FalconFPR( 0.923879532511286756128183189), + new FalconFPR(-0.923879532511286756128183189), new FalconFPR( 0.382683432365089771728459984), + new FalconFPR( 0.980785280403230449126182236), new FalconFPR( 0.195090322016128267848284868), + new FalconFPR(-0.195090322016128267848284868), new FalconFPR( 0.980785280403230449126182236), + new FalconFPR( 0.555570233019602224742830814), new FalconFPR( 0.831469612302545237078788378), + new FalconFPR(-0.831469612302545237078788378), new FalconFPR( 0.555570233019602224742830814), + new FalconFPR( 0.831469612302545237078788378), new FalconFPR( 0.555570233019602224742830814), + new FalconFPR(-0.555570233019602224742830814), new FalconFPR( 0.831469612302545237078788378), + new FalconFPR( 0.195090322016128267848284868), new FalconFPR( 0.980785280403230449126182236), + new FalconFPR(-0.980785280403230449126182236), new FalconFPR( 0.195090322016128267848284868), + new FalconFPR( 0.995184726672196886244836953), new FalconFPR( 0.098017140329560601994195564), + new FalconFPR(-0.098017140329560601994195564), new FalconFPR( 0.995184726672196886244836953), + new FalconFPR( 0.634393284163645498215171613), new FalconFPR( 0.773010453362736960810906610), + new FalconFPR(-0.773010453362736960810906610), new FalconFPR( 0.634393284163645498215171613), + new FalconFPR( 0.881921264348355029712756864), new FalconFPR( 0.471396736825997648556387626), + new FalconFPR(-0.471396736825997648556387626), new FalconFPR( 0.881921264348355029712756864), + new FalconFPR( 0.290284677254462367636192376), new FalconFPR( 0.956940335732208864935797887), + new FalconFPR(-0.956940335732208864935797887), new FalconFPR( 0.290284677254462367636192376), + new FalconFPR( 0.956940335732208864935797887), new FalconFPR( 0.290284677254462367636192376), + new FalconFPR(-0.290284677254462367636192376), new FalconFPR( 0.956940335732208864935797887), + new FalconFPR( 0.471396736825997648556387626), new FalconFPR( 0.881921264348355029712756864), + new FalconFPR(-0.881921264348355029712756864), new FalconFPR( 0.471396736825997648556387626), + new FalconFPR( 0.773010453362736960810906610), new FalconFPR( 0.634393284163645498215171613), + new FalconFPR(-0.634393284163645498215171613), new FalconFPR( 0.773010453362736960810906610), + new FalconFPR( 0.098017140329560601994195564), new FalconFPR( 0.995184726672196886244836953), + new FalconFPR(-0.995184726672196886244836953), new FalconFPR( 0.098017140329560601994195564), + new FalconFPR( 0.998795456205172392714771605), new FalconFPR( 0.049067674327418014254954977), + new FalconFPR(-0.049067674327418014254954977), new FalconFPR( 0.998795456205172392714771605), + new FalconFPR( 0.671558954847018400625376850), new FalconFPR( 0.740951125354959091175616897), + new FalconFPR(-0.740951125354959091175616897), new FalconFPR( 0.671558954847018400625376850), + new FalconFPR( 0.903989293123443331586200297), new FalconFPR( 0.427555093430282094320966857), + new FalconFPR(-0.427555093430282094320966857), new FalconFPR( 0.903989293123443331586200297), + new FalconFPR( 0.336889853392220050689253213), new FalconFPR( 0.941544065183020778412509403), + new FalconFPR(-0.941544065183020778412509403), new FalconFPR( 0.336889853392220050689253213), + new FalconFPR( 0.970031253194543992603984207), new FalconFPR( 0.242980179903263889948274162), + new FalconFPR(-0.242980179903263889948274162), new FalconFPR( 0.970031253194543992603984207), + new FalconFPR( 0.514102744193221726593693839), new FalconFPR( 0.857728610000272069902269984), + new FalconFPR(-0.857728610000272069902269984), new FalconFPR( 0.514102744193221726593693839), + new FalconFPR( 0.803207531480644909806676513), new FalconFPR( 0.595699304492433343467036529), + new FalconFPR(-0.595699304492433343467036529), new FalconFPR( 0.803207531480644909806676513), + new FalconFPR( 0.146730474455361751658850130), new FalconFPR( 0.989176509964780973451673738), + new FalconFPR(-0.989176509964780973451673738), new FalconFPR( 0.146730474455361751658850130), + new FalconFPR( 0.989176509964780973451673738), new FalconFPR( 0.146730474455361751658850130), + new FalconFPR(-0.146730474455361751658850130), new FalconFPR( 0.989176509964780973451673738), + new FalconFPR( 0.595699304492433343467036529), new FalconFPR( 0.803207531480644909806676513), + new FalconFPR(-0.803207531480644909806676513), new FalconFPR( 0.595699304492433343467036529), + new FalconFPR( 0.857728610000272069902269984), new FalconFPR( 0.514102744193221726593693839), + new FalconFPR(-0.514102744193221726593693839), new FalconFPR( 0.857728610000272069902269984), + new FalconFPR( 0.242980179903263889948274162), new FalconFPR( 0.970031253194543992603984207), + new FalconFPR(-0.970031253194543992603984207), new FalconFPR( 0.242980179903263889948274162), + new FalconFPR( 0.941544065183020778412509403), new FalconFPR( 0.336889853392220050689253213), + new FalconFPR(-0.336889853392220050689253213), new FalconFPR( 0.941544065183020778412509403), + new FalconFPR( 0.427555093430282094320966857), new FalconFPR( 0.903989293123443331586200297), + new FalconFPR(-0.903989293123443331586200297), new FalconFPR( 0.427555093430282094320966857), + new FalconFPR( 0.740951125354959091175616897), new FalconFPR( 0.671558954847018400625376850), + new FalconFPR(-0.671558954847018400625376850), new FalconFPR( 0.740951125354959091175616897), + new FalconFPR( 0.049067674327418014254954977), new FalconFPR( 0.998795456205172392714771605), + new FalconFPR(-0.998795456205172392714771605), new FalconFPR( 0.049067674327418014254954977), + new FalconFPR( 0.999698818696204220115765650), new FalconFPR( 0.024541228522912288031734529), + new FalconFPR(-0.024541228522912288031734529), new FalconFPR( 0.999698818696204220115765650), + new FalconFPR( 0.689540544737066924616730630), new FalconFPR( 0.724247082951466920941069243), + new FalconFPR(-0.724247082951466920941069243), new FalconFPR( 0.689540544737066924616730630), + new FalconFPR( 0.914209755703530654635014829), new FalconFPR( 0.405241314004989870908481306), + new FalconFPR(-0.405241314004989870908481306), new FalconFPR( 0.914209755703530654635014829), + new FalconFPR( 0.359895036534988148775104572), new FalconFPR( 0.932992798834738887711660256), + new FalconFPR(-0.932992798834738887711660256), new FalconFPR( 0.359895036534988148775104572), + new FalconFPR( 0.975702130038528544460395766), new FalconFPR( 0.219101240156869797227737547), + new FalconFPR(-0.219101240156869797227737547), new FalconFPR( 0.975702130038528544460395766), + new FalconFPR( 0.534997619887097210663076905), new FalconFPR( 0.844853565249707073259571205), + new FalconFPR(-0.844853565249707073259571205), new FalconFPR( 0.534997619887097210663076905), + new FalconFPR( 0.817584813151583696504920884), new FalconFPR( 0.575808191417845300745972454), + new FalconFPR(-0.575808191417845300745972454), new FalconFPR( 0.817584813151583696504920884), + new FalconFPR( 0.170961888760301226363642357), new FalconFPR( 0.985277642388941244774018433), + new FalconFPR(-0.985277642388941244774018433), new FalconFPR( 0.170961888760301226363642357), + new FalconFPR( 0.992479534598709998156767252), new FalconFPR( 0.122410675199216198498704474), + new FalconFPR(-0.122410675199216198498704474), new FalconFPR( 0.992479534598709998156767252), + new FalconFPR( 0.615231590580626845484913563), new FalconFPR( 0.788346427626606262009164705), + new FalconFPR(-0.788346427626606262009164705), new FalconFPR( 0.615231590580626845484913563), + new FalconFPR( 0.870086991108711418652292404), new FalconFPR( 0.492898192229784036873026689), + new FalconFPR(-0.492898192229784036873026689), new FalconFPR( 0.870086991108711418652292404), + new FalconFPR( 0.266712757474898386325286515), new FalconFPR( 0.963776065795439866686464356), + new FalconFPR(-0.963776065795439866686464356), new FalconFPR( 0.266712757474898386325286515), + new FalconFPR( 0.949528180593036667195936074), new FalconFPR( 0.313681740398891476656478846), + new FalconFPR(-0.313681740398891476656478846), new FalconFPR( 0.949528180593036667195936074), + new FalconFPR( 0.449611329654606600046294579), new FalconFPR( 0.893224301195515320342416447), + new FalconFPR(-0.893224301195515320342416447), new FalconFPR( 0.449611329654606600046294579), + new FalconFPR( 0.757208846506484547575464054), new FalconFPR( 0.653172842953776764084203014), + new FalconFPR(-0.653172842953776764084203014), new FalconFPR( 0.757208846506484547575464054), + new FalconFPR( 0.073564563599667423529465622), new FalconFPR( 0.997290456678690216135597140), + new FalconFPR(-0.997290456678690216135597140), new FalconFPR( 0.073564563599667423529465622), + new FalconFPR( 0.997290456678690216135597140), new FalconFPR( 0.073564563599667423529465622), + new FalconFPR(-0.073564563599667423529465622), new FalconFPR( 0.997290456678690216135597140), + new FalconFPR( 0.653172842953776764084203014), new FalconFPR( 0.757208846506484547575464054), + new FalconFPR(-0.757208846506484547575464054), new FalconFPR( 0.653172842953776764084203014), + new FalconFPR( 0.893224301195515320342416447), new FalconFPR( 0.449611329654606600046294579), + new FalconFPR(-0.449611329654606600046294579), new FalconFPR( 0.893224301195515320342416447), + new FalconFPR( 0.313681740398891476656478846), new FalconFPR( 0.949528180593036667195936074), + new FalconFPR(-0.949528180593036667195936074), new FalconFPR( 0.313681740398891476656478846), + new FalconFPR( 0.963776065795439866686464356), new FalconFPR( 0.266712757474898386325286515), + new FalconFPR(-0.266712757474898386325286515), new FalconFPR( 0.963776065795439866686464356), + new FalconFPR( 0.492898192229784036873026689), new FalconFPR( 0.870086991108711418652292404), + new FalconFPR(-0.870086991108711418652292404), new FalconFPR( 0.492898192229784036873026689), + new FalconFPR( 0.788346427626606262009164705), new FalconFPR( 0.615231590580626845484913563), + new FalconFPR(-0.615231590580626845484913563), new FalconFPR( 0.788346427626606262009164705), + new FalconFPR( 0.122410675199216198498704474), new FalconFPR( 0.992479534598709998156767252), + new FalconFPR(-0.992479534598709998156767252), new FalconFPR( 0.122410675199216198498704474), + new FalconFPR( 0.985277642388941244774018433), new FalconFPR( 0.170961888760301226363642357), + new FalconFPR(-0.170961888760301226363642357), new FalconFPR( 0.985277642388941244774018433), + new FalconFPR( 0.575808191417845300745972454), new FalconFPR( 0.817584813151583696504920884), + new FalconFPR(-0.817584813151583696504920884), new FalconFPR( 0.575808191417845300745972454), + new FalconFPR( 0.844853565249707073259571205), new FalconFPR( 0.534997619887097210663076905), + new FalconFPR(-0.534997619887097210663076905), new FalconFPR( 0.844853565249707073259571205), + new FalconFPR( 0.219101240156869797227737547), new FalconFPR( 0.975702130038528544460395766), + new FalconFPR(-0.975702130038528544460395766), new FalconFPR( 0.219101240156869797227737547), + new FalconFPR( 0.932992798834738887711660256), new FalconFPR( 0.359895036534988148775104572), + new FalconFPR(-0.359895036534988148775104572), new FalconFPR( 0.932992798834738887711660256), + new FalconFPR( 0.405241314004989870908481306), new FalconFPR( 0.914209755703530654635014829), + new 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FalconFPR(-0.997925286198596012623025462), new FalconFPR( 0.064382630929857460819324537), + new FalconFPR( 0.996571145790554847093566910), new FalconFPR( 0.082740264549375693111987083), + new FalconFPR(-0.082740264549375693111987083), new FalconFPR( 0.996571145790554847093566910), + new FalconFPR( 0.646176012983316364832802220), new FalconFPR( 0.763188417263381271704838297), + new FalconFPR(-0.763188417263381271704838297), new FalconFPR( 0.646176012983316364832802220), + new FalconFPR( 0.889048355854664562540777729), new FalconFPR( 0.457813303598877221904961155), + new FalconFPR(-0.457813303598877221904961155), new FalconFPR( 0.889048355854664562540777729), + new FalconFPR( 0.304929229735402406490728633), new FalconFPR( 0.952375012719765858529893608), + new FalconFPR(-0.952375012719765858529893608), new FalconFPR( 0.304929229735402406490728633), + new FalconFPR( 0.961280485811320641748659653), new FalconFPR( 0.275571819310958163076425168), + new FalconFPR(-0.275571819310958163076425168), new FalconFPR( 0.961280485811320641748659653), + new FalconFPR( 0.484869248000791101822951699), new FalconFPR( 0.874586652278176112634431897), + new FalconFPR(-0.874586652278176112634431897), new FalconFPR( 0.484869248000791101822951699), + new FalconFPR( 0.782650596166575738458949301), new FalconFPR( 0.622461279374149972519166721), + new FalconFPR(-0.622461279374149972519166721), new FalconFPR( 0.782650596166575738458949301), + new FalconFPR( 0.113270952177564349018228733), new FalconFPR( 0.993564135520595333782021697), + new FalconFPR(-0.993564135520595333782021697), new FalconFPR( 0.113270952177564349018228733), + new FalconFPR( 0.983662419211730274396237776), new FalconFPR( 0.180022901405699522679906590), + new FalconFPR(-0.180022901405699522679906590), new FalconFPR( 0.983662419211730274396237776), + new FalconFPR( 0.568258952670131549790548489), new FalconFPR( 0.822849781375826332046780034), + new FalconFPR(-0.822849781375826332046780034), new FalconFPR( 0.568258952670131549790548489), + new FalconFPR( 0.839893794195999504583383987), new FalconFPR( 0.542750784864515906586768661), + new FalconFPR(-0.542750784864515906586768661), new FalconFPR( 0.839893794195999504583383987), + new FalconFPR( 0.210111836880469621717489972), new FalconFPR( 0.977677357824509979943404762), + new FalconFPR(-0.977677357824509979943404762), new FalconFPR( 0.210111836880469621717489972), + new FalconFPR( 0.929640895843181265457918066), new FalconFPR( 0.368466829953372331712746222), + new FalconFPR(-0.368466829953372331712746222), new FalconFPR( 0.929640895843181265457918066), + new FalconFPR( 0.396809987416710328595290911), new FalconFPR( 0.917900775621390457642276297), + new FalconFPR(-0.917900775621390457642276297), new FalconFPR( 0.396809987416710328595290911), + new FalconFPR( 0.717870045055731736211325329), new FalconFPR( 0.696177131491462944788582591), + new FalconFPR(-0.696177131491462944788582591), new FalconFPR( 0.717870045055731736211325329), + new FalconFPR( 0.015339206284988101044151868), new FalconFPR( 0.999882347454212525633049627), + new FalconFPR(-0.999882347454212525633049627), new FalconFPR( 0.015339206284988101044151868), + new FalconFPR( 0.999769405351215321657617036), new FalconFPR( 0.021474080275469507418374898), + new FalconFPR(-0.021474080275469507418374898), new FalconFPR( 0.999769405351215321657617036), + new FalconFPR( 0.691759258364157774906734132), new FalconFPR( 0.722128193929215321243607198), + new FalconFPR(-0.722128193929215321243607198), new FalconFPR( 0.691759258364157774906734132), + new FalconFPR( 0.915448716088267819566431292), new FalconFPR( 0.402434650859418441082533934), + new FalconFPR(-0.402434650859418441082533934), new FalconFPR( 0.915448716088267819566431292), + new FalconFPR( 0.362755724367397216204854462), new FalconFPR( 0.931884265581668106718557199), + new FalconFPR(-0.931884265581668106718557199), new FalconFPR( 0.362755724367397216204854462), + new FalconFPR( 0.976369731330021149312732194), new FalconFPR( 0.216106797076219509948385131), + new FalconFPR(-0.216106797076219509948385131), new FalconFPR( 0.976369731330021149312732194), + new FalconFPR( 0.537587076295645482502214932), new FalconFPR( 0.843208239641845437161743865), + new FalconFPR(-0.843208239641845437161743865), new FalconFPR( 0.537587076295645482502214932), + new FalconFPR( 0.819347520076796960824689637), new FalconFPR( 0.573297166698042212820171239), + new FalconFPR(-0.573297166698042212820171239), new FalconFPR( 0.819347520076796960824689637), + new FalconFPR( 0.173983873387463827950700807), new FalconFPR( 0.984748501801904218556553176), + new FalconFPR(-0.984748501801904218556553176), new FalconFPR( 0.173983873387463827950700807), + new FalconFPR( 0.992850414459865090793563344), new FalconFPR( 0.119365214810991364593637790), + new FalconFPR(-0.119365214810991364593637790), new FalconFPR( 0.992850414459865090793563344), + new FalconFPR( 0.617647307937803932403979402), new FalconFPR( 0.786455213599085757522319464), + new FalconFPR(-0.786455213599085757522319464), new FalconFPR( 0.617647307937803932403979402), + new FalconFPR( 0.871595086655951034842481435), new FalconFPR( 0.490226483288291154229598449), + new FalconFPR(-0.490226483288291154229598449), new FalconFPR( 0.871595086655951034842481435), + new FalconFPR( 0.269668325572915106525464462), new FalconFPR( 0.962953266873683886347921481), + new FalconFPR(-0.962953266873683886347921481), new FalconFPR( 0.269668325572915106525464462), + new FalconFPR( 0.950486073949481721759926101), new FalconFPR( 0.310767152749611495835997250), + new FalconFPR(-0.310767152749611495835997250), new FalconFPR( 0.950486073949481721759926101), + new FalconFPR( 0.452349587233770874133026703), new FalconFPR( 0.891840709392342727796478697), + new FalconFPR(-0.891840709392342727796478697), new FalconFPR( 0.452349587233770874133026703), + new FalconFPR( 0.759209188978388033485525443), new FalconFPR( 0.650846684996380915068975573), + new FalconFPR(-0.650846684996380915068975573), new FalconFPR( 0.759209188978388033485525443), + new FalconFPR( 0.076623861392031492278332463), new FalconFPR( 0.997060070339482978987989949), + new FalconFPR(-0.997060070339482978987989949), new FalconFPR( 0.076623861392031492278332463), + new FalconFPR( 0.997511456140303459699448390), new FalconFPR( 0.070504573389613863027351471), + new FalconFPR(-0.070504573389613863027351471), new FalconFPR( 0.997511456140303459699448390), + new FalconFPR( 0.655492852999615385312679701), new FalconFPR( 0.755201376896536527598710756), + new FalconFPR(-0.755201376896536527598710756), new FalconFPR( 0.655492852999615385312679701), + new FalconFPR( 0.894599485631382678433072126), new FalconFPR( 0.446868840162374195353044389), + new FalconFPR(-0.446868840162374195353044389), new FalconFPR( 0.894599485631382678433072126), + new FalconFPR( 0.316593375556165867243047035), new FalconFPR( 0.948561349915730288158494826), + new FalconFPR(-0.948561349915730288158494826), new FalconFPR( 0.316593375556165867243047035), + new FalconFPR( 0.964589793289812723836432159), new FalconFPR( 0.263754678974831383611349322), + new FalconFPR(-0.263754678974831383611349322), new FalconFPR( 0.964589793289812723836432159), + new FalconFPR( 0.495565261825772531150266670), new FalconFPR( 0.868570705971340895340449876), + new FalconFPR(-0.868570705971340895340449876), new FalconFPR( 0.495565261825772531150266670), + new FalconFPR( 0.790230221437310055030217152), new FalconFPR( 0.612810082429409703935211936), + new FalconFPR(-0.612810082429409703935211936), new FalconFPR( 0.790230221437310055030217152), + new FalconFPR( 0.125454983411546238542336453), new FalconFPR( 0.992099313142191757112085445), + new FalconFPR(-0.992099313142191757112085445), new FalconFPR( 0.125454983411546238542336453), + new FalconFPR( 0.985797509167567424700995000), new FalconFPR( 0.167938294974731178054745536), + new FalconFPR(-0.167938294974731178054745536), new FalconFPR( 0.985797509167567424700995000), + new FalconFPR( 0.578313796411655563342245019), new FalconFPR( 0.815814410806733789010772660), + new FalconFPR(-0.815814410806733789010772660), new FalconFPR( 0.578313796411655563342245019), + new FalconFPR( 0.846490938774052078300544488), new FalconFPR( 0.532403127877197971442805218), + new FalconFPR(-0.532403127877197971442805218), new FalconFPR( 0.846490938774052078300544488), + new FalconFPR( 0.222093620973203534094094721), new FalconFPR( 0.975025345066994146844913468), + new FalconFPR(-0.975025345066994146844913468), new FalconFPR( 0.222093620973203534094094721), + new FalconFPR( 0.934092550404258914729877883), new FalconFPR( 0.357030961233430032614954036), + new FalconFPR(-0.357030961233430032614954036), new FalconFPR( 0.934092550404258914729877883), + new FalconFPR( 0.408044162864978680820747499), new FalconFPR( 0.912962190428398164628018233), + new FalconFPR(-0.912962190428398164628018233), new FalconFPR( 0.408044162864978680820747499), + new FalconFPR( 0.726359155084345976817494315), new FalconFPR( 0.687315340891759108199186948), + new FalconFPR(-0.687315340891759108199186948), new FalconFPR( 0.726359155084345976817494315), + new FalconFPR( 0.027608145778965741612354872), new FalconFPR( 0.999618822495178597116830637), + new FalconFPR(-0.999618822495178597116830637), new FalconFPR( 0.027608145778965741612354872), + new FalconFPR( 0.998941293186856850633930266), new FalconFPR( 0.046003182130914628814301788), + new FalconFPR(-0.046003182130914628814301788), new FalconFPR( 0.998941293186856850633930266), + new FalconFPR( 0.673829000378756060917568372), new FalconFPR( 0.738887324460615147933116508), + new FalconFPR(-0.738887324460615147933116508), new FalconFPR( 0.673829000378756060917568372), + new FalconFPR( 0.905296759318118774354048329), new FalconFPR( 0.424779681209108833357226189), + new FalconFPR(-0.424779681209108833357226189), new FalconFPR( 0.905296759318118774354048329), + new FalconFPR( 0.339776884406826857828825803), new FalconFPR( 0.940506070593268323787291309), + new FalconFPR(-0.940506070593268323787291309), new FalconFPR( 0.339776884406826857828825803), + new FalconFPR( 0.970772140728950302138169611), new FalconFPR( 0.240003022448741486568922365), + new FalconFPR(-0.240003022448741486568922365), new FalconFPR( 0.970772140728950302138169611), + new FalconFPR( 0.516731799017649881508753876), new FalconFPR( 0.856147328375194481019630732), + new FalconFPR(-0.856147328375194481019630732), new FalconFPR( 0.516731799017649881508753876), + new FalconFPR( 0.805031331142963597922659282), new FalconFPR( 0.593232295039799808047809426), + new FalconFPR(-0.593232295039799808047809426), new FalconFPR( 0.805031331142963597922659282), + new FalconFPR( 0.149764534677321517229695737), new FalconFPR( 0.988721691960323767604516485), + new FalconFPR(-0.988721691960323767604516485), new FalconFPR( 0.149764534677321517229695737), + new FalconFPR( 0.989622017463200834623694454), new FalconFPR( 0.143695033150294454819773349), + new FalconFPR(-0.143695033150294454819773349), new FalconFPR( 0.989622017463200834623694454), + new FalconFPR( 0.598160706996342311724958652), new FalconFPR( 0.801376171723140219430247777), + new FalconFPR(-0.801376171723140219430247777), new FalconFPR( 0.598160706996342311724958652), + new FalconFPR( 0.859301818357008404783582139), new FalconFPR( 0.511468850437970399504391001), + new FalconFPR(-0.511468850437970399504391001), new FalconFPR( 0.859301818357008404783582139), + new FalconFPR( 0.245955050335794611599924709), new FalconFPR( 0.969281235356548486048290738), + new FalconFPR(-0.969281235356548486048290738), new FalconFPR( 0.245955050335794611599924709), + new FalconFPR( 0.942573197601446879280758735), new FalconFPR( 0.333999651442009404650865481), + new FalconFPR(-0.333999651442009404650865481), new FalconFPR( 0.942573197601446879280758735), + new FalconFPR( 0.430326481340082633908199031), new FalconFPR( 0.902673318237258806751502391), + new FalconFPR(-0.902673318237258806751502391), new FalconFPR( 0.430326481340082633908199031), + new FalconFPR( 0.743007952135121693517362293), new FalconFPR( 0.669282588346636065720696366), + new FalconFPR(-0.669282588346636065720696366), new FalconFPR( 0.743007952135121693517362293), + new FalconFPR( 0.052131704680283321236358216), new FalconFPR( 0.998640218180265222418199049), + new FalconFPR(-0.998640218180265222418199049), new FalconFPR( 0.052131704680283321236358216), + new FalconFPR( 0.995480755491926941769171600), new FalconFPR( 0.094963495329638998938034312), + new FalconFPR(-0.094963495329638998938034312), new FalconFPR( 0.995480755491926941769171600), + new FalconFPR( 0.636761861236284230413943435), new FalconFPR( 0.771060524261813773200605759), + new FalconFPR(-0.771060524261813773200605759), new FalconFPR( 0.636761861236284230413943435), + new FalconFPR( 0.883363338665731594736308015), new FalconFPR( 0.468688822035827933697617870), + new FalconFPR(-0.468688822035827933697617870), new FalconFPR( 0.883363338665731594736308015), + new FalconFPR( 0.293219162694258650606608599), new FalconFPR( 0.956045251349996443270479823), + new FalconFPR(-0.956045251349996443270479823), new FalconFPR( 0.293219162694258650606608599), + new FalconFPR( 0.957826413027532890321037029), new FalconFPR( 0.287347459544729526477331841), + new FalconFPR(-0.287347459544729526477331841), new FalconFPR( 0.957826413027532890321037029), + new FalconFPR( 0.474100214650550014398580015), new FalconFPR( 0.880470889052160770806542929), + new FalconFPR(-0.880470889052160770806542929), new FalconFPR( 0.474100214650550014398580015), + new FalconFPR( 0.774953106594873878359129282), new FalconFPR( 0.632018735939809021909403706), + new FalconFPR(-0.632018735939809021909403706), new FalconFPR( 0.774953106594873878359129282), + new FalconFPR( 0.101069862754827824987887585), new FalconFPR( 0.994879330794805620591166107), + new FalconFPR(-0.994879330794805620591166107), new FalconFPR( 0.101069862754827824987887585), + new FalconFPR( 0.981379193313754574318224190), new FalconFPR( 0.192080397049892441679288205), + new FalconFPR(-0.192080397049892441679288205), new FalconFPR( 0.981379193313754574318224190), + new FalconFPR( 0.558118531220556115693702964), new FalconFPR( 0.829761233794523042469023765), + new FalconFPR(-0.829761233794523042469023765), new FalconFPR( 0.558118531220556115693702964), + new FalconFPR( 0.833170164701913186439915922), new FalconFPR( 0.553016705580027531764226988), + new FalconFPR(-0.553016705580027531764226988), new FalconFPR( 0.833170164701913186439915922), + new FalconFPR( 0.198098410717953586179324918), new FalconFPR( 0.980182135968117392690210009), + new FalconFPR(-0.980182135968117392690210009), new FalconFPR( 0.198098410717953586179324918), + new FalconFPR( 0.925049240782677590302371869), new FalconFPR( 0.379847208924051170576281147), + new FalconFPR(-0.379847208924051170576281147), new FalconFPR( 0.925049240782677590302371869), + new FalconFPR( 0.385516053843918864075607949), new FalconFPR( 0.922701128333878570437264227), + new FalconFPR(-0.922701128333878570437264227), new FalconFPR( 0.385516053843918864075607949), + new FalconFPR( 0.709272826438865651316533772), new FalconFPR( 0.704934080375904908852523758), + new FalconFPR(-0.704934080375904908852523758), new FalconFPR( 0.709272826438865651316533772), + new FalconFPR( 0.003067956762965976270145365), new FalconFPR( 0.999995293809576171511580126), + new FalconFPR(-0.999995293809576171511580126), new FalconFPR( 0.003067956762965976270145365) + }; + + internal FalconFPR[] fpr_p2_tab = { + new FalconFPR( 2.00000000000 ), + new FalconFPR( 1.00000000000 ), + new FalconFPR( 0.50000000000 ), + new FalconFPR( 0.25000000000 ), + new FalconFPR( 0.12500000000 ), + new FalconFPR( 0.06250000000 ), + new FalconFPR( 0.03125000000 ), + new FalconFPR( 0.01562500000 ), + new FalconFPR( 0.00781250000 ), + new FalconFPR( 0.00390625000 ), + new FalconFPR( 0.00195312500 ) + }; + internal FalconFPR fpr_log2 = new FalconFPR(0.69314718055994530941723212146); + internal FalconFPR fpr_inv_log2 = new FalconFPR(1.4426950408889634073599246810); + internal FalconFPR fpr_bnorm_max = new FalconFPR(16822.4121); + internal FalconFPR fpr_zero = new FalconFPR(0.0); + internal FalconFPR fpr_one = new FalconFPR(1.0); + internal FalconFPR fpr_two = new FalconFPR(2.0); + internal FalconFPR fpr_onehalf = new FalconFPR(0.5); + internal FalconFPR fpr_invsqrt2 = new FalconFPR(0.707106781186547524400844362105); + internal FalconFPR fpr_invsqrt8 = new FalconFPR(0.353553390593273762200422181052); + internal FalconFPR fpr_ptwo31 = new FalconFPR(2147483648.0); + internal FalconFPR fpr_ptwo31m1 = new FalconFPR(2147483647.0); + internal FalconFPR fpr_mtwo31m1 = new FalconFPR(-2147483647.0); + internal FalconFPR fpr_ptwo63m1 = new FalconFPR(9223372036854775807.0); + internal FalconFPR fpr_mtwo63m1 = new FalconFPR(-9223372036854775807.0); + internal FalconFPR fpr_ptwo63 = new FalconFPR(9223372036854775808.0); + internal FalconFPR fpr_q = new FalconFPR(12289.0); + internal FalconFPR fpr_inverse_of_q = new FalconFPR(1.0 / 12289.0); + internal FalconFPR fpr_inv_2sqrsigma0 = new FalconFPR(0.150865048875372721532312163019); + internal FalconFPR[] fpr_inv_sigma = { + new FalconFPR( 0.0 ), /* unused */ + new FalconFPR( 0.0069054793295940891952143765991630516 ), + new FalconFPR( 0.0068102267767177975961393730687908629 ), + new FalconFPR( 0.0067188101910722710707826117910434131 ), + new FalconFPR( 0.0065883354370073665545865037227681924 ), + new FalconFPR( 0.0064651781207602900738053897763485516 ), + new FalconFPR( 0.0063486788828078995327741182928037856 ), + new FalconFPR( 0.0062382586529084374473367528433697537 ), + new FalconFPR( 0.0061334065020930261548984001431770281 ), + new FalconFPR( 0.0060336696681577241031668062510953022 ), + new FalconFPR( 0.0059386453095331159950250124336477482 ) + }; + internal FalconFPR[] fpr_sigma_min = { + new FalconFPR( 0.0 ), /* unused */ + new FalconFPR( 1.1165085072329102588881898380334015 ), + new FalconFPR( 1.1321247692325272405718031785357108 ), + new FalconFPR( 1.1475285353733668684571123112513188 ), + new FalconFPR( 1.1702540788534828939713084716509250 ), + new FalconFPR( 1.1925466358390344011122170489094133 ), + new FalconFPR( 1.2144300507766139921088487776957699 ), + new FalconFPR( 1.2359260567719808790104525941706723 ), + new FalconFPR( 1.2570545284063214162779743112075080 ), + new FalconFPR( 1.2778336969128335860256340575729042 ), + new FalconFPR( 1.2982803343442918539708792538826807 ) + }; + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconCodec.cs b/crypto/src/pqc/crypto/falcon/FalconCodec.cs new file mode 100644 index 000000000..062e006e4 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconCodec.cs @@ -0,0 +1,576 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconCodec + { + + internal FalconCodec() { + + } + + /* + * License from the reference C code (the code was copied then modified + * to function in C#): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + + internal int modq_encode( + byte[] outarrsrc, int outarr, int max_out_len, + ushort[] xsrc, int x, uint logn) + { + int n, out_len, u; + int buf; + uint acc; + int acc_len; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + if (xsrc[x+u] >= 12289) { + return 0; + } + } + out_len = ((n * 14) + 7) >> 3; + if (outarrsrc == null) { + return out_len; + } + if (out_len > max_out_len) { + return 0; + } + buf = outarr; + acc = 0; + acc_len = 0; + for (u = 0; u < n; u ++) { + acc = (acc << 14) | xsrc[x+u]; + acc_len += 14; + while (acc_len >= 8) { + acc_len -= 8; + outarrsrc[buf ++] = (byte)(acc >> acc_len); + } + } + if (acc_len > 0) { + outarrsrc[buf] = (byte)(acc << (8 - acc_len)); + } + return out_len; + } + + internal int modq_decode( + ushort[] xsrc, int x, uint logn, + byte[] inarrsrc, int inarr, int max_in_len) + { + int n, in_len, u; + int buf; + uint acc; + int acc_len; + + n = (int)1 << (int)logn; + in_len = ((n * 14) + 7) >> 3; + if (in_len > max_in_len) { + return 0; + } + buf = inarr; + acc = 0; + acc_len = 0; + u = 0; + while (u < n) { + acc = (acc << 8) | (inarrsrc[buf ++]); + acc_len += 8; + if (acc_len >= 14) { + uint w; + + acc_len -= 14; + w = (acc >> acc_len) & 0x3FFF; + if (w >= 12289) { + return 0; + } + xsrc[x + u] = (ushort)w; + u++; + } + } + if ((acc & (((uint)1 << acc_len) - 1)) != 0) { + return 0; + } + return in_len; + } + + internal int trim_i16_encode( + byte[] outarrsrc, int outarr, int max_out_len, + short[] xsrc, int x, uint logn, uint bits) + { + int n, u, out_len; + int minv, maxv; + int buf; + uint acc, mask; + uint acc_len; + + n = (int)1 << (int)logn; + maxv = (1 << (int)(bits - 1)) - 1; + minv = -maxv; + for (u = 0; u < n; u ++) { + if (xsrc[x+u] < minv || xsrc[x+u] > maxv) { + return 0; + } + } + out_len = (int)((n * bits) + 7) >> 3; + if (outarrsrc == null) { + return out_len; + } + if (out_len > max_out_len) { + return 0; + } + buf = outarr; + acc = 0; + acc_len = 0; + mask = ((uint)1 << (int)bits) - 1; + for (u = 0; u < n; u ++) { + acc = (acc << (int)bits) | ((ushort)xsrc[x+u] & mask); + acc_len += bits; + while (acc_len >= 8) { + acc_len -= 8; + outarrsrc[buf ++] = (byte)(acc >> (int)acc_len); + } + } + if (acc_len > 0) { + outarrsrc[buf ++] = (byte)(acc << (int)(8 - acc_len)); + } + return out_len; + } + + internal int trim_i16_decode( + short[] xsrc, int x, uint logn, uint bits, + byte[] inarrsrc, int inarr, int max_in_len) + { + int n, in_len; + int buf; + int u; + uint acc, mask1, mask2; + uint acc_len; + + n = (int)1 << (int)logn; + in_len = (int)((n * bits) + 7) >> 3; + if (in_len > max_in_len) { + return 0; + } + buf = inarr; + u = 0; + acc = 0; + acc_len = 0; + mask1 = ((uint)1 << (int)bits) - 1; + mask2 = (uint)1 << (int)(bits - 1); + while (u < n) { + acc = (acc << 8) | inarrsrc[buf ++]; + acc_len += 8; + while (acc_len >= bits && u < n) { + uint w; + + acc_len -= bits; + w = (acc >> (int)acc_len) & mask1; + w = (uint)(w | -(w & mask2)); + w |= (uint)(-(w & mask2)); + if (w == -mask2) { + /* + * The -2^(bits-1) value is forbidden. + */ + return 0; + } + w |= (uint)(-(w & mask2)); + //xsrc[x + u] = (short)*(int *)&w; + xsrc[x + u] = (short)(int)w; + u++; + } + } + if ((acc & (((uint)1 << (int)acc_len) - 1)) != 0) { + /* + * Extra bits in the last byte must be zero. + */ + return 0; + } + return in_len; + } + + internal int trim_i8_encode( + byte[] outarrsrc, int outarr, int max_out_len, + sbyte[] xsrc, int x, uint logn, uint bits) + { + int n, u, out_len; + int minv, maxv; + int buf; + uint acc, mask; + uint acc_len; + + n = (int)1 << (int)logn; + maxv = (1 << (int)(bits - 1)) - 1; + minv = -maxv; + for (u = 0; u < n; u ++) { + if (xsrc[x+u] < minv || xsrc[x+u] > maxv) { + return 0; + } + } + out_len = (int)((n * bits) + 7) >> 3; + if (outarrsrc == null) { + return out_len; + } + if (out_len > max_out_len) { + return 0; + } + buf = outarr; + acc = 0; + acc_len = 0; + mask = ((uint)1 << (int)bits) - 1; + for (u = 0; u < n; u ++) { + acc = (acc << (int)bits) | ((byte)xsrc[x+u] & mask); + acc_len += bits; + while (acc_len >= 8) { + acc_len -= 8; + outarrsrc[buf ++] = (byte)(acc >> (int)acc_len); + } + } + if (acc_len > 0) { + outarrsrc[buf ++] = (byte)(acc << (int)(8 - acc_len)); + } + return out_len; + } + + internal int trim_i8_decode( + sbyte[] xsrc, int x, uint logn, uint bits, + byte[] inarrsrc, int inarr, int max_in_len) + { + int n, in_len; + int buf; + int u; + uint acc, mask1, mask2; + uint acc_len; + + n = (int)1 << (int)logn; + in_len = (int)((n * bits) + 7) >> 3; + if (in_len > max_in_len) { + return 0; + } + buf = inarr; + u = 0; + acc = 0; + acc_len = 0; + mask1 = ((uint)1 << (int)bits) - 1; + mask2 = (uint)1 << (int)(bits - 1); + while (u < n) { + acc = (acc << 8) | inarrsrc[buf ++]; + acc_len += 8; + while (acc_len >= bits && u < n) { + uint w; + + acc_len -= bits; + w = (acc >> (int)acc_len) & mask1; + w |= (uint)(-(w & mask2)); + if (w == -mask2) { + /* + * The -2^(bits-1) value is forbidden. + */ + return 0; + } + //xsrc[x + u] = (sbyte)*(int *)&w; + xsrc[x + u] = (sbyte)(int)w; + u++; + } + } + if ((acc & (((uint)1 << (int)acc_len) - 1)) != 0) { + /* + * Extra bits in the last byte must be zero. + */ + return 0; + } + return in_len; + } + + internal int comp_encode( + byte[] outarrsrc, int outarr, int max_out_len, + short[] xsrc, int x, uint logn) + { + int buf; + int n, u, v; + uint acc; + uint acc_len; + + n = (int)1 << (int)logn; + buf = outarr; + + /* + * Make sure that all values are within the -2047..+2047 range. + */ + for (u = 0; u < n; u ++) { + if (xsrc[x+u] < -2047 || xsrc[x+u] > +2047) { + return 0; + } + } + + acc = 0; + acc_len = 0; + v = 0; + for (u = 0; u < n; u ++) { + int t; + uint w; + + /* + * Get sign and absolute value of next integer; push the + * sign bit. + */ + acc <<= 1; + t = xsrc[x+u]; + if (t < 0) { + t = -t; + acc |= 1; + } + w = (uint)t; + + /* + * Push the low 7 bits of the absolute value. + */ + acc <<= 7; + acc |= w & 127u; + w >>= 7; + + /* + * We pushed exactly 8 bits. + */ + acc_len += 8; + + /* + * Push as many zeros as necessary, then a one. Since the + * absolute value is at most 2047, w can only range up to + * 15 at this point, thus we will add at most 16 bits + * here. With the 8 bits above and possibly up to 7 bits + * from previous iterations, we may go up to 31 bits, which + * will fit in the accumulator, which is an uint. + */ + acc <<= (int)(w + 1); + acc |= 1; + acc_len += w + 1; + + /* + * Produce all full bytes. + */ + while (acc_len >= 8) { + acc_len -= 8; + if (outarrsrc != null) { + if (v >= max_out_len) { + return 0; + } + outarrsrc[buf+v] = (byte)(acc >> (int)acc_len); + } + v ++; + } + } + + /* + * Flush remaining bits (if any). + */ + if (acc_len > 0) { + if (outarrsrc != null) { + if (v >= max_out_len) { + return 0; + } + outarrsrc[buf+v] = (byte)(acc << (int)(8 - acc_len)); + } + v ++; + } + + return v; + } + + internal int comp_decode( + short[] xsrc, int x, uint logn, + byte[] inarrsrc, int inarr, int max_in_len) + { + int buf; + int n, u, v; + uint acc; + uint acc_len; + + n = (int)1 << (int)logn; + buf = inarr; + acc = 0; + acc_len = 0; + v = 0; + for (u = 0; u < n; u ++) { + uint b, s, m; + + /* + * Get next eight bits: sign and low seven bits of the + * absolute value. + */ + if (v >= max_in_len) { + return 0; + } + acc = (acc << 8) | (uint)inarrsrc[buf + v]; + v++; + b = acc >> (int)acc_len; + s = b & 128; + m = b & 127; + + /* + * Get next bits until a 1 is reached. + */ + for (;;) { + if (acc_len == 0) { + if (v >= max_in_len) { + return 0; + } + acc = (acc << 8) | (uint)inarrsrc[buf + v]; + v++; + acc_len = 8; + } + acc_len --; + if (((acc >> (int)acc_len) & 1) != 0) { + break; + } + m += 128; + if (m > 2047) { + return 0; + } + } + + /* + * "-0" is forbidden. + */ + if (s != 0 && m == 0) { + return 0; + } + + xsrc[x+u] = (short)(s != 0 ? -(int)m : (int)m); + } + + /* + * Unused bits in the last byte must be zero. + */ + if ((acc & ((1u << (int)acc_len) - 1u)) != 0) { + return 0; + } + + return v; + } + + /* + * Key elements and signatures are polynomials with small integer + * coefficients. Here are some statistics gathered over many + * generated key pairs (10000 or more for each degree): + * + * log(n) n max(f,g) std(f,g) max(F,G) std(F,G) + * 1 2 129 56.31 143 60.02 + * 2 4 123 40.93 160 46.52 + * 3 8 97 28.97 159 38.01 + * 4 16 100 21.48 154 32.50 + * 5 32 71 15.41 151 29.36 + * 6 64 59 11.07 138 27.77 + * 7 128 39 7.91 144 27.00 + * 8 256 32 5.63 148 26.61 + * 9 512 22 4.00 137 26.46 + * 10 1024 15 2.84 146 26.41 + * + * We want a compact storage format for private key, and, as part of + * key generation, we are allowed to reject some keys which would + * otherwise be fine (this does not induce any noticeable vulnerability + * as long as we reject only a small proportion of possible keys). + * Hence, we enforce at key generation time maximum values for the + * elements of f, g, F and G, so that their encoding can be expressed + * in fixed-width values. Limits have been chosen so that generated + * keys are almost always within bounds, thus not impacting neither + * security or performance. + * + * IMPORTANT: the code assumes that all coefficients of f, g, F and G + * ultimately fit in the -127..+127 range. Thus, none of the elements + * of max_fg_bits[] and max_FG_bits[] shall be greater than 8. + */ + + internal byte[] max_fg_bits = { + 0, /* unused */ + 8, + 8, + 8, + 8, + 8, + 7, + 7, + 6, + 6, + 5 + }; + + internal byte[] max_FG_bits = { + 0, /* unused */ + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8 + }; + + /* + * When generating a new key pair, we can always reject keys which + * feature an abnormally large coefficient. This can also be done for + * signatures, albeit with some care: in case the signature process is + * used in a derandomized setup (explicitly seeded with the message and + * private key), we have to follow the specification faithfully, and the + * specification only enforces a limit on the L2 norm of the signature + * vector. The limit on the L2 norm implies that the absolute value of + * a coefficient of the signature cannot be more than the following: + * + * log(n) n max sig coeff (theoretical) + * 1 2 412 + * 2 4 583 + * 3 8 824 + * 4 16 1166 + * 5 32 1649 + * 6 64 2332 + * 7 128 3299 + * 8 256 4665 + * 9 512 6598 + * 10 1024 9331 + * + * However, the largest observed signature coefficients during our + * experiments was 1077 (in absolute value), hence we can assume that, + * with overwhelming probability, signature coefficients will fit + * in -2047..2047, i.e. 12 bits. + */ + + internal byte[] max_sig_bits = { + 0, /* unused */ + 10, + 11, + 11, + 12, + 12, + 12, + 12, + 12, + 12, + 12 + }; + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconCommon.cs b/crypto/src/pqc/crypto/falcon/FalconCommon.cs new file mode 100644 index 000000000..e92237936 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconCommon.cs @@ -0,0 +1,304 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconCommon + { + /* + * License from the reference C code (the code was copied then modified + * to function in C#): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + internal void hash_to_point_vartime( + SHAKE256 sc, + ushort[] xsrc, int x, uint logn) + { + /* + * This is the straightforward per-the-spec implementation. It + * is not constant-time, thus it might reveal information on the + * plaintext (at least, enough to check the plaintext against a + * list of potential plaintexts) in a scenario where the + * attacker does not have access to the signature value or to + * the public key, but knows the nonce (without knowledge of the + * nonce, the hashed output cannot be matched against potential + * plaintexts). + */ + int n; + + n = (int)1 << (int)logn; + while (n > 0) { + byte[] buf = new byte[2]; + uint w; + sc.i_shake256_extract(buf, 0, 2); + // inner_shake256_extract(sc, (void *)buf, sizeof buf); + w = ((uint)buf[0] << 8) | (uint)buf[1]; + if (w < 61445) { + while (w >= 12289) { + w -= 12289; + } + xsrc[x ++] = (ushort)w; + n --; + } + } + } + + // void hash_to_point_ct( + // SHAKE256 sc, + // ushort[] xsrc, int x, uint logn, byte *tmp) + // { + // /* + // * Each 16-bit sample is a value in 0..65535. The value is + // * kept if it falls in 0..61444 (because 61445 = 5*12289) + // * and rejected otherwise; thus, each sample has probability + // * about 0.93758 of being selected. + // * + // * We want to oversample enough to be sure that we will + // * have enough values with probability at least 1 - 2^(-256). + // * Depending on degree N, this leads to the following + // * required oversampling: + // * + // * logn n oversampling + // * 1 2 65 + // * 2 4 67 + // * 3 8 71 + // * 4 16 77 + // * 5 32 86 + // * 6 64 100 + // * 7 128 122 + // * 8 256 154 + // * 9 512 205 + // * 10 1024 287 + // * + // * If logn >= 7, then the provided temporary buffer is large + // * enough. Otherwise, we use a stack buffer of 63 entries + // * (i.e. 126 bytes) for the values that do not fit in tmp[]. + // */ + + // const ushort[] overtab = { + // 0, /* unused */ + // 65, + // 67, + // 71, + // 77, + // 86, + // 100, + // 122, + // 154, + // 205, + // 287 + // }; + + // uint n, n2, u, m, p, over; + // int tt1; + // ushort[] tt2 = new ushort[63]; + + // /* + // * We first generate m 16-bit value. Values 0..n-1 go to x[]. + // * Values n..2*n-1 go to tt1[]. Values 2*n and later go to tt2[]. + // * We also reduce modulo q the values; rejected values are set + // * to 0xFFFF. + // */ + // n = 1U << logn; + // n2 = n << 1; + // over = overtab[logn]; + // m = n + over; + // tt1 = tmp; + // for (u = 0; u < m; u ++) { + // byte[] buf = new byte[2]; + // uint w, wr; + + // // inner_shake256_extract(sc, buf, sizeof buf); + // sc.i_shake256_extract(buf, 2); + // w = ((uint)buf[0] << 8) | (uint)buf[1]; + // wr = w - ((uint)24578 & (((w - 24578) >> 31) - 1)); + // wr = wr - ((uint)24578 & (((wr - 24578) >> 31) - 1)); + // wr = wr - ((uint)12289 & (((wr - 12289) >> 31) - 1)); + // wr |= ((w - 61445) >> 31) - 1; + // if (u < n) { + // x[u] = (ushort)wr; + // } else if (u < n2) { + // tt1[u - n] = (ushort)wr; + // } else { + // tt2[u - n2] = (ushort)wr; + // } + // } + + // /* + // * Now we must "squeeze out" the invalid values. We do this in + // * a logarithmic sequence of passes; each pass computes where a + // * value should go, and moves it down by 'p' slots if necessary, + // * where 'p' uses an increasing powers-of-two scale. It can be + // * shown that in all cases where the loop decides that a value + // * has to be moved down by p slots, the destination slot is + // * "free" (i.e. contains an invalid value). + // */ + // for (p = 1; p <= over; p <<= 1) { + // uint v; + + // /* + // * In the loop below: + // * + // * - v contains the index of the final destination of + // * the value; it is recomputed dynamically based on + // * whether values are valid or not. + // * + // * - u is the index of the value we consider ("source"); + // * its address is s. + // * + // * - The loop may swap the value with the one at index + // * u-p. The address of the swap destination is d. + // */ + // v = 0; + // for (u = 0; u < m; u ++) { + // ushort *s; + // ushort *d; + // uint j, sv, dv, mk; + + // if (u < n) { + // s = &x[u]; + // } else if (u < n2) { + // s = &tt1[u - n]; + // } else { + // s = &tt2[u - n2]; + // } + // sv = *s; + + // /* + // * The value in sv should ultimately go to + // * address v, i.e. jump back by u-v slots. + // */ + // j = u - v; + + // /* + // * We increment v for the next iteration, but + // * only if the source value is valid. The mask + // * 'mk' is -1 if the value is valid, 0 otherwise, + // * so we _subtract_ mk. + // */ + // mk = (sv >> 15) - 1U; + // v -= mk; + + // /* + // * In this loop we consider jumps by p slots; if + // * u < p then there is nothing more to do. + // */ + // if (u < p) { + // continue; + // } + + // /* + // * Destination for the swap: value at address u-p. + // */ + // if ((u - p) < n) { + // d = &x[u - p]; + // } else if ((u - p) < n2) { + // d = &tt1[(u - p) - n]; + // } else { + // d = &tt2[(u - p) - n2]; + // } + // dv = *d; + + // /* + // * The swap should be performed only if the source + // * is valid AND the jump j has its 'p' bit set. + // */ + // mk &= -(((j & p) + 0x1FF) >> 9); + + // *s = (ushort)(sv ^ (mk & (sv ^ dv))); + // *d = (ushort)(dv ^ (mk & (sv ^ dv))); + // } + // } + // } + + /* + * Acceptance bound for the (squared) l2-norm of the signature depends + * on the degree. This array is indexed by logn (1 to 10). These bounds + * are _inclusive_ (they are equal to floor(beta^2)). + */ + internal uint[] l2bound = { + 0, /* unused */ + 101498, + 208714, + 428865, + 892039, + 1852696, + 3842630, + 7959734, + 16468416, + 34034726, + 70265242 + }; + + internal bool is_short( + short[] s1src, int s1, short[] s2src, int s2, uint logn) + { + /* + * We use the l2-norm. Code below uses only 32-bit operations to + * compute the square of the norm with saturation to 2^32-1 if + * the value exceeds 2^31-1. + */ + int n, u; + uint s, ng; + + n = (int)1 << (int)logn; + s = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int z; + + z = s1src[s1+u]; + s += (uint)(z * z); + ng |= s; + z = s2src[s2+u]; + s += (uint)(z * z); + ng |= s; + } + s |= (uint)(-(ng >> 31)); + + return s <= l2bound[logn]; + } + + internal bool is_short_half( + uint sqn, short[] s2src, int s2, uint logn) + { + int n, u; + uint ng; + + n = (int)1 << (int)logn; + ng = (uint)(-(sqn >> 31)); + for (u = 0; u < n; u ++) { + int z; + + z = s2src[s2 + u]; + sqn += (uint)(z * z); + ng |= sqn; + } + sqn |= (uint)(-(ng >> 31)); + + return sqn <= l2bound[logn]; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconConversions.cs b/crypto/src/pqc/crypto/falcon/FalconConversions.cs new file mode 100644 index 000000000..36ef56fb4 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconConversions.cs @@ -0,0 +1,66 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconConversions + { + internal FalconConversions(){} + + internal byte[] int_to_bytes(int x) + { + byte[] res = new byte[4]; + res[0] = (byte)(x >> 0); + res[1] = (byte)(x >> 8); + res[2] = (byte)(x >> 16); + res[3] = (byte)(x >> 24); + return res; + } + internal uint bytes_to_uint(byte[] src, int pos) + { + uint acc = 0; + acc = ((uint)src[pos + 0]) << 0 | + ((uint)src[pos + 1]) << 8 | + ((uint)src[pos + 2]) << 16 | + ((uint)src[pos + 3]) << 24; + return acc; + } + + internal byte[] ulong_to_bytes(ulong x) + { + byte[] res = new byte[8]; + res[0] = (byte)(x >> 0); + res[1] = (byte)(x >> 8); + res[2] = (byte)(x >> 16); + res[3] = (byte)(x >> 24); + res[4] = (byte)(x >> 32); + res[5] = (byte)(x >> 40); + res[6] = (byte)(x >> 48); + res[7] = (byte)(x >> 56); + return res; + } + + internal ulong bytes_to_ulong(byte[] src, int pos) + { + ulong acc = 0; + acc = ((ulong)src[pos + 0]) << 0 | + ((ulong)src[pos + 1]) << 8 | + ((ulong)src[pos + 2]) << 16 | + ((ulong)src[pos + 3]) << 24 | + ((ulong)src[pos + 4]) << 32 | + ((ulong)src[pos + 5]) << 40 | + ((ulong)src[pos + 6]) << 48 | + ((ulong)src[pos + 7]) << 56; + return acc; + } + + internal uint[] bytes_to_uint_array(byte[] src, int pos, int num) + { + uint[] res = new uint[num]; + for (int i = 0; i < num; i++) + { + res[i] = bytes_to_uint(src, pos + (4 * i)); + } + return res; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconFFT.cs b/crypto/src/pqc/crypto/falcon/FalconFFT.cs new file mode 100644 index 000000000..aa862cc23 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconFFT.cs @@ -0,0 +1,711 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconFFT + { + FPREngine fpre; + internal FalconFFT() { + fpre = new FPREngine(); + } + internal FalconFFT(FPREngine fprengine) { + this.fpre = fprengine; + } + + /* + * License from the reference C code (the code was copied then modified + * to function in C#): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + /* + * Addition of two complex numbers (d = a + b). + */ + internal FalconFPR[] FPC_ADD(FalconFPR a_re, FalconFPR a_im, + FalconFPR b_re, FalconFPR b_im) { + FalconFPR fpct_re, fpct_im; + fpct_re = this.fpre.fpr_add(a_re, b_re); + fpct_im = this.fpre.fpr_add(a_im, b_im); + //d_re.Set(fpct_re); + //d_im.Set(fpct_im); + return new FalconFPR[] { fpct_re, fpct_im }; + } + + /* + * Subtraction of two complex numbers (d = a - b). + */ + internal FalconFPR[] FPC_SUB(FalconFPR a_re, FalconFPR a_im, + FalconFPR b_re, FalconFPR b_im) { + FalconFPR fpct_re, fpct_im; + fpct_re = this.fpre.fpr_sub(a_re, b_re); + fpct_im = this.fpre.fpr_sub(a_im, b_im); + return new FalconFPR[] { fpct_re, fpct_im }; + } + + /* + * Multplication of two complex numbers (d = a * b). + */ + internal FalconFPR[] FPC_MUL(FalconFPR a_re, FalconFPR a_im, + FalconFPR b_re, FalconFPR b_im) { + FalconFPR fpct_a_re, fpct_a_im; + FalconFPR fpct_b_re, fpct_b_im; + FalconFPR fpct_d_re, fpct_d_im; + fpct_a_re = a_re; + fpct_a_im = a_im; + fpct_b_re = b_re; + fpct_b_im = b_im; + fpct_d_re = this.fpre.fpr_sub( + this.fpre.fpr_mul(fpct_a_re, fpct_b_re), + this.fpre.fpr_mul(fpct_a_im, fpct_b_im)); + fpct_d_im = this.fpre.fpr_add( + this.fpre.fpr_mul(fpct_a_re, fpct_b_im), + this.fpre.fpr_mul(fpct_a_im, fpct_b_re)); + return new FalconFPR[] {fpct_d_re, fpct_d_im}; + } + + /* + * Squaring of a complex number (d = a * a). + */ + internal FalconFPR[] FPC_SQR(FalconFPR d_re, FalconFPR d_im, + FalconFPR a_re, FalconFPR a_im) { + FalconFPR fpct_a_re, fpct_a_im; + FalconFPR fpct_d_re, fpct_d_im; + fpct_a_re = a_re; + fpct_a_im = a_im; + fpct_d_re = this.fpre.fpr_sub(this.fpre.fpr_sqr(fpct_a_re), this.fpre.fpr_sqr(fpct_a_im)); + fpct_d_im = this.fpre.fpr_double(this.fpre.fpr_mul(fpct_a_re, fpct_a_im)); + return new FalconFPR[] {fpct_d_re, fpct_d_im}; + } + + /* + * Inversion of a complex number (d = 1 / a). + */ + internal FalconFPR[] FPC_INV(FalconFPR a_re, FalconFPR a_im) { + FalconFPR fpct_a_re, fpct_a_im; + FalconFPR fpct_d_re, fpct_d_im; + FalconFPR fpct_m; + fpct_a_re = a_re; + fpct_a_im = a_im; + fpct_m = this.fpre.fpr_add(this.fpre.fpr_sqr(fpct_a_re), this.fpre.fpr_sqr(fpct_a_im)); + fpct_m = this.fpre.fpr_inv(fpct_m); + fpct_d_re = this.fpre.fpr_mul(fpct_a_re, fpct_m); + fpct_d_im = this.fpre.fpr_mul(this.fpre.fpr_neg(fpct_a_im), fpct_m); + return new FalconFPR[] { fpct_d_re, fpct_d_im }; + } + /* + * Division of complex numbers (d = a / b). + */ + internal FalconFPR[] FPC_DIV(FalconFPR a_re, FalconFPR a_im, + FalconFPR b_re, FalconFPR b_im) { + FalconFPR fpct_a_re, fpct_a_im; + FalconFPR fpct_b_re, fpct_b_im; + FalconFPR fpct_d_re, fpct_d_im; + FalconFPR fpct_m; + fpct_a_re = (a_re); + fpct_a_im = (a_im); + fpct_b_re = (b_re); + fpct_b_im = (b_im); + fpct_m = this.fpre.fpr_add(this.fpre.fpr_sqr(fpct_b_re), this.fpre.fpr_sqr(fpct_b_im)); + fpct_m = this.fpre.fpr_inv(fpct_m); + fpct_b_re = this.fpre.fpr_mul(fpct_b_re, fpct_m); + fpct_b_im = this.fpre.fpr_mul(this.fpre.fpr_neg(fpct_b_im), fpct_m); + fpct_d_re = this.fpre.fpr_sub( + this.fpre.fpr_mul(fpct_a_re, fpct_b_re), + this.fpre.fpr_mul(fpct_a_im, fpct_b_im)); + fpct_d_im = this.fpre.fpr_add( + this.fpre.fpr_mul(fpct_a_re, fpct_b_im), + this.fpre.fpr_mul(fpct_a_im, fpct_b_re)); + return new FalconFPR[] { fpct_d_re, fpct_d_im }; + } + + /* + * Let w = exp(i*pi/N); w is a primitive 2N-th root of 1. We define the + * values w_j = w^(2j+1) for all j from 0 to N-1: these are the roots + * of X^N+1 in the field of complex numbers. A crucial property is that + * w_{N-1-j} = conj(w_j) = 1/w_j for all j. + * + * FFT representation of a polynomial f (taken modulo X^N+1) is the + * set of values f(w_j). Since f is real, conj(f(w_j)) = f(conj(w_j)), + * thus f(w_{N-1-j}) = conj(f(w_j)). We thus store only half the values, + * for j = 0 to N/2-1; the other half can be recomputed easily when (if) + * needed. A consequence is that FFT representation has the same size + * as normal representation: N/2 complex numbers use N real numbers (each + * complex number is the combination of a real and an imaginary part). + * + * We use a specific ordering which makes computations easier. Let rev() + * be the bit-reversal function over log(N) bits. For j in 0..N/2-1, we + * store the real and imaginary parts of f(w_j) in slots: + * + * Re(f(w_j)) -> slot rev(j)/2 + * Im(f(w_j)) -> slot rev(j)/2+N/2 + * + * (Note that rev(j) is even for j < N/2.) + */ + + internal void FFT(FalconFPR[] fsrc, int f, uint logn) + { + /* + * FFT algorithm in bit-reversal order uses the following + * iterative algorithm: + * + * t = N + * for m = 1; m < N; m *= 2: + * ht = t/2 + * for i1 = 0; i1 < m; i1 ++: + * j1 = i1 * t + * s = GM[m + i1] + * for j = j1; j < (j1 + ht); j ++: + * x = fsrc[f + j] + * y = s * fsrc[f + j + ht] + * fsrc[f + j] = x + y + * fsrc[f + j + ht] = x - y + * t = ht + * + * GM[k] contains w^rev(k) for primitive root w = exp(i*pi/N). + * + * In the description above, fsrc[f + ] is supposed to contain complex + * numbers. In our in-memory representation, the real and + * imaginary parts of fsrc[f + k] are in array slots k and k+N/2. + * + * We only keep the first half of the complex numbers. We can + * see that after the first iteration, the first and second halves + * of the array of complex numbers have separate lives, so we + * simply ignore the second part. + */ + + uint u; + int t, n, hn, m; + + /* + * First iteration: compute fsrc[f + j] + i * fsrc[f + j+N/2] for all j < N/2 + * (because GM[1] = w^rev(1) = w^(N/2) = i). + * In our chosen representation, this is a no-op: everything is + * already where it should be. + */ + + /* + * Subsequent iterations are truncated to use only the first + * half of values. + */ + n = (int)1 << (int)logn; + hn = n >> 1; + t = hn; + for (u = 1, m = 2; u < logn; u ++, m <<= 1) { + int ht, hm, i1, j1; + + ht = t >> 1; + hm = m >> 1; + for (i1 = 0, j1 = 0; i1 < hm; i1 ++, j1 += t) { + int j, j2; + + j2 = j1 + ht; + FalconFPR s_re, s_im; + + s_re = this.fpre.fpr_gm_tab[((m + i1) << 1) + 0]; + s_im = this.fpre.fpr_gm_tab[((m + i1) << 1) + 1]; + for (j = j1; j < j2; j ++) { + FalconFPR x_re, x_im, y_re, y_im; + FalconFPR[] res; + + x_re = fsrc[f + j]; + x_im = fsrc[f + j + hn]; + y_re = fsrc[f + j + ht]; + y_im = fsrc[f + j + ht + hn]; + res = FPC_MUL(y_re, y_im, s_re, s_im); + y_re = res[0]; y_im = res[1]; + res = FPC_ADD(x_re, x_im, y_re, y_im); + fsrc[f + j] = res[0]; fsrc[f + j + hn] = res[1]; + res = FPC_SUB(x_re, x_im, y_re, y_im); + fsrc[f + j + ht] = res[0]; fsrc[f + j + ht + hn] = res[1]; + } + } + t = ht; + } + } + + internal void iFFT(FalconFPR[] fsrc, int f, uint logn) + { + /* + * Inverse FFT algorithm in bit-reversal order uses the following + * iterative algorithm: + * + * t = 1 + * for m = N; m > 1; m /= 2: + * hm = m/2 + * dt = t*2 + * for i1 = 0; i1 < hm; i1 ++: + * j1 = i1 * dt + * s = iGM[hm + i1] + * for j = j1; j < (j1 + t); j ++: + * x = fsrc[f + j] + * y = fsrc[f + j + t] + * fsrc[f + j] = x + y + * fsrc[f + j + t] = s * (x - y) + * t = dt + * for i1 = 0; i1 < N; i1 ++: + * fsrc[f + i1] = fsrc[f + i1] / N + * + * iGM[k] contains (1/w)^rev(k) for primitive root w = exp(i*pi/N) + * (actually, iGM[k] = 1/GM[k] = conj(GM[k])). + * + * In the main loop (not counting the final division loop), in + * all iterations except the last, the first and second half of fsrc[f + ] + * (as an array of complex numbers) are separate. In our chosen + * representation, we do not keep the second half. + * + * The last iteration recombines the recomputed half with the + * implicit half, and should yield only real numbers since the + * target polynomial is real; moreover, s = i at that step. + * Thus, when considering x and y: + * y = conj(x) since the final fsrc[f + j] must be real + * Therefore, fsrc[f + j] is filled with 2*Re(x), and fsrc[f + j + t] is + * filled with 2*Im(x). + * But we already have Re(x) and Im(x) in array slots j and j+t + * in our chosen representation. That last iteration is thus a + * simple doubling of the values in all the array. + * + * We make the last iteration a no-op by tweaking the final + * division into a division by N/2, not N. + */ + int u, n, hn, t, m; + + n = (int)1 << (int)logn; + t = 1; + m = n; + hn = n >> 1; + for (u = (int)logn; u > 1; u --) { + int hm, dt, i1, j1; + + hm = m >> 1; + dt = t << 1; + for (i1 = 0, j1 = 0; j1 < hn; i1 ++, j1 += dt) { + int j, j2; + + j2 = j1 + t; + FalconFPR s_re, s_im; + + s_re = this.fpre.fpr_gm_tab[((hm + i1) << 1) + 0]; + s_im = this.fpre.fpr_neg(this.fpre.fpr_gm_tab[((hm + i1) << 1) + 1]); + for (j = j1; j < j2; j ++) { + FalconFPR x_re, x_im, y_re, y_im; + FalconFPR[] res; + + x_re = fsrc[f + j]; + x_im = fsrc[f + j + hn]; + y_re = fsrc[f + j + t]; + y_im = fsrc[f + j + t + hn]; + res = FPC_ADD(x_re, x_im, y_re, y_im); + fsrc[f + j] = res[0]; fsrc[f + j + hn] = res[1]; + + res = FPC_SUB(x_re, x_im, y_re, y_im); + x_re = res[0]; x_im = res[1]; + res = FPC_MUL(x_re, x_im, s_re, s_im); + fsrc[f + j + t] = res[0]; fsrc[f + j + t + hn] = res[1]; + } + } + t = dt; + m = hm; + } + + /* + * Last iteration is a no-op, provided that we divide by N/2 + * instead of N. We need to make a special case for logn = 0. + */ + if (logn > 0) { + FalconFPR ni; + + ni = this.fpre.fpr_p2_tab[logn]; + for (u = 0; u < n; u ++) { + fsrc[f+u] = this.fpre.fpr_mul(fsrc[f+u], ni); + } + } + } + + internal void poly_add( + FalconFPR[] asrc, int a, FalconFPR[] bsrc, int b, uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + asrc[a + u] = this.fpre.fpr_add(asrc[a + u], bsrc[b + u]); + } + } + + internal void poly_sub( + FalconFPR[] asrc, int a, FalconFPR[] bsrc, int b, uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + asrc[a + u] = this.fpre.fpr_sub(asrc[a + u], bsrc[b + u]); + } + } + + internal void poly_neg(FalconFPR[] asrc, int a, uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + asrc[a + u] = this.fpre.fpr_neg(asrc[a + u]); + } + } + + internal void poly_adj_fft(FalconFPR[] asrc, int a, uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + for (u = (n >> 1); u < n; u ++) { + asrc[a + u] = this.fpre.fpr_neg(asrc[a + u]); + } + } + + internal void poly_mul_fft( + FalconFPR[] asrc, int a, FalconFPR[] bsrc, int b, uint logn) + { + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + FalconFPR a_re, a_im, b_re, b_im; + FalconFPR[] res; + + a_re = asrc[a + u]; + a_im = asrc[a + u + hn]; + b_re = bsrc[b + u]; + b_im = bsrc[b + u + hn]; + res = FPC_MUL(a_re, a_im, b_re, b_im); + asrc[a + u] = res[0]; asrc[a + u + hn] = res[1]; + } + } + + internal void poly_muladj_fft( + FalconFPR[] asrc, int a, FalconFPR[] bsrc, int b, uint logn) + { + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + FalconFPR a_re, a_im, b_re, b_im; + FalconFPR[] res; + + a_re = asrc[a + u]; + a_im = asrc[a + u + hn]; + b_re = bsrc[b + u]; + b_im = this.fpre.fpr_neg(bsrc[b + u + hn]); + res = FPC_MUL(a_re, a_im, b_re, b_im); + asrc[a + u] = res[0]; asrc[a + u + hn] = res[1]; + } + } + + internal void poly_mulselfadj_fft(FalconFPR[] asrc, int a, uint logn) + { + /* + * Since each coefficient is multiplied with its own conjugate, + * the result contains only real values. + */ + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + FalconFPR a_re, a_im; + + a_re = asrc[a + u]; + a_im = asrc[a + u + hn]; + asrc[a + u] = this.fpre.fpr_add(this.fpre.fpr_sqr(a_re), this.fpre.fpr_sqr(a_im)); + asrc[a + u + hn] = this.fpre.fpr_zero; + } + } + + internal void poly_mulconst(FalconFPR[] asrc, int a, FalconFPR x, uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + asrc[a + u] = this.fpre.fpr_mul(asrc[a + u], x); + } + } + + internal void poly_div_fft( + FalconFPR[] asrc, int a, FalconFPR[] bsrc, int b, uint logn) + { + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + FalconFPR a_re, a_im, b_re, b_im; + FalconFPR[] res; + + a_re = asrc[a + u]; + a_im = asrc[a + u + hn]; + b_re = bsrc[b + u]; + b_im = bsrc[b + u + hn]; + res = FPC_DIV(a_re, a_im, b_re, b_im); + asrc[a + u] = res[0]; asrc[a + u + hn] = res[1]; + } + } + + internal void poly_invnorm2_fft(FalconFPR[] dsrc, int d, + FalconFPR[] asrc, int a, FalconFPR[] bsrc, int b, uint logn) + { + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + FalconFPR a_re, a_im; + FalconFPR b_re, b_im; + + a_re = asrc[a + u]; + a_im = asrc[a + u + hn]; + b_re = bsrc[b + u]; + b_im = bsrc[b + u + hn]; + dsrc[d + u] = this.fpre.fpr_inv(this.fpre.fpr_add( + this.fpre.fpr_add(this.fpre.fpr_sqr(a_re), this.fpre.fpr_sqr(a_im)), + this.fpre.fpr_add(this.fpre.fpr_sqr(b_re), this.fpre.fpr_sqr(b_im)))); + } + } + + internal void poly_add_muladj_fft(FalconFPR[] dsrc, int d, + FalconFPR[] Fsrc, int F, FalconFPR[] Gsrc, int G, + FalconFPR[] fsrc, int f, FalconFPR[] gsrc, int g, uint logn) + { + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + FalconFPR F_re, F_im, G_re, G_im; + FalconFPR f_re, f_im, g_re, g_im; + FalconFPR a_re, a_im, b_re, b_im; + FalconFPR[] res; + + + F_re = Fsrc[F + u]; + F_im = Fsrc[F + u + hn]; + G_re = Gsrc[G + u]; + G_im = Gsrc[G + u + hn]; + f_re = fsrc[f + u]; + f_im = fsrc[f + u + hn]; + g_re = gsrc[g + u]; + g_im = gsrc[g + u + hn]; + + res = FPC_MUL(F_re, F_im, f_re, this.fpre.fpr_neg(f_im)); + a_re = res[0]; a_im = res[1]; + res = FPC_MUL(G_re, G_im, g_re, this.fpre.fpr_neg(g_im)); + b_re = res[0]; b_im = res[1]; + dsrc[d + u] = this.fpre.fpr_add(a_re, b_re); + dsrc[d + u + hn] = this.fpre.fpr_add(a_im, b_im); + } + } + + internal void poly_mul_autoadj_fft( + FalconFPR[] asrc, int a, FalconFPR[] bsrc, int b, uint logn) + { + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + asrc[a + u] = this.fpre.fpr_mul(asrc[a + u], bsrc[b + u]); + asrc[a + u + hn] = this.fpre.fpr_mul(asrc[a + u + hn], bsrc[b + u]); + } + } + + internal void poly_div_autoadj_fft( + FalconFPR[] asrc, int a, FalconFPR[] bsrc, int b, uint logn) + { + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + FalconFPR ib; + + ib = this.fpre.fpr_inv(bsrc[b + u]); + asrc[a + u] = this.fpre.fpr_mul(asrc[a + u], ib); + asrc[a + u + hn] = this.fpre.fpr_mul(asrc[a + u + hn], ib); + } + } + + internal void poly_LDL_fft( + FalconFPR[] g00src, int g00, + FalconFPR[] g01src, int g01, FalconFPR[] g11src, int g11, uint logn) + { + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + FalconFPR g00_re, g00_im, g01_re, g01_im, g11_re, g11_im; + FalconFPR[] res; + FalconFPR mu_re, mu_im; + + g00_re = g00src[g00 + u]; + g00_im = g00src[g00 + u + hn]; + g01_re = g01src[g01 + u]; + g01_im = g01src[g01 + u + hn]; + g11_re = g11src[g11 + u]; + g11_im = g11src[g11 + u + hn]; + res = FPC_DIV(g01_re, g01_im, g00_re, g00_im); + mu_re = res[0]; mu_im = res[1]; + res = FPC_MUL(mu_re, mu_im, g01_re, this.fpre.fpr_neg(g01_im)); + g01_re = res[0]; g01_im = res[1]; + res = FPC_SUB(g11_re, g11_im, g01_re, g01_im); + g11src[g11 + u] = res[0]; g11src[g11 + u + hn] = res[1]; + g01src[g01 + u] = mu_re; + g01src[g01 + u + hn] = this.fpre.fpr_neg(mu_im); + } + } + + internal void poly_LDLmv_fft( + FalconFPR[] d11src, int d11, FalconFPR[] l10src, int l10, + FalconFPR[] g00src, int g00, FalconFPR[] g01src, int g01, + FalconFPR[] g11src, int g11, uint logn) + { + int n, hn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + for (u = 0; u < hn; u ++) { + FalconFPR g00_re, g00_im, g01_re, g01_im, g11_re, g11_im; + FalconFPR[] res; + FalconFPR mu_re, mu_im; + + g00_re = g00src[g00 + u]; + g00_im = g00src[g00 + u + hn]; + g01_re = g01src[g01 + u]; + g01_im = g01src[g01 + u + hn]; + g11_re = g11src[g11 + u]; + g11_im = g11src[g11 + u + hn]; + res = FPC_DIV(g01_re, g01_im, g00_re, g00_im); + mu_re = res[0]; mu_im = res[1]; + res = FPC_MUL(mu_re, mu_im, g01_re, this.fpre.fpr_neg(g01_im)); + g01_re = res[0]; g01_im = res[1]; + res = FPC_SUB(g11_re, g11_im, g01_re, g01_im); + d11src[d11 + u] = res[0]; d11src[d11 + u + hn] = res[1]; + l10src[l10 + u] = mu_re; + l10src[l10 + u + hn] = this.fpre.fpr_neg(mu_im); + } + } + + internal void poly_split_fft( + FalconFPR[] f0src, int f0, FalconFPR[] f1src, int f1, + FalconFPR[] fsrc, int f, uint logn) + { + /* + * The FFT representation we use is in bit-reversed order + * (element i contains f(w^(rev(i))), where rev() is the + * bit-reversal function over the ring degree. This changes + * indexes with regards to the Falcon specification. + */ + int n, hn, qn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + qn = hn >> 1; + + /* + * We process complex values by pairs. For logn = 1, there is only + * one complex value (the other one is the implicit conjugate), + * so we add the two lines below because the loop will be + * skipped. + */ + f0src[f0 + 0] = fsrc[f + 0]; + f1src[f1 + 0] = fsrc[f + hn]; + + for (u = 0; u < qn; u ++) { + FalconFPR a_re, a_im, b_re, b_im, t_re, t_im; + FalconFPR[] res; + + a_re = fsrc[f + (u << 1) + 0]; + a_im = fsrc[f + (u << 1) + 0 + hn]; + b_re = fsrc[f + (u << 1) + 1]; + b_im = fsrc[f + (u << 1) + 1 + hn]; + + res = FPC_ADD(a_re, a_im, b_re, b_im); + t_re = res[0]; t_im = res[1]; + f0src[f0 + u] = this.fpre.fpr_half(t_re); + f0src[f0 + u + qn] = this.fpre.fpr_half(t_im); + + res = FPC_SUB(a_re, a_im, b_re, b_im); + t_re = res[0]; t_im = res[1]; + res = FPC_MUL(t_re, t_im, + this.fpre.fpr_gm_tab[((u + hn) << 1) + 0], + this.fpre.fpr_neg(this.fpre.fpr_gm_tab[((u + hn) << 1) + 1])); + t_re = res[0]; t_im = res[1]; + f1src[f1 + u] = this.fpre.fpr_half(t_re); + f1src[f1 + u + qn] = this.fpre.fpr_half(t_im); + } + } + + internal void poly_merge_fft( + FalconFPR[] fsrc, int f, + FalconFPR[] f0src, int f0, FalconFPR[] f1src, int f1, uint logn) + { + int n, hn, qn, u; + + n = (int)1 << (int)logn; + hn = n >> 1; + qn = hn >> 1; + + /* + * An extra copy to handle the special case logn = 1. + */ + fsrc[f + 0] = f0src[f0 + 0]; + fsrc[f + hn] = f1src[f1 + 0]; + + for (u = 0; u < qn; u ++) { + FalconFPR a_re, a_im, + b_re, b_im; + FalconFPR t_re, t_im; + FalconFPR[] res; + + a_re = f0src[f0 + u]; + a_im = f0src[f0 + u + qn]; + res = FPC_MUL(f1src[f1 + u], f1src[f1 + u + qn], + this.fpre.fpr_gm_tab[((u + hn) << 1) + 0], + this.fpre.fpr_gm_tab[((u + hn) << 1) + 1]); + b_re = res[0]; b_im = res[1]; + res = FPC_ADD(a_re, a_im, b_re, b_im); + t_re = res[0]; t_im = res[1]; + fsrc[f + (u << 1) + 0] = t_re; + fsrc[f + (u << 1) + 0 + hn] = t_im; + res = FPC_SUB(a_re, a_im, b_re, b_im); + t_re = res[0]; t_im = res[1]; + fsrc[f + (u << 1) + 1] = t_re; + fsrc[f + (u << 1) + 1 + hn] = t_im; + } + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconFPR.cs b/crypto/src/pqc/crypto/falcon/FalconFPR.cs new file mode 100644 index 000000000..b3f99f944 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconFPR.cs @@ -0,0 +1,13 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconFPR + { + internal double v; + + internal FalconFPR(double v) { + this.v = v; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconKeyGenerationParameters.cs b/crypto/src/pqc/crypto/falcon/FalconKeyGenerationParameters.cs new file mode 100644 index 000000000..3531a6670 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconKeyGenerationParameters.cs @@ -0,0 +1,22 @@ +using Org.BouncyCastle.Crypto; +using Org.BouncyCastle.Security; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + public class FalconKeyGenerationParameters + : KeyGenerationParameters + { + private FalconParameters parameters; + + public FalconKeyGenerationParameters(SecureRandom random, FalconParameters parameters) + : base(random, 320) + { + this.parameters = parameters; + } + + public FalconParameters GetParameters() + { + return this.parameters; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconKeyPairGenerator.cs b/crypto/src/pqc/crypto/falcon/FalconKeyPairGenerator.cs new file mode 100644 index 000000000..018dcd3d2 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconKeyPairGenerator.cs @@ -0,0 +1,55 @@ +using Org.BouncyCastle.Crypto; +using Org.BouncyCastle.Security; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + public class FalconKeyPairGenerator + : IAsymmetricCipherKeyPairGenerator + { + private FalconKeyGenerationParameters parameters; + private SecureRandom random; + private FalconNIST nist; + private uint logn; + private uint noncelen; + + private int pk_size; + private int sk_size; + + public void Init(KeyGenerationParameters param) + { + this.parameters = (FalconKeyGenerationParameters)param; + this.random = param.Random; + this.logn = ((FalconKeyGenerationParameters)param).GetParameters().GetLogN(); + this.noncelen = ((FalconKeyGenerationParameters)param).GetParameters().GetNonceLength(); + this.nist = new FalconNIST(random, logn, noncelen); + int n = 1 << (int)this.logn; + int sk_coeff_size = 8; + if (n == 1024) + { + sk_coeff_size = 5; + } + else if (n == 256 || n == 512) + { + sk_coeff_size = 6; + } + else if (n == 64 || n == 128) + { + sk_coeff_size = 7; + } + this.pk_size = 1 + (14 * n / 8); + this.sk_size = 1 + (2 * sk_coeff_size * n / 8) + (n); + } + + public AsymmetricCipherKeyPair GenerateKeyPair() + { + byte[] pk, sk; + pk = new byte[pk_size]; + sk = new byte[sk_size]; + nist.crypto_sign_keypair(pk, 0, sk, 0); + FalconParameters p = ((FalconKeyGenerationParameters)this.parameters).GetParameters(); + FalconPrivateKeyParameters privk = new FalconPrivateKeyParameters(p, sk); + FalconPublicKeyParameters pubk = new FalconPublicKeyParameters(p, pk); + return new AsymmetricCipherKeyPair(pubk, privk); + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconKeyParameters.cs b/crypto/src/pqc/crypto/falcon/FalconKeyParameters.cs new file mode 100644 index 000000000..87b0eaec7 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconKeyParameters.cs @@ -0,0 +1,22 @@ +using Org.BouncyCastle.Crypto; + + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + public class FalconKeyParameters + : AsymmetricKeyParameter + { + private FalconParameters parameters; + + public FalconKeyParameters(bool isprivate, FalconParameters parameters) + : base(isprivate) + { + this.parameters = parameters; + } + + public FalconParameters GetParameters() + { + return parameters; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconKeygen.cs b/crypto/src/pqc/crypto/falcon/FalconKeygen.cs new file mode 100644 index 000000000..7fe83056a --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconKeygen.cs @@ -0,0 +1,3673 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconKeygen + { + FPREngine fpre; + FalconFFT ffte; + FalconSmallPrime[] PRIMES; + FalconCodec codec; + FalconVrfy vrfy; + internal FalconKeygen() { + this.fpre = new FPREngine(); + this.PRIMES = new FalconSmallPrimes().PRIMES; + this.ffte = new FalconFFT(this.fpre); + this.codec = new FalconCodec(); + this.vrfy = new FalconVrfy(); + } + internal FalconKeygen(FalconCodec codec, FalconVrfy vrfy) { + this.fpre = new FPREngine(); + this.PRIMES = new FalconSmallPrimes().PRIMES; + this.ffte = new FalconFFT(); + this.codec = codec; + this.vrfy = vrfy; + } + + /* + * License from the reference C code (the code was copied then modified + * to function in C#): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + + /* + * Reduce a small signed integer modulo a small prime. The source + * value x MUST be such that -p < x < p. + */ + uint modp_set(int x, uint p) + { + uint w; + + w = (uint)x; + w += (uint)(p & -(w >> 31)); + return w; + } + + /* + * Normalize a modular integer around 0. + */ + int modp_norm(uint x, uint p) + { + return (int)(x - (p & (((x - ((p + 1) >> 1)) >> 31) - 1))); + } + + /* + * Compute -1/p mod 2^31. This works for all odd integers p that fit + * on 31 bits. + */ + uint modp_ninv31(uint p) + { + uint y; + + y = 2 - p; + y *= 2 - p * y; + y *= 2 - p * y; + y *= 2 - p * y; + y *= 2 - p * y; + return (uint)(0x7FFFFFFF & -y); + } + + /* + * Compute R = 2^31 mod p. + */ + uint modp_R(uint p) + { + /* + * Since 2^30 < p < 2^31, we know that 2^31 mod p is simply + * 2^31 - p. + */ + return ((uint)1 << 31) - p; + } + + /* + * Addition modulo p. + */ + uint modp_add(uint a, uint b, uint p) + { + uint d; + + d = a + b - p; + d += (uint)(p & -(d >> 31)); + return d; + } + + /* + * Subtraction modulo p. + */ + uint modp_sub(uint a, uint b, uint p) + { + uint d; + + d = a - b; + d += (uint)(p & -(d >> 31)); + return d; + } + + /* + * Halving modulo p. + */ + /* unused + uint modp_half(uint a, uint p) + { + a += p & -(a & 1); + return a >> 1; + } + */ + + /* + * Montgomery multiplication modulo p. The 'p0i' value is -1/p mod 2^31. + * It is required that p is an odd integer. + */ + uint modp_montymul(uint a, uint b, uint p, uint p0i) + { + ulong z, w; + uint d; + + z = (ulong)a * (ulong)b; + w = ((z * p0i) & (ulong)0x7FFFFFFF) * p; + d = (uint)((z + w) >> 31) - p; + d += (uint)(p & -(d >> 31)); + return d; + } + + /* + * Compute R2 = 2^62 mod p. + */ + uint modp_R2(uint p, uint p0i) + { + uint z; + + /* + * Compute z = 2^31 mod p (this is the value 1 in Montgomery + * representation), then double it with an addition. + */ + z = modp_R(p); + z = modp_add(z, z, p); + + /* + * Square it five times to obtain 2^32 in Montgomery representation + * (i.e. 2^63 mod p). + */ + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + z = modp_montymul(z, z, p, p0i); + + /* + * Halve the value mod p to get 2^62. + */ + z = (uint)((z + (p & -(z & 1))) >> 1); + return z; + } + + /* + * Compute 2^(31*x) modulo p. This works for integers x up to 2^11. + * p must be prime such that 2^30 < p < 2^31; p0i must be equal to + * -1/p mod 2^31; R2 must be equal to 2^62 mod p. + */ + uint modp_Rx(uint x, uint p, uint p0i, uint R2) + { + int i; + uint r, z; + + /* + * 2^(31*x) = (2^31)*(2^(31*(x-1))); i.e. we want the Montgomery + * representation of (2^31)^e mod p, where e = x-1. + * R2 is 2^31 in Montgomery representation. + */ + x --; + r = R2; + z = modp_R(p); + for (i = 0; (1U << i) <= x; i ++) { + if ((x & (1U << i)) != 0) { + z = modp_montymul(z, r, p, p0i); + } + r = modp_montymul(r, r, p, p0i); + } + return z; + } + + /* + * Division modulo p. If the divisor (b) is 0, then 0 is returned. + * This function computes proper results only when p is prime. + * Parameters: + * a dividend + * b divisor + * p odd prime modulus + * p0i -1/p mod 2^31 + * R 2^31 mod R + */ + uint modp_div(uint a, uint b, uint p, uint p0i, uint R) + { + uint z, e; + int i; + + e = p - 2; + z = R; + for (i = 30; i >= 0; i --) { + uint z2; + + z = modp_montymul(z, z, p, p0i); + z2 = modp_montymul(z, b, p, p0i); + z ^= (uint)((z ^ z2) & -(uint)((e >> i) & 1)); + } + + /* + * The loop above just assumed that b was in Montgomery + * representation, i.e. really contained b*R; under that + * assumption, it returns 1/b in Montgomery representation, + * which is R/b. But we gave it b in normal representation, + * so the loop really returned R/(b/R) = R^2/b. + * + * We want a/b, so we need one Montgomery multiplication with a, + * which also remove one of the R factors, and another such + * multiplication to remove the second R factor. + */ + z = modp_montymul(z, 1, p, p0i); + return modp_montymul(a, z, p, p0i); + } + + /* + * Bit-reversal index table. + */ + ushort[] REV10 = { + 0, 512, 256, 768, 128, 640, 384, 896, 64, 576, 320, 832, + 192, 704, 448, 960, 32, 544, 288, 800, 160, 672, 416, 928, + 96, 608, 352, 864, 224, 736, 480, 992, 16, 528, 272, 784, + 144, 656, 400, 912, 80, 592, 336, 848, 208, 720, 464, 976, + 48, 560, 304, 816, 176, 688, 432, 944, 112, 624, 368, 880, + 240, 752, 496, 1008, 8, 520, 264, 776, 136, 648, 392, 904, + 72, 584, 328, 840, 200, 712, 456, 968, 40, 552, 296, 808, + 168, 680, 424, 936, 104, 616, 360, 872, 232, 744, 488, 1000, + 24, 536, 280, 792, 152, 664, 408, 920, 88, 600, 344, 856, + 216, 728, 472, 984, 56, 568, 312, 824, 184, 696, 440, 952, + 120, 632, 376, 888, 248, 760, 504, 1016, 4, 516, 260, 772, + 132, 644, 388, 900, 68, 580, 324, 836, 196, 708, 452, 964, + 36, 548, 292, 804, 164, 676, 420, 932, 100, 612, 356, 868, + 228, 740, 484, 996, 20, 532, 276, 788, 148, 660, 404, 916, + 84, 596, 340, 852, 212, 724, 468, 980, 52, 564, 308, 820, + 180, 692, 436, 948, 116, 628, 372, 884, 244, 756, 500, 1012, + 12, 524, 268, 780, 140, 652, 396, 908, 76, 588, 332, 844, + 204, 716, 460, 972, 44, 556, 300, 812, 172, 684, 428, 940, + 108, 620, 364, 876, 236, 748, 492, 1004, 28, 540, 284, 796, + 156, 668, 412, 924, 92, 604, 348, 860, 220, 732, 476, 988, + 60, 572, 316, 828, 188, 700, 444, 956, 124, 636, 380, 892, + 252, 764, 508, 1020, 2, 514, 258, 770, 130, 642, 386, 898, + 66, 578, 322, 834, 194, 706, 450, 962, 34, 546, 290, 802, + 162, 674, 418, 930, 98, 610, 354, 866, 226, 738, 482, 994, + 18, 530, 274, 786, 146, 658, 402, 914, 82, 594, 338, 850, + 210, 722, 466, 978, 50, 562, 306, 818, 178, 690, 434, 946, + 114, 626, 370, 882, 242, 754, 498, 1010, 10, 522, 266, 778, + 138, 650, 394, 906, 74, 586, 330, 842, 202, 714, 458, 970, + 42, 554, 298, 810, 170, 682, 426, 938, 106, 618, 362, 874, + 234, 746, 490, 1002, 26, 538, 282, 794, 154, 666, 410, 922, + 90, 602, 346, 858, 218, 730, 474, 986, 58, 570, 314, 826, + 186, 698, 442, 954, 122, 634, 378, 890, 250, 762, 506, 1018, + 6, 518, 262, 774, 134, 646, 390, 902, 70, 582, 326, 838, + 198, 710, 454, 966, 38, 550, 294, 806, 166, 678, 422, 934, + 102, 614, 358, 870, 230, 742, 486, 998, 22, 534, 278, 790, + 150, 662, 406, 918, 86, 598, 342, 854, 214, 726, 470, 982, + 54, 566, 310, 822, 182, 694, 438, 950, 118, 630, 374, 886, + 246, 758, 502, 1014, 14, 526, 270, 782, 142, 654, 398, 910, + 78, 590, 334, 846, 206, 718, 462, 974, 46, 558, 302, 814, + 174, 686, 430, 942, 110, 622, 366, 878, 238, 750, 494, 1006, + 30, 542, 286, 798, 158, 670, 414, 926, 94, 606, 350, 862, + 222, 734, 478, 990, 62, 574, 318, 830, 190, 702, 446, 958, + 126, 638, 382, 894, 254, 766, 510, 1022, 1, 513, 257, 769, + 129, 641, 385, 897, 65, 577, 321, 833, 193, 705, 449, 961, + 33, 545, 289, 801, 161, 673, 417, 929, 97, 609, 353, 865, + 225, 737, 481, 993, 17, 529, 273, 785, 145, 657, 401, 913, + 81, 593, 337, 849, 209, 721, 465, 977, 49, 561, 305, 817, + 177, 689, 433, 945, 113, 625, 369, 881, 241, 753, 497, 1009, + 9, 521, 265, 777, 137, 649, 393, 905, 73, 585, 329, 841, + 201, 713, 457, 969, 41, 553, 297, 809, 169, 681, 425, 937, + 105, 617, 361, 873, 233, 745, 489, 1001, 25, 537, 281, 793, + 153, 665, 409, 921, 89, 601, 345, 857, 217, 729, 473, 985, + 57, 569, 313, 825, 185, 697, 441, 953, 121, 633, 377, 889, + 249, 761, 505, 1017, 5, 517, 261, 773, 133, 645, 389, 901, + 69, 581, 325, 837, 197, 709, 453, 965, 37, 549, 293, 805, + 165, 677, 421, 933, 101, 613, 357, 869, 229, 741, 485, 997, + 21, 533, 277, 789, 149, 661, 405, 917, 85, 597, 341, 853, + 213, 725, 469, 981, 53, 565, 309, 821, 181, 693, 437, 949, + 117, 629, 373, 885, 245, 757, 501, 1013, 13, 525, 269, 781, + 141, 653, 397, 909, 77, 589, 333, 845, 205, 717, 461, 973, + 45, 557, 301, 813, 173, 685, 429, 941, 109, 621, 365, 877, + 237, 749, 493, 1005, 29, 541, 285, 797, 157, 669, 413, 925, + 93, 605, 349, 861, 221, 733, 477, 989, 61, 573, 317, 829, + 189, 701, 445, 957, 125, 637, 381, 893, 253, 765, 509, 1021, + 3, 515, 259, 771, 131, 643, 387, 899, 67, 579, 323, 835, + 195, 707, 451, 963, 35, 547, 291, 803, 163, 675, 419, 931, + 99, 611, 355, 867, 227, 739, 483, 995, 19, 531, 275, 787, + 147, 659, 403, 915, 83, 595, 339, 851, 211, 723, 467, 979, + 51, 563, 307, 819, 179, 691, 435, 947, 115, 627, 371, 883, + 243, 755, 499, 1011, 11, 523, 267, 779, 139, 651, 395, 907, + 75, 587, 331, 843, 203, 715, 459, 971, 43, 555, 299, 811, + 171, 683, 427, 939, 107, 619, 363, 875, 235, 747, 491, 1003, + 27, 539, 283, 795, 155, 667, 411, 923, 91, 603, 347, 859, + 219, 731, 475, 987, 59, 571, 315, 827, 187, 699, 443, 955, + 123, 635, 379, 891, 251, 763, 507, 1019, 7, 519, 263, 775, + 135, 647, 391, 903, 71, 583, 327, 839, 199, 711, 455, 967, + 39, 551, 295, 807, 167, 679, 423, 935, 103, 615, 359, 871, + 231, 743, 487, 999, 23, 535, 279, 791, 151, 663, 407, 919, + 87, 599, 343, 855, 215, 727, 471, 983, 55, 567, 311, 823, + 183, 695, 439, 951, 119, 631, 375, 887, 247, 759, 503, 1015, + 15, 527, 271, 783, 143, 655, 399, 911, 79, 591, 335, 847, + 207, 719, 463, 975, 47, 559, 303, 815, 175, 687, 431, 943, + 111, 623, 367, 879, 239, 751, 495, 1007, 31, 543, 287, 799, + 159, 671, 415, 927, 95, 607, 351, 863, 223, 735, 479, 991, + 63, 575, 319, 831, 191, 703, 447, 959, 127, 639, 383, 895, + 255, 767, 511, 1023 + }; + + /* + * Compute the roots for NTT and inverse NTT (binary case). Input + * parameter g is a primitive 2048-th root of 1 modulo p (i.e. g^1024 = + * -1 mod p). This fills gm[] and igm[] with powers of g and 1/g: + * gm[rev(i)] = g^i mod p + * igm[rev(i)] = (1/g)^i mod p + * where rev() is the "bit reversal" function over 10 bits. It fills + * the arrays only up to N = 2^logn values. + * + * The values stored in gm[] and igm[] are in Montgomery representation. + * + * p must be a prime such that p = 1 mod 2048. + */ + void modp_mkgm2(uint[] gmsrc, int gm, uint[] igmsrc, int igm, uint logn, + uint g, uint p, uint p0i) + { + int u, n; + uint k; + uint ig, x1, x2, R2; + + n = (int)1 << (int)logn; + + /* + * We want g such that g^(2N) = 1 mod p, but the provided + * generator has order 2048. We must square it a few times. + */ + R2 = modp_R2(p, p0i); + g = modp_montymul(g, R2, p, p0i); + for (k = logn; k < 10; k ++) { + g = modp_montymul(g, g, p, p0i); + } + + ig = modp_div(R2, g, p, p0i, modp_R(p)); + k = 10 - logn; + x1 = x2 = modp_R(p); + for (u = 0; u < n; u ++) { + int v; + + v = REV10[u << (int)k]; + gmsrc[gm+v] = x1; + igmsrc[igm+v] = x2; + x1 = modp_montymul(x1, g, p, p0i); + x2 = modp_montymul(x2, ig, p, p0i); + } + } + + /* + * Compute the NTT over a polynomial (binary case). Polynomial elements + * are a[0], a[stride], a[2 * stride]... + */ + void modp_NTT2_ext(uint[] asrc, int a, int stride, uint[] gmsrc, int gm, uint logn, + uint p, uint p0i) + { + int t, m, n; + + if (logn == 0) { + return; + } + n = (int)1 << (int)logn; + t = n; + for (m = 1; m < n; m <<= 1) { + int ht, u, v1; + + ht = t >> 1; + for (u = 0, v1 = 0; u < m; u ++, v1 += t) { + uint s; + int v; + int r1; + int r2; + + s = gmsrc[gm+m + u]; + r1 = a + v1 * stride; + r2 = r1 + ht * stride; + for (v = 0; v < ht; v ++, r1 += stride, r2 += stride) { + uint x, y; + + x = asrc[r1]; + y = modp_montymul(asrc[r2], s, p, p0i); + asrc[r1] = modp_add(x, y, p); + asrc[r2] = modp_sub(x, y, p); + } + } + t = ht; + } + } + + /* + * Compute the inverse NTT over a polynomial (binary case). + */ + void modp_iNTT2_ext(uint[] asrc, int a, int stride, uint[] igmsrc, int igm, uint logn, + uint p, uint p0i) + { + int t, m, n, k; + uint ni; + int r; + + if (logn == 0) { + return; + } + n = (int)1 << (int)logn; + t = 1; + for (m = n; m > 1; m >>= 1) { + int hm, dt, u, v1; + + hm = m >> 1; + dt = t << 1; + for (u = 0, v1 = 0; u < hm; u ++, v1 += dt) { + uint s; + int v; + int r1; + int r2; + + s = igmsrc[igm+hm + u]; + r1 = a + v1 * stride; + r2 = r1 + t * stride; + for (v = 0; v < t; v ++, r1 += stride, r2 += stride) { + uint x, y; + + x = asrc[r1]; + y = asrc[r2]; + asrc[r1] = modp_add(x, y, p); + asrc[r2] = modp_montymul( + modp_sub(x, y, p), s, p, p0i);; + } + } + t = dt; + } + + /* + * We need 1/n in Montgomery representation, i.e. R/n. Since + * 1 <= logn <= 10, R/n is an integer; morever, R/n <= 2^30 < p, + * thus a simple shift will do. + */ + ni = (uint)1 << (int)(31 - logn); + for (k = 0, r = a; k < n; k ++, r += stride) { + asrc[r] = modp_montymul(asrc[r], ni, p, p0i); + } + } + + /* + * Simplified macros for NTT and iNTT (binary case) when the elements + * are consecutive in RAM. + */ + void modp_NTT2(uint[] asrc, int a, uint[] gmsrc, int gm, uint logn, uint p, uint p0i) { + this.modp_NTT2_ext(asrc, a, 1, gmsrc, gm, logn, p, p0i); + } + void modp_iNTT2(uint[] asrc, int a, uint[] igmsrc, int igm, uint logn, uint p, uint p0i) { + this.modp_iNTT2_ext(asrc, a, 1, igmsrc, igm, logn, p, p0i); + } + + /* + * Given polynomial f in NTT representation modulo p, compute f' of degree + * less than N/2 such that f' = f0^2 - X*f1^2, where f0 and f1 are + * polynomials of degree less than N/2 such that f = f0(X^2) + X*f1(X^2). + * + * The new polynomial is written "in place" over the first N/2 elements + * of f. + * + * If applied logn times successively on a given polynomial, the resulting + * degree-0 polynomial is the resultant of f and X^N+1 modulo p. + * + * This function applies only to the binary case; it is invoked from + * solve_NTRU_binary_depth1(). + */ + void modp_poly_rec_res(uint[] fsrc, int f, uint logn, + uint p, uint p0i, uint R2) + { + int hn, u; + + hn = (int)1 << (int)(logn - 1); + for (u = 0; u < hn; u ++) { + uint w0, w1; + + w0 = fsrc[f + (u << 1) + 0]; + w1 = fsrc[f + (u << 1) + 1]; + fsrc[f + u] = modp_montymul(modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + } + + /* ==================================================================== */ + /* + * Custom bignum implementation. + * + * This is a very reduced set of functionalities. We need to do the + * following operations: + * + * - Rebuild the resultant and the polynomial coefficients from their + * values modulo small primes (of length 31 bits each). + * + * - Compute an extended GCD between the two computed resultants. + * + * - Extract top bits and add scaled values during the successive steps + * of Babai rounding. + * + * When rebuilding values using CRT, we must also recompute the product + * of the small prime factors. We always do it one small factor at a + * time, so the "complicated" operations can be done modulo the small + * prime with the modp_* functions. CRT coefficients (inverses) are + * precomputed. + * + * All values are positive until the last step: when the polynomial + * coefficients have been rebuilt, we normalize them around 0. But then, + * only additions and subtractions on the upper few bits are needed + * afterwards. + * + * We keep big integers as arrays of 31-bit words (in uint values); + * the top bit of each uint is kept equal to 0. Using 31-bit words + * makes it easier to keep track of carries. When negative values are + * used, two's complement is used. + */ + + /* + * Subtract integer b from integer a. Both integers are supposed to have + * the same size. The carry (0 or 1) is returned. Source arrays a and b + * MUST be distinct. + * + * The operation is performed as described above if ctr = 1. If + * ctl = 0, the value a[] is unmodified, but all memory accesses are + * still performed, and the carry is computed and returned. + */ + uint zint_sub(uint[] asrc, int a, uint[] bsrc, int b, int len, + uint ctl) + { + int u; + uint cc, m; + + cc = 0; + m = (uint)(-ctl); + for (u = 0; u < len; u ++) { + uint aw, w; + + aw = asrc[a + u]; + w = aw - bsrc[b + u] - cc; + cc = w >> 31; + aw ^= ((w & 0x7FFFFFFF) ^ aw) & m; + asrc[a + u] = aw; + } + return cc; + } + + /* + * Mutiply the provided big integer m with a small value x. + * This function assumes that x < 2^31. The carry word is returned. + */ + uint zint_mul_small(uint[] msrc, int m, int mlen, uint x) + { + int u; + uint cc; + + cc = 0; + for (u = 0; u < mlen; u ++) { + ulong z; + + z = (ulong)msrc[m+u] * (ulong)x + cc; + msrc[m+u] = (uint)z & 0x7FFFFFFF; + cc = (uint)(z >> 31); + } + return cc; + } + + /* + * Reduce a big integer d modulo a small integer p. + * Rules: + * d is uint + * p is prime + * 2^30 < p < 2^31 + * p0i = -(1/p) mod 2^31 + * R2 = 2^62 mod p + */ + uint zint_mod_small_uint(uint[] dsrc, int d, int dlen, + uint p, uint p0i, uint R2) + { + uint x; + int u; + + /* + * Algorithm: we inject words one by one, starting with the high + * word. Each step is: + * - multiply x by 2^31 + * - add new word + */ + x = 0; + u = dlen; + while (u -- > 0) { + uint w; + + x = modp_montymul(x, R2, p, p0i); + w = dsrc[d+u] - p; + w += (uint)(p & -(w >> 31)); + x = modp_add(x, w, p); + } + return x; + } + + /* + * Similar to zint_mod_small_uint(), except that d may be signed. + * Extra parameter is Rx = 2^(31*dlen) mod p. + */ + uint zint_mod_small_signed(uint[] dsrc, int d, int dlen, + uint p, uint p0i, uint R2, uint Rx) + { + uint z; + + if (dlen == 0) { + return 0; + } + z = zint_mod_small_uint(dsrc, d, dlen, p, p0i, R2); + z = modp_sub(z, (uint)(Rx & -(dsrc[d + dlen - 1] >> 30)), p); + return z; + } + + /* + * Add y*s to x. x and y initially have length 'len' words; the new x + * has length 'len+1' words. 's' must fit on 31 bits. x[] and y[] must + * not overlap. + */ + void zint_add_mul_small(uint[] xsrc, int x, + uint[] ysrc, int y, int len, uint s) + { + int u; + uint cc; + + cc = 0; + for (u = 0; u < len; u ++) { + uint xw, yw; + ulong z; + + xw = xsrc[x+u]; + yw = ysrc[y+u]; + z = (ulong)yw * (ulong)s + (ulong)xw + (ulong)cc; + xsrc[x+u] = (uint)z & 0x7FFFFFFF; + cc = (uint)(z >> 31); + } + xsrc[x+len] = cc; + } + + /* + * Normalize a modular integer around 0: if x > p/2, then x is replaced + * with x - p (signed encoding with two's complement); otherwise, x is + * untouched. The two integers x and p are encoded over the same length. + */ + void zint_norm_zero(uint[] xsrc, int x, uint[] psrc, int p, int len) + { + int u; + uint r, bb; + + /* + * Compare x with p/2. We use the shifted version of p, and p + * is odd, so we really compare with (p-1)/2; we want to perform + * the subtraction if and only if x > (p-1)/2. + */ + r = 0; + bb = 0; + u = len; + while (u -- > 0) { + uint wx, wp, cc; + + /* + * Get the two words to compare in wx and wp (both over + * 31 bits exactly). + */ + wx = xsrc[x+u]; + wp = (psrc[p+u] >> 1) | (bb << 30); + bb = psrc[p+u] & 1; + + /* + * We set cc to -1, 0 or 1, depending on whether wp is + * lower than, equal to, or greater than wx. + */ + cc = wp - wx; + cc = (uint)(((uint)(-cc) >> 31) | (uint)-(cc >> 31)); + + /* + * If r != 0 then it is either 1 or -1, and we keep its + * value. Otherwise, if r = 0, then we replace it with cc. + */ + r |= cc & ((r & 1) - 1); + } + + /* + * At this point, r = -1, 0 or 1, depending on whether (p-1)/2 + * is lower than, equal to, or greater than x. We thus want to + * do the subtraction only if r = -1. + */ + zint_sub(xsrc, x, psrc, p, len, r >> 31); + } + + /* + * Rebuild integers from their RNS representation. There are 'num' + * integers, and each consists in 'xlen' words. 'xx' points at that + * first word of the first integer; subsequent integers are accessed + * by adding 'xstride' repeatedly. + * + * The words of an integer are the RNS representation of that integer, + * using the provided 'primes' are moduli. This function replaces + * each integer with its multi-word value (little-endian order). + * + * If "normalize_signed" is non-zero, then the returned value is + * normalized to the -m/2..m/2 interval (where m is the product of all + * small prime moduli); two's complement is used for negative values. + */ + void zint_rebuild_CRT(uint[] xxsrc, int xx, int xlen, int xstride, + int num, FalconSmallPrime[] primes, int normalize_signed, + uint[] tmpsrc, int tmp) + { + int u; + int x; + + tmpsrc[tmp + 0] = primes[0].p; + for (u = 1; u < xlen; u ++) { + /* + * At the entry of each loop iteration: + * - the first u words of each array have been + * reassembled; + * - the first u words of tmp[] contains the + * product of the prime moduli processed so far. + * + * We call 'q' the product of all previous primes. + */ + uint p, p0i, s, R2; + int v; + + p = primes[u].p; + s = primes[u].s; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + for (v = 0, x = xx; v < num; v ++, x += xstride) { + uint xp, xq, xr; + /* + * xp = the integer x modulo the prime p for this + * iteration + * xq = (x mod q) mod p + */ + xp = xxsrc[x + u]; + xq = zint_mod_small_uint(xxsrc, x, u, p, p0i, R2); + + /* + * New value is (x mod q) + q * (s * (xp - xq) mod p) + */ + xr = modp_montymul(s, modp_sub(xp, xq, p), p, p0i); + zint_add_mul_small(xxsrc, x, tmpsrc, tmp, u, xr); + } + + /* + * Update product of primes in tmp[]. + */ + tmpsrc[tmp + u] = zint_mul_small(tmpsrc, tmp, u, p); + } + + /* + * Normalize the reconstructed values around 0. + */ + if (normalize_signed != 0) { + for (u = 0, x = xx; u < num; u ++, x += xstride) { + zint_norm_zero(xxsrc, x, tmpsrc, tmp, xlen); + } + } + } + + /* + * Negate a big integer conditionally: value a is replaced with -a if + * and only if ctl = 1. Control value ctl must be 0 or 1. + */ + void zint_negate(uint[] asrc, int a, int len, uint ctl) + { + int u; + uint cc, m; + + /* + * If ctl = 1 then we flip the bits of a by XORing with + * 0x7FFFFFFF, and we add 1 to the value. If ctl = 0 then we XOR + * with 0 and add 0, which leaves the value unchanged. + */ + cc = ctl; + m = ((uint)-ctl >> 1); + for (u = 0; u < len; u ++) { + uint aw; + + aw = asrc[a+u]; + aw = (aw ^ m) + cc; + asrc[a+u] = aw & 0x7FFFFFFF; + cc = aw >> 31; + } + } + + /* + * Replace a with (a*xa+b*xb)/(2^31) and b with (a*ya+b*yb)/(2^31). + * The low bits are dropped (the caller should compute the coefficients + * such that these dropped bits are all zeros). If either or both + * yields a negative value, then the value is negated. + * + * Returned value is: + * 0 both values were positive + * 1 new a had to be negated + * 2 new b had to be negated + * 3 both new a and new b had to be negated + * + * Coefficients xa, xb, ya and yb may use the full signed 32-bit range. + */ + uint zint_co_reduce(uint[] asrc, int a, uint[] bsrc, int b, int len, + long xa, long xb, long ya, long yb) + { + int u; + long cca, ccb; + uint nega, negb; + + cca = 0; + ccb = 0; + for (u = 0; u < len; u ++) { + uint wa, wb; + ulong za, zb; + + wa = asrc[a + u]; + wb = bsrc[b + u]; + za = (ulong)((long)wa * xa + (long)wb * xb + cca); + zb = (ulong)((long)wa * ya + (long)wb * yb + ccb); + if (u > 0) { + asrc[a + u - 1] = (uint)za & 0x7FFFFFFF; + bsrc[b + u - 1] = (uint)zb & 0x7FFFFFFF; + } + //cca = *(long *)&za >> 31; + cca = (long)za >> 31; + ccb = (long)zb >> 31; + //ccb = *(long *)&zb >> 31; + } + asrc[a + len - 1] = (uint)cca; + bsrc[b + len - 1] = (uint)ccb; + + nega = (uint)((ulong)cca >> 63); + negb = (uint)((ulong)ccb >> 63); + zint_negate(asrc, a, len, nega); + zint_negate(bsrc, b, len, negb); + return nega | (negb << 1); + } + + /* + * Finish modular reduction. Rules on input parameters: + * + * if neg = 1, then -m <= a < 0 + * if neg = 0, then 0 <= a < 2*m + * + * If neg = 0, then the top word of a[] is allowed to use 32 bits. + * + * Modulus m must be odd. + */ + void zint_finish_mod(uint[] asrc, int a, int len, uint[] msrc, int m, uint neg) + { + int u; + uint cc, xm, ym; + + /* + * First pass: compare a (assumed nonnegative) with m. Note that + * if the top word uses 32 bits, subtracting m must yield a + * value less than 2^31 since a < 2*m. + */ + cc = 0; + for (u = 0; u < len; u ++) { + cc = (asrc[a+u] - msrc[m+u] - cc) >> 31; + } + + /* + * If neg = 1 then we must add m (regardless of cc) + * If neg = 0 and cc = 0 then we must subtract m + * If neg = 0 and cc = 1 then we must do nothing + * + * In the loop below, we conditionally subtract either m or -m + * from a. Word xm is a word of m (if neg = 0) or -m (if neg = 1); + * but if neg = 0 and cc = 1, then ym = 0 and it forces mw to 0. + */ + xm = ((uint)-neg >> 1); + ym = (uint)(-(neg | (1 - cc))); + cc = neg; + for (u = 0; u < len; u ++) { + uint aw, mw; + + aw = asrc[a+u]; + mw = (msrc[m+u] ^ xm) & ym; + aw = aw - mw - cc; + asrc[a+u] = aw & 0x7FFFFFFF; + cc = aw >> 31; + } + } + + /* + * Replace a with (a*xa+b*xb)/(2^31) mod m, and b with + * (a*ya+b*yb)/(2^31) mod m. Modulus m must be odd; m0i = -1/m[0] mod 2^31. + */ + void zint_co_reduce_mod(uint[] asrc, int a, uint[] bsrc, int b, uint[] msrc, int m, int len, + uint m0i, long xa, long xb, long ya, long yb) + { + int u; + long cca, ccb; + uint fa, fb; + + /* + * These are actually four combined Montgomery multiplications. + */ + cca = 0; + ccb = 0; + fa = ((asrc[a + 0] * (uint)xa + bsrc[b + 0] * (uint)xb) * m0i) & 0x7FFFFFFF; + fb = ((asrc[a + 0] * (uint)ya + bsrc[b + 0] * (uint)yb) * m0i) & 0x7FFFFFFF; + for (u = 0; u < len; u ++) { + uint wa, wb; + ulong za, zb; + + wa = asrc[a + u]; + wb = bsrc[b + u]; + //za = wa * (ulong)xa + wb * (ulong)xb + // + msrc[m + u] * (ulong)fa + (ulong)cca; + //zb = wa * (ulong)ya + wb * (ulong)yb + // + msrc[m + u] * (ulong)fb + (ulong)ccb; + za = (ulong)((long)wa * xa + (long)wb * xb + + (long)msrc[m + u] * fa + cca); + zb = (ulong)((long)wa * ya + (long)wb * yb + + (long)msrc[m + u] * fb + ccb); + if (u > 0) { + asrc[a + u - 1] = (uint)za & 0x7FFFFFFF; + bsrc[b + u - 1] = (uint)zb & 0x7FFFFFFF; + } + //cca = *(long *)&za >> 31; + //ccb = *(long *)&zb >> 31; + cca = (long)za >> 31; + ccb = (long)zb >> 31; + } + asrc[a + len - 1] = (uint)cca; + bsrc[b + len - 1] = (uint)ccb; + + /* + * At this point: + * -m <= a < 2*m + * -m <= b < 2*m + * (this is a case of Montgomery reduction) + * The top words of 'a' and 'b' may have a 32-th bit set. + * We want to add or subtract the modulus, as required. + */ + zint_finish_mod(asrc, a, len, msrc, m, (uint)((ulong)cca >> 63)); + zint_finish_mod(bsrc, b, len, msrc, m, (uint)((ulong)ccb >> 63)); + } + + /* + * Compute a GCD between two positive big integers x and y. The two + * integers must be odd. Returned value is 1 if the GCD is 1, 0 + * otherwise. When 1 is returned, arrays u and v are filled with values + * such that: + * 0 <= u <= y + * 0 <= v <= x + * x*u - y*v = 1 + * x[] and y[] are unmodified. Both input values must have the same + * encoded length. Temporary array must be large enough to accommodate 4 + * extra values of that length. Arrays u, v and tmp may not overlap with + * each other, or with either x or y. + */ + int zint_bezout(uint[] usrc, int u, uint[] vsrc, int v, + uint[] xsrc, int x, uint[] ysrc, int y, + int len, uint[] tmpsrc, int tmp) + { + /* + * Algorithm is an extended binary GCD. We maintain 6 values + * a, b, u0, u1, v0 and v1 with the following invariants: + * + * a = x*u0 - y*v0 + * b = x*u1 - y*v1 + * 0 <= a <= x + * 0 <= b <= y + * 0 <= u0 < y + * 0 <= v0 < x + * 0 <= u1 <= y + * 0 <= v1 < x + * + * Initial values are: + * + * a = x u0 = 1 v0 = 0 + * b = y u1 = y v1 = x-1 + * + * Each iteration reduces either a or b, and maintains the + * invariants. Algorithm stops when a = b, at which point their + * common value is GCD(a,b) and (u0,v0) (or (u1,v1)) contains + * the values (u,v) we want to return. + * + * The formal definition of the algorithm is a sequence of steps: + * + * - If a is even, then: + * a <- a/2 + * u0 <- u0/2 mod y + * v0 <- v0/2 mod x + * + * - Otherwise, if b is even, then: + * b <- b/2 + * u1 <- u1/2 mod y + * v1 <- v1/2 mod x + * + * - Otherwise, if a > b, then: + * a <- (a-b)/2 + * u0 <- (u0-u1)/2 mod y + * v0 <- (v0-v1)/2 mod x + * + * - Otherwise: + * b <- (b-a)/2 + * u1 <- (u1-u0)/2 mod y + * v1 <- (v1-v0)/2 mod y + * + * We can show that the operations above preserve the invariants: + * + * - If a is even, then u0 and v0 are either both even or both + * odd (since a = x*u0 - y*v0, and x and y are both odd). + * If u0 and v0 are both even, then (u0,v0) <- (u0/2,v0/2). + * Otherwise, (u0,v0) <- ((u0+y)/2,(v0+x)/2). Either way, + * the a = x*u0 - y*v0 invariant is preserved. + * + * - The same holds for the case where b is even. + * + * - If a and b are odd, and a > b, then: + * + * a-b = x*(u0-u1) - y*(v0-v1) + * + * In that situation, if u0 < u1, then x*(u0-u1) < 0, but + * a-b > 0; therefore, it must be that v0 < v1, and the + * first part of the update is: (u0,v0) <- (u0-u1+y,v0-v1+x), + * which preserves the invariants. Otherwise, if u0 > u1, + * then u0-u1 >= 1, thus x*(u0-u1) >= x. But a <= x and + * b >= 0, hence a-b <= x. It follows that, in that case, + * v0-v1 >= 0. The first part of the update is then: + * (u0,v0) <- (u0-u1,v0-v1), which again preserves the + * invariants. + * + * Either way, once the subtraction is done, the new value of + * a, which is the difference of two odd values, is even, + * and the remaining of this step is a subcase of the + * first algorithm case (i.e. when a is even). + * + * - If a and b are odd, and b > a, then the a similar + * argument holds. + * + * The values a and b start at x and y, respectively. Since x + * and y are odd, their GCD is odd, and it is easily seen that + * all steps conserve the GCD (GCD(a-b,b) = GCD(a, b); + * GCD(a/2,b) = GCD(a,b) if GCD(a,b) is odd). Moreover, either a + * or b is reduced by at least one bit at each iteration, so + * the algorithm necessarily converges on the case a = b, at + * which point the common value is the GCD. + * + * In the algorithm expressed above, when a = b, the fourth case + * applies, and sets b = 0. Since a contains the GCD of x and y, + * which are both odd, a must be odd, and subsequent iterations + * (if any) will simply divide b by 2 repeatedly, which has no + * consequence. Thus, the algorithm can run for more iterations + * than necessary; the final GCD will be in a, and the (u,v) + * coefficients will be (u0,v0). + * + * + * The presentation above is bit-by-bit. It can be sped up by + * noticing that all decisions are taken based on the low bits + * and high bits of a and b. We can extract the two top words + * and low word of each of a and b, and compute reduction + * parameters pa, pb, qa and qb such that the new values for + * a and b are: + * a' = (a*pa + b*pb) / (2^31) + * b' = (a*qa + b*qb) / (2^31) + * the two divisions being exact. The coefficients are obtained + * just from the extracted words, and may be slightly off, requiring + * an optional correction: if a' < 0, then we replace pa with -pa + * and pb with -pb. Each such step will reduce the total length + * (sum of lengths of a and b) by at least 30 bits at each + * iteration. + */ + int u0, u1, v0, v1, a, b; + uint x0i, y0i; + uint num, rc; + int j; + + if (len == 0) { + return 0; + } + + /* + * u0 and v0 are the u and v result buffers; the four other + * values (u1, v1, a and b) are taken from tmp[]. + */ + u0 = u; // usrc + v0 = v; // vsrc + u1 = tmp; // tmpsrc + v1 = u1 + len; // tmpsrc + a = v1 + len; // tmpsrc + b = a + len; // tmpsrc + + /* + * We'll need the Montgomery reduction coefficients. + */ + x0i = modp_ninv31(xsrc[x + 0]); + y0i = modp_ninv31(ysrc[y + 0]); + + /* + * Initialize a, b, u0, u1, v0 and v1. + * a = x u0 = 1 v0 = 0 + * b = y u1 = y v1 = x-1 + * Note that x is odd, so computing x-1 is easy. + */ + // memcpy(a, x, len * sizeof *x); + Array.Copy(xsrc, x, tmpsrc, a, len); + // memcpy(b, y, len * sizeof *y); + Array.Copy(ysrc, y, tmpsrc, b, len); + usrc[u0+0] = 1; + // memset(u0 + 1, 0, (len - 1) * sizeof *u0); + // memset(v0, 0, len * sizeof *v0); + for (int i = 1; i < len; i++) { + usrc[u0+i] = 0; + vsrc[v0+i] = 0; + } + vsrc[v0+0] = 0; + // memcpy(u1, y, len * sizeof *u1); + Array.Copy(ysrc, y, tmpsrc, u1, len); + // memcpy(v1, x, len * sizeof *v1); + Array.Copy(xsrc, x, tmpsrc, v1, len); + tmpsrc[v1+0] --; + + /* + * Each input operand may be as large as 31*len bits, and we + * reduce the total length by at least 30 bits at each iteration. + */ + for (num = 62 * (uint)len + 30; num >= 30; num -= 30) { + uint c0, c1; + uint a0, a1, b0, b1; + ulong a_hi, b_hi; + uint a_lo, b_lo; + long pa, pb, qa, qb; + int i; + uint r; + + /* + * Extract the top words of a and b. If j is the highest + * index >= 1 such that a[j] != 0 or b[j] != 0, then we + * want (a[j] << 31) + a[j-1] and (b[j] << 31) + b[j-1]. + * If a and b are down to one word each, then we use + * a[0] and b[0]. + */ + //c0 = (uint)-1; + //c1 = (uint)-1; + c0 = uint.MaxValue; + c1 = uint.MaxValue; + a0 = 0; + a1 = 0; + b0 = 0; + b1 = 0; + j = len; + while (j -- > 0) { + uint aw, bw; + + aw = tmpsrc[a+j]; + bw = tmpsrc[b+j]; + a0 ^= (a0 ^ aw) & c0; + a1 ^= (a1 ^ aw) & c1; + b0 ^= (b0 ^ bw) & c0; + b1 ^= (b1 ^ bw) & c1; + c1 = c0; + c0 &= (((aw | bw) + 0x7FFFFFFF) >> 31) - (uint)1; + } + + /* + * If c1 = 0, then we grabbed two words for a and b. + * If c1 != 0 but c0 = 0, then we grabbed one word. It + * is not possible that c1 != 0 and c0 != 0, because that + * would mean that both integers are zero. + */ + a1 |= a0 & c1; + a0 &= ~c1; + b1 |= b0 & c1; + b0 &= ~c1; + a_hi = ((ulong)a0 << 31) + a1; + b_hi = ((ulong)b0 << 31) + b1; + a_lo = tmpsrc[a+0]; + b_lo = tmpsrc[b+0]; + + /* + * Compute reduction factors: + * + * a' = a*pa + b*pb + * b' = a*qa + b*qb + * + * such that a' and b' are both multiple of 2^31, but are + * only marginally larger than a and b. + */ + pa = 1; + pb = 0; + qa = 0; + qb = 1; + for (i = 0; i < 31; i ++) { + /* + * At each iteration: + * + * a <- (a-b)/2 if: a is odd, b is odd, a_hi > b_hi + * b <- (b-a)/2 if: a is odd, b is odd, a_hi <= b_hi + * a <- a/2 if: a is even + * b <- b/2 if: a is odd, b is even + * + * We multiply a_lo and b_lo by 2 at each + * iteration, thus a division by 2 really is a + * non-multiplication by 2. + */ + uint rt, oa, ob, cAB, cBA, cA; + ulong rz; + + /* + * rt = 1 if a_hi > b_hi, 0 otherwise. + */ + rz = b_hi - a_hi; + rt = (uint)((rz ^ ((a_hi ^ b_hi) + & (a_hi ^ rz))) >> 63); + + /* + * cAB = 1 if b must be subtracted from a + * cBA = 1 if a must be subtracted from b + * cA = 1 if a must be divided by 2 + * + * Rules: + * + * cAB and cBA cannot both be 1. + * If a is not divided by 2, b is. + */ + oa = (a_lo >> i) & 1; + ob = (b_lo >> i) & 1; + cAB = oa & ob & rt; + cBA = (uint)(oa & ob & ~(int)rt); + cA = cAB | (oa ^ 1); + + /* + * Conditional subtractions. + */ + a_lo -= (uint)(b_lo & -cAB); + a_hi -= b_hi & (ulong)-(long)cAB; + pa -= (qa & -(long)cAB); + pb -= (qb & -(long)cAB); + b_lo -= (uint)(a_lo & -cBA); + b_hi -= a_hi & (ulong)-(long)cBA; + qa -= pa & -(long)cBA; + qb -= pb & -(long)cBA; + + /* + * Shifting. + */ + a_lo += a_lo & (cA - 1); + pa += pa & ((long)cA - 1); + pb += pb & ((long)cA - 1); + a_hi ^= (a_hi ^ (a_hi >> 1)) & (ulong)-(long)cA; + b_lo += (uint)(b_lo & -cA); + qa += qa & -(long)cA; + qb += qb & -(long)cA; + b_hi ^= (b_hi ^ (b_hi >> 1)) & ((ulong)cA - 1); + } + + /* + * Apply the computed parameters to our values. We + * may have to correct pa and pb depending on the + * returned value of zint_co_reduce() (when a and/or b + * had to be negated). + */ + r = zint_co_reduce(tmpsrc, a, tmpsrc, b, len, pa, pb, qa, qb); + pa -= (pa + pa) & -(long)(r & 1); + pb -= (pb + pb) & -(long)(r & 1); + qa -= (qa + qa) & -(long)(r >> 1); + qb -= (qb + qb) & -(long)(r >> 1); + zint_co_reduce_mod(usrc, u0, tmpsrc, u1, ysrc, y, len, y0i, pa, pb, qa, qb); + zint_co_reduce_mod(vsrc, v0, tmpsrc, v1, xsrc, x, len, x0i, pa, pb, qa, qb); + } + + /* + * At that point, array a[] should contain the GCD, and the + * results (u,v) should already be set. We check that the GCD + * is indeed 1. We also check that the two operands x and y + * are odd. + */ + rc = tmpsrc[a+0] ^ 1; + for (j = 1; j < len; j ++) { + rc |= tmpsrc[a+j]; + } + return (int)((1 - ((rc | -rc) >> 31)) & xsrc[x+0] & ysrc[y+0]); + } + + /* + * Add k*y*2^sc to x. The result is assumed to fit in the array of + * size xlen (truncation is applied if necessary). + * Scale factor 'sc' is provided as sch and scl, such that: + * sch = sc / 31 + * scl = sc % 31 + * xlen MUST NOT be lower than ylen. + * + * x[] and y[] are both signed integers, using two's complement for + * negative values. + */ + void zint_add_scaled_mul_small(uint[] xsrc, int x, int xlen, + uint[] ysrc, int y, int ylen, int k, + uint sch, uint scl) + { + int u; + uint ysign, tw; + int cc; + + if (ylen == 0) { + return; + } + + ysign = ((uint)-(ysrc[y + ylen - 1] >> 30) >> 1); + tw = 0; + cc = 0; + for (u = (int)sch; u < xlen; u ++) { + int v; + uint wy, wys, ccu; + ulong z; + + /* + * Get the next word of y (scaled). + */ + v = u - (int)sch; + wy = v < ylen ? ysrc[y + v] : ysign; + wys = ((wy << (int)scl) & 0x7FFFFFFF) | tw; + tw = wy >> (31 - (int)scl); + + /* + * The expression below does not overflow. + */ + z = (ulong)((long)wys * (long)k + (long)xsrc[x+u] + cc); + xsrc[x+u] = (uint)z & 0x7FFFFFFF; + + /* + * Right-shifting the signed value z would yield + * implementation-defined results (arithmetic shift is + * not guaranteed). However, we can cast to uint, + * and get the next carry as an uint word. We can + * then convert it back to signed by using the guaranteed + * fact that 'int' uses two's complement with no + * trap representation or padding bit, and with a layout + * compatible with that of 'uint'. + */ + ccu = (uint)(z >> 31); + //cc = *(int *)&ccu; + cc = (int)ccu; + } + } + + /* + * Subtract y*2^sc from x. The result is assumed to fit in the array of + * size xlen (truncation is applied if necessary). + * Scale factor 'sc' is provided as sch and scl, such that: + * sch = sc / 31 + * scl = sc % 31 + * xlen MUST NOT be lower than ylen. + * + * x[] and y[] are both signed integers, using two's complement for + * negative values. + */ + void zint_sub_scaled(uint[] xsrc, int x, int xlen, + uint[] ysrc, int y, int ylen, uint sch, uint scl) + { + int u; + uint ysign, tw; + uint cc; + + if (ylen == 0) { + return; + } + + ysign = (uint)(-(ysrc[y + ylen - 1] >> 30) >> 1); + tw = 0; + cc = 0; + for (u = (int)sch; u < xlen; u ++) { + int v; + uint w, wy, wys; + + /* + * Get the next word of y (scaled). + */ + v = u - (int)sch; + wy = v < ylen ? ysrc[y + v] : ysign; + wys = ((wy << (int)scl) & 0x7FFFFFFF) | tw; + tw = wy >> (int)(31 - scl); + + w = xsrc[x+u] - wys - cc; + xsrc[x+u] = w & 0x7FFFFFFF; + cc = w >> 31; + } + } + + /* + * Convert a one-word signed big integer into a signed value. + */ + int zint_one_to_plain(uint[] xsrc, int x) + { + uint w; + + w = xsrc[x+0]; + w |= (w & 0x40000000) << 1; + //return *(int *)&w; + return (int)w; + } + + /* ==================================================================== */ + + /* + * Convert a polynomial to floating-point values. + * + * Each coefficient has length flen words, and starts fstride words after + * the previous. + * + * IEEE-754 binary64 values can represent values in a finite range, + * roughly 2^(-1023) to 2^(+1023); thus, if coefficients are too large, + * they should be "trimmed" by pointing not to the lowest word of each, + * but upper. + */ + void poly_big_to_fp(FalconFPR[] dsrc, int d, uint[] fsrc, int f, int flen, int fstride, + uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + if (flen == 0) { + for (u = 0; u < n; u ++) { + dsrc[d + u] = this.fpre.fpr_zero; + } + return; + } + for (u = 0; u < n; u ++, f += fstride) { + int v; + uint neg, cc, xm; + FalconFPR x, fsc; + + /* + * Get sign of the integer; if it is negative, then we + * will load its absolute value instead, and negate the + * result. + */ + neg = (uint)(-(fsrc[f + flen - 1] >> 30)); + xm = neg >> 1; + cc = neg & 1; + x = this.fpre.fpr_zero; + fsc = this.fpre.fpr_one; + for (v = 0; v < flen; v ++, fsc = this.fpre.fpr_mul(fsc, this.fpre.fpr_ptwo31)) { + uint w; + + w = (fsrc[f + v] ^ xm) + cc; + cc = w >> 31; + w &= 0x7FFFFFFF; + w -= (w << 1) & neg; + //x = this.fpre.fpr_add(x, this.fpre.fpr_mul(this.fpre.fpr_of(*(int*)&w), fsc)); + x = this.fpre.fpr_add(x, this.fpre.fpr_mul(this.fpre.fpr_of((int)w), fsc)); + } + dsrc[d + u] = x; + } + } + + /* + * Convert a polynomial to small integers. Source values are supposed + * to be one-word integers, signed over 31 bits. Returned value is 0 + * if any of the coefficients exceeds the provided limit (in absolute + * value), or 1 on success. + * + * This is not constant-time; this is not a problem here, because on + * any failure, the NTRU-solving process will be deemed to have failed + * and the (f,g) polynomials will be discarded. + */ + int poly_big_to_small(sbyte[] dsrc, int d, uint[] ssrc, int s, int lim, uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + int z; + + z = zint_one_to_plain(ssrc, s + u); + if (z < -lim || z > lim) { + return 0; + } + dsrc[d+u] = (sbyte)z; + } + return 1; + } + + /* + * Subtract k*f from F, where F, f and k are polynomials modulo X^N+1. + * Coefficients of polynomial k are small integers (signed values in the + * -2^31..2^31 range) scaled by 2^sc. Value sc is provided as sch = sc / 31 + * and scl = sc % 31. + * + * This function implements the basic quadratic multiplication algorithm, + * which is efficient in space (no extra buffer needed) but slow at + * high degree. + */ + void poly_sub_scaled(uint[] Fsrc, int F, int Flen, int Fstride, + uint[] fsrc, int f, int flen, int fstride, + int[] ksrc, int k, uint sch, uint scl, uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + int kf; + int v; + int x; + int y; + + kf = -ksrc[k+u]; + x = F + u * Fstride; + y = f; + for (v = 0; v < n; v ++) { + zint_add_scaled_mul_small( + Fsrc, x, Flen, fsrc, y, flen, kf, sch, scl); + if (u + v == n - 1) { + x = F; + kf = -kf; + } else { + x += Fstride; + } + y += fstride; + } + } + } + + /* + * Subtract k*f from F. Coefficients of polynomial k are small integers + * (signed values in the -2^31..2^31 range) scaled by 2^sc. This function + * assumes that the degree is large, and integers relatively small. + * The value sc is provided as sch = sc / 31 and scl = sc % 31. + */ + void poly_sub_scaled_ntt(uint[] Fsrc, int F, int Flen, int Fstride, + uint[] fsrc, int f, int flen, int fstride, + int[] ksrc, int k, uint sch, uint scl, uint logn, + uint[] tmpsrc, int tmp) + { + int gm, igm, fk, t1, x; + int y; + int n, u, tlen; + FalconSmallPrime[] primes; + + n = (int)1 << (int)logn; + tlen = flen + 1; + gm = tmp; + igm = gm + n; + fk = igm + n; + t1 = fk + n * tlen; + + primes = this.PRIMES; + + /* + * Compute k*f in fk[], in RNS notation. + */ + for (u = 0; u < tlen; u ++) { + uint p, p0i, R2, Rx; + int v; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((uint)flen, p, p0i, R2); + modp_mkgm2(tmpsrc, gm, tmpsrc, igm, logn, primes[u].g, p, p0i); + + for (v = 0; v < n; v ++) { + tmpsrc[t1+v] = modp_set(ksrc[k+v], p); + } + modp_NTT2(tmpsrc, t1, tmpsrc, gm, logn, p, p0i); + for (v = 0, y = f, x = fk + u; + v < n; v ++, y += fstride, x += tlen) + { + tmpsrc[x] = zint_mod_small_signed(tmpsrc, y, flen, p, p0i, R2, Rx); + } + modp_NTT2_ext(tmpsrc, fk + u, tlen, tmpsrc, gm, logn, p, p0i); + for (v = 0, x = fk + u; v < n; v ++, x += tlen) { + tmpsrc[x] = modp_montymul( + modp_montymul(tmpsrc[t1+v], tmpsrc[x], p, p0i), R2, p, p0i); + } + modp_iNTT2_ext(tmpsrc, fk + u, tlen, tmpsrc, igm, logn, p, p0i); + } + + /* + * Rebuild k*f. + */ + zint_rebuild_CRT(tmpsrc, fk, tlen, tlen, n, primes, 1, tmpsrc, t1); + + /* + * Subtract k*f, scaled, from F. + */ + for (u = 0, x = F, y = fk; u < n; u ++, x += Fstride, y += tlen) { + zint_sub_scaled(tmpsrc, x, Flen, tmpsrc, y, tlen, sch, scl); + } + } + + /* ==================================================================== */ + + /* + * Get a random 8-byte integer from a SHAKE-based RNG. This function + * ensures consistent interpretation of the SHAKE output so that + * the same values will be obtained over different platforms, in case + * a known seed is used. + */ + ulong get_rng_u64(SHAKE256 rng) + { + /* + * We enforce little-endian representation. + */ + + byte[] tmp = new byte[8]; + + rng.i_shake256_extract(tmp, 0, 8); + return (ulong)tmp[0] + | ((ulong)tmp[1] << 8) + | ((ulong)tmp[2] << 16) + | ((ulong)tmp[3] << 24) + | ((ulong)tmp[4] << 32) + | ((ulong)tmp[5] << 40) + | ((ulong)tmp[6] << 48) + | ((ulong)tmp[7] << 56); + } + + + /* + * Table below incarnates a discrete Gaussian distribution: + * D(x) = exp(-(x^2)/(2*sigma^2)) + * where sigma = 1.17*sqrt(q/(2*N)), q = 12289, and N = 1024. + * Element 0 of the table is P(x = 0). + * For k > 0, element k is P(x >= k+1 | x > 0). + * Probabilities are scaled up by 2^63. + */ + ulong[] gauss_1024_12289 = { + 1283868770400643928u, 6416574995475331444u, 4078260278032692663u, + 2353523259288686585u, 1227179971273316331u, 575931623374121527u, + 242543240509105209u, 91437049221049666u, 30799446349977173u, + 9255276791179340u, 2478152334826140u, 590642893610164u, + 125206034929641u, 23590435911403u, 3948334035941u, + 586753615614u, 77391054539u, 9056793210u, + 940121950u, 86539696u, 7062824u, + 510971u, 32764u, 1862u, + 94u, 4u, 0u + }; + + /* + * Generate a random value with a Gaussian distribution centered on 0. + * The RNG must be ready for extraction (already flipped). + * + * Distribution has standard deviation 1.17*sqrt(q/(2*N)). The + * precomputed table is for N = 1024. Since the sum of two independent + * values of standard deviation sigma has standard deviation + * sigma*sqrt(2), then we can just generate more values and add them + * together for lower dimensions. + */ + int mkgauss(SHAKE256 rng, uint logn) + { + uint u, g; + int val; + + g = 1U << (int)(10 - logn); + val = 0; + for (u = 0; u < g; u ++) { + /* + * Each iteration generates one value with the + * Gaussian distribution for N = 1024. + * + * We use two random 64-bit values. First value + * decides on whether the generated value is 0, and, + * if not, the sign of the value. Second random 64-bit + * word is used to generate the non-zero value. + * + * For constant-time code we have to read the complete + * table. This has negligible cost, compared with the + * remainder of the keygen process (solving the NTRU + * equation). + */ + ulong r; + uint f, v, k, neg; + + /* + * First value: + * - flag 'neg' is randomly selected to be 0 or 1. + * - flag 'f' is set to 1 if the generated value is zero, + * or set to 0 otherwise. + */ + r = get_rng_u64(rng); + neg = (uint)(r >> 63); + r &= ~((ulong)1 << 63); + f = (uint)((r - gauss_1024_12289[0]) >> 63); + + /* + * We produce a new random 63-bit integer r, and go over + * the array, starting at index 1. We store in v the + * index of the first array element which is not greater + * than r, unless the flag f was already 1. + */ + v = 0; + r = get_rng_u64(rng); + r &= ~((ulong)1 << 63); + for (k = 1; k < gauss_1024_12289.Length; k ++) + { + uint t; + + t = (uint)((r - gauss_1024_12289[k]) >> 63) ^ 1; + v |= (uint)(k & -(t & (f ^ 1))); + f |= t; + } + + /* + * We apply the sign ('neg' flag). If the value is zero, + * the sign has no effect. + */ + v = (uint)((v ^ -neg) + neg); + + /* + * Generated value is added to val. + */ + //val += *(int *)&v; + val += (int)v; + } + return val; + } + + /* + * The MAX_BL_SMALL[] and MAX_BL_LARGE[] contain the lengths, in 31-bit + * words, of intermediate values in the computation: + * + * MAX_BL_SMALL[depth]: length for the input f and g at that depth + * MAX_BL_LARGE[depth]: length for the unreduced F and G at that depth + * + * Rules: + * + * - Within an array, values grow. + * + * - The 'SMALL' array must have an entry for maximum depth, corresponding + * to the size of values used in the binary GCD. There is no such value + * for the 'LARGE' array (the binary GCD yields already reduced + * coefficients). + * + * - MAX_BL_LARGE[depth] >= MAX_BL_SMALL[depth + 1]. + * + * - Values must be large enough to handle the common cases, with some + * margins. + * + * - Values must not be "too large" either because we will convert some + * integers into floating-point values by considering the top 10 words, + * i.e. 310 bits; hence, for values of length more than 10 words, we + * should take care to have the length centered on the expected size. + * + * The following average lengths, in bits, have been measured on thousands + * of random keys (fg = max length of the absolute value of coefficients + * of f and g at that depth; FG = idem for the unreduced F and G; for the + * maximum depth, F and G are the output of binary GCD, multiplied by q; + * for each value, the average and standard deviation are provided). + * + * Binary case: + * depth: 10 fg: 6307.52 (24.48) FG: 6319.66 (24.51) + * depth: 9 fg: 3138.35 (12.25) FG: 9403.29 (27.55) + * depth: 8 fg: 1576.87 ( 7.49) FG: 4703.30 (14.77) + * depth: 7 fg: 794.17 ( 4.98) FG: 2361.84 ( 9.31) + * depth: 6 fg: 400.67 ( 3.10) FG: 1188.68 ( 6.04) + * depth: 5 fg: 202.22 ( 1.87) FG: 599.81 ( 3.87) + * depth: 4 fg: 101.62 ( 1.02) FG: 303.49 ( 2.38) + * depth: 3 fg: 50.37 ( 0.53) FG: 153.65 ( 1.39) + * depth: 2 fg: 24.07 ( 0.25) FG: 78.20 ( 0.73) + * depth: 1 fg: 10.99 ( 0.08) FG: 39.82 ( 0.41) + * depth: 0 fg: 4.00 ( 0.00) FG: 19.61 ( 0.49) + * + * Integers are actually represented either in binary notation over + * 31-bit words (signed, using two's complement), or in RNS, modulo + * many small primes. These small primes are close to, but slightly + * lower than, 2^31. Use of RNS loses less than two bits, even for + * the largest values. + * + * IMPORTANT: if these values are modified, then the temporary buffer + * sizes (FALCON_KEYGEN_TEMP_*, in inner.h) must be recomputed + * accordingly. + */ + + int[] MAX_BL_SMALL = { + 1, 1, 2, 2, 4, 7, 14, 27, 53, 106, 209 + }; + + int[] MAX_BL_LARGE = { + 2, 2, 5, 7, 12, 21, 40, 78, 157, 308 + }; + + /* + * Average and standard deviation for the maximum size (in bits) of + * coefficients of (f,g), depending on depth. These values are used + * to compute bounds for Babai's reduction. + */ + int[] BITLENGTH_avg = { // BITLENGTH[i][0] = avg, [i][1] = std + 4, + 11, + 24, + 50, + 102, + 202, + 401, + 794, + 1577, + 3138, + 6308, + }; + int[] BITLENGTH_std = { // BITLENGTH[i][0] = avg, [i][1] = std + 0, + 1, + 1, + 1, + 1, + 2, + 4, + 5, + 8, + 13, + 25 + }; + + /* + * Minimal recursion depth at which we rebuild intermediate values + * when reconstructing f and g. + */ + const int DEPTH_INT_FG = 4; + + /* + * Compute squared norm of a short vector. Returned value is saturated to + * 2^32-1 if it is not lower than 2^31. + */ + uint poly_small_sqnorm(sbyte[] fsrc, int f, uint logn) + { + int n, u; + uint s, ng; + + n = (int)1 << (int)logn; + s = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int z; + + z = fsrc[f+u]; + s += (uint)(z * z); + ng |= s; + } + return (uint)(s | -(ng >> 31)); + } + + /* + * Convert a small vector to floating point. + */ + void poly_small_to_fp(FalconFPR[] xsrc, int x, sbyte[] fsrc, int f, uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + xsrc[x + u] = this.fpre.fpr_of(fsrc[f + u]); + } + } + + /* + * Input: f,g of degree N = 2^logn; 'depth' is used only to get their + * individual length. + * + * Output: f',g' of degree N/2, with the length for 'depth+1'. + * + * Values are in RNS; input and/or output may also be in NTT. + */ + void make_fg_step(uint[] datasrc, int data, uint logn, uint depth, + int in_ntt, int out_ntt) + { + int n, hn, u; + int slen, tlen; + int fd, gd; + int fs, gs; + int gm, igm, t1; + FalconSmallPrime[] primes; + + n = (int)1 << (int)logn; + hn = n >> 1; + slen = MAX_BL_SMALL[depth]; + tlen = MAX_BL_SMALL[depth + 1]; + primes = this.PRIMES; + + /* + * Prepare room for the result. + */ + fd = data; + gd = fd + hn * tlen; + fs = gd + hn * tlen; + gs = fs + n * slen; + gm = gs + n * slen; + igm = gm + n; + t1 = igm + n; + // memmove(fs, data, 2 * n * slen * sizeof *data); + Array.Copy(datasrc, data, datasrc, fs, 2 * n * slen); + + /* + * First slen words: we use the input values directly, and apply + * inverse NTT as we go. + */ + for (u = 0; u < slen; u ++) { + uint p, p0i, R2; + int v; + int x; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + modp_mkgm2(datasrc, gm, datasrc, igm, logn, primes[u].g, p, p0i); + + for (v = 0, x = fs + u; v < n; v ++, x += slen) { + datasrc[t1 + v] = datasrc[x]; + } + if (in_ntt == 0) { + modp_NTT2(datasrc, t1, datasrc, gm, logn, p, p0i); + } + for (v = 0, x = fd + u; v < hn; v ++, x += tlen) { + uint w0, w1; + + w0 = datasrc[t1 + (v << 1) + 0]; + w1 = datasrc[t1 + (v << 1) + 1]; + datasrc[x] = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + if (in_ntt != 0) { + modp_iNTT2_ext(datasrc, fs + u, slen, datasrc, igm, logn, p, p0i); + } + + for (v = 0, x = gs + u; v < n; v ++, x += slen) { + datasrc[t1 + v] = datasrc[x]; + } + if (in_ntt == 0) { + modp_NTT2(datasrc, t1, datasrc, gm, logn, p, p0i); + } + for (v = 0, x = gd + u; v < hn; v ++, x += tlen) { + uint w0, w1; + + w0 = datasrc[t1 + (v << 1) + 0]; + w1 = datasrc[t1 + (v << 1) + 1]; + datasrc[x] = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + if (in_ntt != 0) { + modp_iNTT2_ext(datasrc, gs + u, slen, datasrc, igm, logn, p, p0i); + } + + if (out_ntt == 0) { + modp_iNTT2_ext(datasrc, fd + u, tlen, datasrc, igm, logn - 1, p, p0i); + modp_iNTT2_ext(datasrc, gd + u, tlen, datasrc, igm, logn - 1, p, p0i); + } + } + + /* + * Since the fs and gs words have been de-NTTized, we can use the + * CRT to rebuild the values. + */ + zint_rebuild_CRT(datasrc, fs, slen, slen, n, primes, 1, datasrc, gm); + zint_rebuild_CRT(datasrc, gs, slen, slen, n, primes, 1, datasrc, gm); + + /* + * Remaining words: use modular reductions to extract the values. + */ + for (u = slen; u < tlen; u ++) { + uint p, p0i, R2, Rx; + int v; + int x; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((uint)slen, p, p0i, R2); + modp_mkgm2(datasrc, gm, datasrc, igm, logn, primes[u].g, p, p0i); + for (v = 0, x = fs; v < n; v ++, x += slen) { + datasrc[t1 + v] = zint_mod_small_signed(datasrc, x, slen, p, p0i, R2, Rx); + } + modp_NTT2(datasrc, t1, datasrc, gm, logn, p, p0i); + for (v = 0, x = fd + u; v < hn; v ++, x += tlen) { + uint w0, w1; + + w0 = datasrc[t1 + (v << 1) + 0]; + w1 = datasrc[t1 + (v << 1) + 1]; + datasrc[x] = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + for (v = 0, x = gs; v < n; v ++, x += slen) { + datasrc[t1 + v] = zint_mod_small_signed(datasrc, x, slen, p, p0i, R2, Rx); + } + modp_NTT2(datasrc, t1, datasrc, gm, logn, p, p0i); + for (v = 0, x = gd + u; v < hn; v ++, x += tlen) { + uint w0, w1; + + w0 = datasrc[t1 + (v << 1) + 0]; + w1 = datasrc[t1 + (v << 1) + 1]; + datasrc[x] = modp_montymul( + modp_montymul(w0, w1, p, p0i), R2, p, p0i); + } + + if (out_ntt == 0) { + modp_iNTT2_ext(datasrc, fd + u, tlen, datasrc, igm, logn - 1, p, p0i); + modp_iNTT2_ext(datasrc, gd + u, tlen, datasrc, igm, logn - 1, p, p0i); + } + } + } + + /* + * Compute f and g at a specific depth, in RNS notation. + * + * Returned values are stored in the data[] array, at slen words per integer. + * + * Conditions: + * 0 <= depth <= logn + * + * Space use in data[]: enough room for any two successive values (f', g', + * f and g). + */ + void make_fg(uint[] datasrc, int data, sbyte[] fsrc, int f, sbyte[] gsrc, int g, + uint logn, uint depth, int out_ntt) + { + int n, u; + int ft, gt; + uint p0; + uint d; + FalconSmallPrime[] primes; + + n = (int)1 << (int)logn; + ft = data; + gt = ft + n; + primes = this.PRIMES; + p0 = primes[0].p; + for (u = 0; u < n; u ++) { + datasrc[ft + u] = modp_set(fsrc[f+u], p0); + datasrc[gt + u] = modp_set(gsrc[g+u], p0); + } + + if (depth == 0 && out_ntt != 0) { + int gm, igm; + uint p, p0i; + + p = primes[0].p; + p0i = modp_ninv31(p); + gm = gt + n; + igm = gm + n; + modp_mkgm2(datasrc, gm, datasrc, igm, logn, primes[0].g, p, p0i); + modp_NTT2(datasrc, ft, datasrc, gm, logn, p, p0i); + modp_NTT2(datasrc, gt, datasrc, gm, logn, p, p0i); + return; + } + + for (d = 0; d < depth; d ++) { + make_fg_step(datasrc, data, logn - d, d, + d != 0 ? 1 : 0, ((d + 1) < depth || out_ntt != 0)? 1 : 0); + } + } + + /* + * Solving the NTRU equation, deepest level: compute the resultants of + * f and g with X^N+1, and use binary GCD. The F and G values are + * returned in tmp[]. + * + * Returned value: 1 on success, 0 on error. + */ + int solve_NTRU_deepest(uint logn_top, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, uint[] tmpsrc, int tmp) + { + int len; + int Fp, Gp; + int fp, gp; + int t1; + uint q; + FalconSmallPrime[] primes; + + len = MAX_BL_SMALL[logn_top]; + primes = this.PRIMES; + + Fp = tmp; + Gp = Fp + len; + fp = Gp + len; + gp = fp + len; + t1 = gp + len; + + make_fg(tmpsrc, fp, fsrc, f, gsrc, g, logn_top, logn_top, 0); + + /* + * We use the CRT to rebuild the resultants as big integers. + * There are two such big integers. The resultants are always + * nonnegative. + */ + zint_rebuild_CRT(tmpsrc, fp, len, len, 2, primes, 0, tmpsrc, t1); + + /* + * Apply the binary GCD. The zint_bezout() function works only + * if both inputs are odd. + * + * We can test on the result and return 0 because that would + * imply failure of the NTRU solving equation, and the (f,g) + * values will be abandoned in that case. + */ + if (zint_bezout(tmpsrc, Gp, tmpsrc, Fp, tmpsrc, fp, tmpsrc, gp, len, tmpsrc, t1) == 0) { + return 0; + } + + /* + * Multiply the two values by the target value q. Values must + * fit in the destination arrays. + * We can again test on the returned words: a non-zero output + * of zint_mul_small() means that we exceeded our array + * capacity, and that implies failure and rejection of (f,g). + */ + q = 12289; + if (zint_mul_small(tmpsrc, Fp, len, q) != 0 + || zint_mul_small(tmpsrc, Gp, len, q) != 0) + { + return 0; + } + + return 1; + } + + /* + * Solving the NTRU equation, intermediate level. Upon entry, the F and G + * from the previous level should be in the tmp[] array. + * This function MAY be invoked for the top-level (in which case depth = 0). + * + * Returned value: 1 on success, 0 on error. + */ + int solve_NTRU_intermediate(uint logn_top, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, uint depth, uint[] tmpsrc, int tmp) + { + /* + * In this function, 'logn' is the log2 of the degree for + * this step. If N = 2^logn, then: + * - the F and G values already in fk->tmp (from the deeper + * levels) have degree N/2; + * - this function should return F and G of degree N. + */ + uint logn; + int n, hn, slen, dlen, llen, rlen, FGlen, u; + int Fd, Gd; + int Ft, Gt; + int ft, gt, t1; + FalconFPR[] rt1; FalconFPR[] rt2; + FalconFPR[] rt3; FalconFPR[] rt4; FalconFPR[] rt5; + int scale_fg, minbl_fg, maxbl_fg, maxbl_FG, scale_k; + int x, y; + int[] k; + FalconSmallPrime[] primes; + + logn = logn_top - depth; + n = (int)1 << (int)logn; + hn = n >> 1; + + /* + * slen = size for our input f and g; also size of the reduced + * F and G we return (degree N) + * + * dlen = size of the F and G obtained from the deeper level + * (degree N/2 or N/3) + * + * llen = size for intermediary F and G before reduction (degree N) + * + * We build our non-reduced F and G as two independent halves each, + * of degree N/2 (F = F0 + X*F1, G = G0 + X*G1). + */ + slen = MAX_BL_SMALL[depth]; + dlen = MAX_BL_SMALL[depth + 1]; + llen = MAX_BL_LARGE[depth]; + primes = this.PRIMES; + + /* + * Fd and Gd are the F and G from the deeper level. + */ + Fd = tmp; + Gd = Fd + dlen * hn; + + /* + * Compute the input f and g for this level. Note that we get f + * and g in RNS + NTT representation. + */ + ft = Gd + dlen * hn; + make_fg(tmpsrc, ft, fsrc, f, gsrc, g, logn_top, depth, 1); + + /* + * Move the newly computed f and g to make room for our candidate + * F and G (unreduced). + */ + Ft = tmp; + Gt = Ft + n * llen; + t1 = Gt + n * llen; + // memmove(t1, ft, 2 * n * slen * sizeof *ft); + Array.Copy(tmpsrc, ft, tmpsrc, t1, 2 * n * slen); + ft = t1; + gt = ft + slen * n; + t1 = gt + slen * n; + + /* + * Move Fd and Gd _after_ f and g. + */ + // memmove(t1, Fd, 2 * hn * dlen * sizeof *Fd); + Array.Copy(tmpsrc, Fd, tmpsrc, t1, 2 * hn * dlen); + Fd = t1; + Gd = Fd + hn * dlen; + + /* + * We reduce Fd and Gd modulo all the small primes we will need, + * and store the values in Ft and Gt (only n/2 values in each). + */ + for (u = 0; u < llen; u ++) { + uint p, p0i, R2, Rx; + int v; + int xs, ys, xd, yd; + + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((uint)dlen, p, p0i, R2); + for (v = 0, xs = Fd, ys = Gd, xd = Ft + u, yd = Gt + u; + v < hn; + v ++, xs += dlen, ys += dlen, xd += llen, yd += llen) + { + tmpsrc[xd] = zint_mod_small_signed(tmpsrc, xs, dlen, p, p0i, R2, Rx); + tmpsrc[yd] = zint_mod_small_signed(tmpsrc, ys, dlen, p, p0i, R2, Rx); + } + } + + /* + * We do not need Fd and Gd after that point. + */ + + /* + * Compute our F and G modulo sufficiently many small primes. + */ + for (u = 0; u < llen; u ++) { + uint p, p0i, R2; + int gm, igm; + int fx, gx; + int Fp, Gp; + int v; + + /* + * All computations are done modulo p. + */ + p = primes[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + /* + * If we processed slen words, then f and g have been + * de-NTTized, and are in RNS; we can rebuild them. + */ + if (u == slen) { + zint_rebuild_CRT(tmpsrc, ft, slen, slen, n, primes, 1, tmpsrc, t1); + zint_rebuild_CRT(tmpsrc, gt, slen, slen, n, primes, 1, tmpsrc, t1); + } + + gm = t1; + igm = gm + n; + fx = igm + n; + gx = fx + n; + + modp_mkgm2(tmpsrc, gm, tmpsrc, igm, logn, primes[u].g, p, p0i); + + if (u < slen) { + for (v = 0, x = ft + u, y = gt + u; + v < n; v ++, x += slen, y += slen) + { + tmpsrc[fx+v] = tmpsrc[x]; + tmpsrc[gx+v] = tmpsrc[y]; + } + modp_iNTT2_ext(tmpsrc, ft + u, slen, tmpsrc, igm, logn, p, p0i); + modp_iNTT2_ext(tmpsrc, gt + u, slen, tmpsrc, igm, logn, p, p0i); + } else { + uint Rx; + + Rx = modp_Rx((uint)slen, p, p0i, R2); + for (v = 0, x = ft, y = gt; + v < n; v ++, x += slen, y += slen) + { + tmpsrc[fx+v] = zint_mod_small_signed(tmpsrc, x, slen, + p, p0i, R2, Rx); + tmpsrc[gx+v] = zint_mod_small_signed(tmpsrc, y, slen, + p, p0i, R2, Rx); + } + modp_NTT2(tmpsrc, fx, tmpsrc, gm, logn, p, p0i); + modp_NTT2(tmpsrc, gx, tmpsrc, gm, logn, p, p0i); + } + + /* + * Get F' and G' modulo p and in NTT representation + * (they have degree n/2). These values were computed in + * a previous step, and stored in Ft and Gt. + */ + Fp = gx + n; + Gp = Fp + hn; + for (v = 0, x = Ft + u, y = Gt + u; + v < hn; v ++, x += llen, y += llen) + { + tmpsrc[Fp+v] = tmpsrc[x]; + tmpsrc[Gp+v] = tmpsrc[y]; + } + modp_NTT2(tmpsrc, Fp, tmpsrc, gm, logn - 1, p, p0i); + modp_NTT2(tmpsrc, Gp, tmpsrc, gm, logn - 1, p, p0i); + + /* + * Compute our F and G modulo p. + * + * General case: + * + * we divide degree by d = 2 or 3 + * f'(x^d) = N(f)(x^d) = f * adj(f) + * g'(x^d) = N(g)(x^d) = g * adj(g) + * f'*G' - g'*F' = q + * F = F'(x^d) * adj(g) + * G = G'(x^d) * adj(f) + * + * We compute things in the NTT. We group roots of phi + * such that all roots x in a group share the same x^d. + * If the roots in a group are x_1, x_2... x_d, then: + * + * N(f)(x_1^d) = f(x_1)*f(x_2)*...*f(x_d) + * + * Thus, we have: + * + * G(x_1) = f(x_2)*f(x_3)*...*f(x_d)*G'(x_1^d) + * G(x_2) = f(x_1)*f(x_3)*...*f(x_d)*G'(x_1^d) + * ... + * G(x_d) = f(x_1)*f(x_2)*...*f(x_{d-1})*G'(x_1^d) + * + * In all cases, we can thus compute F and G in NTT + * representation by a few simple multiplications. + * Moreover, in our chosen NTT representation, roots + * from the same group are consecutive in RAM. + */ + for (v = 0, x = Ft + u, y = Gt + u; v < hn; + v ++, x += (llen << 1), y += (llen << 1)) + { + uint ftA, ftB, gtA, gtB; + uint mFp, mGp; + + ftA = tmpsrc[fx + (v << 1) + 0]; + ftB = tmpsrc[fx + (v << 1) + 1]; + gtA = tmpsrc[gx + (v << 1) + 0]; + gtB = tmpsrc[gx + (v << 1) + 1]; + mFp = modp_montymul(tmpsrc[Fp+v], R2, p, p0i); + mGp = modp_montymul(tmpsrc[Gp+v], R2, p, p0i); + tmpsrc[x+0] = modp_montymul(gtB, mFp, p, p0i); + tmpsrc[x+llen] = modp_montymul(gtA, mFp, p, p0i); + tmpsrc[y+0] = modp_montymul(ftB, mGp, p, p0i); + tmpsrc[y+llen] = modp_montymul(ftA, mGp, p, p0i); + } + modp_iNTT2_ext(tmpsrc, Ft + u, llen, tmpsrc, igm, logn, p, p0i); + modp_iNTT2_ext(tmpsrc, Gt + u, llen, tmpsrc, igm, logn, p, p0i); + } + + /* + * Rebuild F and G with the CRT. + */ + zint_rebuild_CRT(tmpsrc, Ft, llen, llen, n, primes, 1, tmpsrc, t1); + zint_rebuild_CRT(tmpsrc, Gt, llen, llen, n, primes, 1, tmpsrc, t1); + + /* + * At that point, Ft, Gt, ft and gt are consecutive in RAM (in that + * order). + */ + + /* + * Apply Babai reduction to bring back F and G to size slen. + * + * We use the FFT to compute successive approximations of the + * reduction coefficient. We first isolate the top bits of + * the coefficients of f and g, and convert them to floating + * point; with the FFT, we compute adj(f), adj(g), and + * 1/(f*adj(f)+g*adj(g)). + * + * Then, we repeatedly apply the following: + * + * - Get the top bits of the coefficients of F and G into + * floating point, and use the FFT to compute: + * (F*adj(f)+G*adj(g))/(f*adj(f)+g*adj(g)) + * + * - Convert back that value into normal representation, and + * round it to the nearest integers, yielding a polynomial k. + * Proper scaling is applied to f, g, F and G so that the + * coefficients fit on 32 bits (signed). + * + * - Subtract k*f from F and k*g from G. + * + * Under normal conditions, this process reduces the size of F + * and G by some bits at each iteration. For constant-time + * operation, we do not want to measure the actual length of + * F and G; instead, we do the following: + * + * - f and g are converted to floating-point, with some scaling + * if necessary to keep values in the representable range. + * + * - For each iteration, we _assume_ a maximum size for F and G, + * and use the values at that size. If we overreach, then + * we get zeros, which is harmless: the resulting coefficients + * of k will be 0 and the value won't be reduced. + * + * - We conservatively assume that F and G will be reduced by + * at least 25 bits at each iteration. + * + * Even when reaching the bottom of the reduction, reduction + * coefficient will remain low. If it goes out-of-range, then + * something wrong occurred and the whole NTRU solving fails. + */ + + /* + * Memory layout: + * - We need to compute and keep adj(f), adj(g), and + * 1/(f*adj(f)+g*adj(g)) (sizes N, N and N/2 fp numbers, + * respectively). + * - At each iteration we need two extra fp buffer (N fp values), + * and produce a k (N 32-bit words). k will be shared with one + * of the fp buffers. + * - To compute k*f and k*g efficiently (with the NTT), we need + * some extra room; we reuse the space of the temporary buffers. + * + * Arrays of 'fpr' are obtained from the temporary array itself. + * We ensure that the base is at a properly aligned offset (the + * source array tmp[] is supposed to be already aligned). + */ + + // rt3 = align_fpr(tmp, t1); + rt1 = new FalconFPR[n]; + rt2 = new FalconFPR[n]; + rt3 = new FalconFPR[n]; + rt4 = new FalconFPR[n]; + rt5 = new FalconFPR[n >> 1]; + k = new int[n]; + /* + * Get f and g into rt3 and rt4 as floating-point approximations. + * + * We need to "scale down" the floating-point representation of + * coefficients when they are too big. We want to keep the value + * below 2^310 or so. Thus, when values are larger than 10 words, + * we consider only the top 10 words. Array lengths have been + * computed so that average maximum length will fall in the + * middle or the upper half of these top 10 words. + */ + rlen = (slen > 10) ? 10 : slen; + poly_big_to_fp(rt3, 0, tmpsrc, ft + slen - rlen, rlen, slen, logn); + poly_big_to_fp(rt4, 0, tmpsrc, gt + slen - rlen, rlen, slen, logn); + + /* + * Values in rt3 and rt4 are downscaled by 2^(scale_fg). + */ + scale_fg = 31 * (int)(slen - rlen); + + /* + * Estimated boundaries for the maximum size (in bits) of the + * coefficients of (f,g). We use the measured average, and + * allow for a deviation of at most six times the standard + * deviation. + */ + minbl_fg = BITLENGTH_avg[depth] - 6 * BITLENGTH_std[depth]; + maxbl_fg = BITLENGTH_avg[depth] + 6 * BITLENGTH_std[depth]; + + /* + * Compute 1/(f*adj(f)+g*adj(g)) in rt5. We also keep adj(f) + * and adj(g) in rt3 and rt4, respectively. + */ + this.ffte.FFT(rt3, 0, logn); + this.ffte.FFT(rt4, 0, logn); + this.ffte.poly_invnorm2_fft(rt5, 0, rt3, 0, rt4, 0, logn); + this.ffte.poly_adj_fft(rt3, 0, logn); + this.ffte.poly_adj_fft(rt4, 0, logn); + + /* + * Reduce F and G repeatedly. + * + * The expected maximum bit length of coefficients of F and G + * is kept in maxbl_FG, with the corresponding word length in + * FGlen. + */ + FGlen = llen; + maxbl_FG = 31 * (int)llen; + + /* + * Each reduction operation computes the reduction polynomial + * "k". We need that polynomial to have coefficients that fit + * on 32-bit signed integers, with some scaling; thus, we use + * a descending sequence of scaling values, down to zero. + * + * The size of the coefficients of k is (roughly) the difference + * between the size of the coefficients of (F,G) and the size + * of the coefficients of (f,g). Thus, the maximum size of the + * coefficients of k is, at the start, maxbl_FG - minbl_fg; + * this is our starting scale value for k. + * + * We need to estimate the size of (F,G) during the execution of + * the algorithm; we are allowed some overestimation but not too + * much (poly_big_to_fp() uses a 310-bit window). Generally + * speaking, after applying a reduction with k scaled to + * scale_k, the size of (F,G) will be size(f,g) + scale_k + dd, + * where 'dd' is a few bits to account for the fact that the + * reduction is never perfect (intuitively, dd is on the order + * of sqrt(N), so at most 5 bits; we here allow for 10 extra + * bits). + * + * The size of (f,g) is not known exactly, but maxbl_fg is an + * upper bound. + */ + scale_k = maxbl_FG - minbl_fg; + + for (;;) { + int scale_FG, dc, new_maxbl_FG; + uint scl, sch; + FalconFPR pdc, pt; + + /* + * Convert current F and G into floating-point. We apply + * scaling if the current length is more than 10 words. + */ + rlen = (FGlen > 10) ? 10 : FGlen; + scale_FG = 31 * (int)(FGlen - rlen); + poly_big_to_fp(rt1, 0, tmpsrc, Ft + FGlen - rlen, rlen, llen, logn); + poly_big_to_fp(rt2, 0, tmpsrc, Gt + FGlen - rlen, rlen, llen, logn); + + /* + * Compute (F*adj(f)+G*adj(g))/(f*adj(f)+g*adj(g)) in rt2. + */ + this.ffte.FFT(rt1, 0, logn); + this.ffte.FFT(rt2, 0, logn); + this.ffte.poly_mul_fft(rt1, 0, rt3, 0, logn); + this.ffte.poly_mul_fft(rt2, 0, rt4, 0, logn); + this.ffte.poly_add(rt2, 0, rt1, 0, logn); + this.ffte.poly_mul_autoadj_fft(rt2, 0, rt5, 0, logn); + this.ffte.iFFT(rt2, 0, logn); + + /* + * (f,g) are scaled by 'scale_fg', meaning that the + * numbers in rt3/rt4 should be multiplied by 2^(scale_fg) + * to have their true mathematical value. + * + * (F,G) are similarly scaled by 'scale_FG'. Therefore, + * the value we computed in rt2 is scaled by + * 'scale_FG-scale_fg'. + * + * We want that value to be scaled by 'scale_k', hence we + * apply a corrective scaling. After scaling, the values + * should fit in -2^31-1..+2^31-1. + */ + dc = scale_k - scale_FG + scale_fg; + + /* + * We will need to multiply values by 2^(-dc). The value + * 'dc' is not secret, so we can compute 2^(-dc) with a + * non-constant-time process. + * (We could use ldexp(), but we prefer to avoid any + * dependency on libm. When using FP emulation, we could + * use our this.fpre.fpr_ldexp(), which is constant-time.) + */ + if (dc < 0) { + dc = -dc; + pt = this.fpre.fpr_two; + } else { + pt = this.fpre.fpr_onehalf; + } + pdc = this.fpre.fpr_one; + while (dc != 0) { + if ((dc & 1) != 0) { + pdc = this.fpre.fpr_mul(pdc, pt); + } + dc >>= 1; + pt = this.fpre.fpr_sqr(pt); + } + + for (u = 0; u < n; u ++) { + FalconFPR xv; + + xv = this.fpre.fpr_mul(rt2[u], pdc); + + /* + * Sometimes the values can be out-of-bounds if + * the algorithm fails; we must not call + * this.fpre.fpr_rint() (and cast to int) if the value + * is not in-bounds. Note that the test does not + * break constant-time discipline, since any + * failure here implies that we discard the current + * secret key (f,g). + */ + if (!this.fpre.fpr_lt(this.fpre.fpr_mtwo31m1, xv) + || !this.fpre.fpr_lt(xv, this.fpre.fpr_ptwo31m1)) + { + return 0; + } + k[u] = (int)this.fpre.fpr_rint(xv); + } + + /* + * Values in k[] are integers. They really are scaled + * down by maxbl_FG - minbl_fg bits. + * + * If we are at low depth, then we use the NTT to + * compute k*f and k*g. + */ + sch = (uint)(scale_k / 31); + scl = (uint)(scale_k % 31); + if (depth <= DEPTH_INT_FG) { + poly_sub_scaled_ntt(tmpsrc, Ft, FGlen, llen, tmpsrc, ft, slen, slen, + k, 0, sch, scl, logn, tmpsrc, t1); + poly_sub_scaled_ntt(tmpsrc, Gt, FGlen, llen, tmpsrc, gt, slen, slen, + k, 0, sch, scl, logn, tmpsrc, t1); + } else { + poly_sub_scaled(tmpsrc, Ft, FGlen, llen, tmpsrc, ft, slen, slen, + k, 0, sch, scl, logn); + poly_sub_scaled(tmpsrc, Gt, FGlen, llen, tmpsrc, gt, slen, slen, + k, 0, sch, scl, logn); + } + + /* + * We compute the new maximum size of (F,G), assuming that + * (f,g) has _maximal_ length (i.e. that reduction is + * "late" instead of "early". We also adjust FGlen + * accordingly. + */ + new_maxbl_FG = scale_k + maxbl_fg + 10; + if (new_maxbl_FG < maxbl_FG) { + maxbl_FG = new_maxbl_FG; + if ((int)FGlen * 31 >= maxbl_FG + 31) { + FGlen --; + } + } + + /* + * We suppose that scaling down achieves a reduction by + * at least 25 bits per iteration. We stop when we have + * done the loop with an unscaled k. + */ + if (scale_k <= 0) { + break; + } + scale_k -= 25; + if (scale_k < 0) { + scale_k = 0; + } + } + + /* + * If (F,G) length was lowered below 'slen', then we must take + * care to re-extend the sign. + */ + if (FGlen < slen) { + for (u = 0; u < n; u ++, Ft += llen, Gt += llen) { + int v; + uint sw; + + sw = ((uint)-(tmpsrc[Ft+FGlen - 1] >> 30) >> 1); + for (v = FGlen; v < slen; v ++) { + tmpsrc[Ft+v] = sw; + } + sw = ((uint)-(tmpsrc[Gt+FGlen - 1] >> 30) >> 1); + for (v = FGlen; v < slen; v ++) { + tmpsrc[Gt+v] = sw; + } + } + } + + /* + * Compress encoding of all values to 'slen' words (this is the + * expected output format). + */ + for (u = 0, x = tmp, y = tmp; + u < (n << 1); u ++, x += slen, y += llen) + { + // memmove(x, y, slen * sizeof *y); + Array.Copy(tmpsrc, y, tmpsrc, x, slen); + } + return 1; + } + + /* + * Solving the NTRU equation, binary case, depth = 1. Upon entry, the + * F and G from the previous level should be in the tmp[] array. + * + * Returned value: 1 on success, 0 on error. + */ + int solve_NTRU_binary_depth1(uint logn_top, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, uint[] tmpsrc, int tmp) + { + /* + * The first half of this function is a copy of the corresponding + * part in solve_NTRU_intermediate(), for the reconstruction of + * the unreduced F and G. The second half (Babai reduction) is + * done differently, because the unreduced F and G fit in 53 bits + * of precision, allowing a much simpler process with lower RAM + * usage. + */ + uint depth, logn; + int n_top, n, hn, slen, dlen, llen, u; + int Fd, Gd, Ft, Gt; + int ft, gt, t1; + FalconFPR[] rt1; FalconFPR[] rt2; FalconFPR[] rt3; + FalconFPR[] rt4; FalconFPR[] rt5; FalconFPR[] rt6; + int x, y; + + depth = 1; + n_top = (int)1 << (int)logn_top; + logn = logn_top - depth; + n = (int)1 << (int)logn; + hn = n >> 1; + + /* + * Equations are: + * + * f' = f0^2 - X^2*f1^2 + * g' = g0^2 - X^2*g1^2 + * F' and G' are a solution to f'G' - g'F' = q (from deeper levels) + * F = F'*(g0 - X*g1) + * G = G'*(f0 - X*f1) + * + * f0, f1, g0, g1, f', g', F' and G' are all "compressed" to + * degree N/2 (their odd-indexed coefficients are all zero). + */ + + /* + * slen = size for our input f and g; also size of the reduced + * F and G we return (degree N) + * + * dlen = size of the F and G obtained from the deeper level + * (degree N/2) + * + * llen = size for intermediary F and G before reduction (degree N) + * + * We build our non-reduced F and G as two independent halves each, + * of degree N/2 (F = F0 + X*F1, G = G0 + X*G1). + */ + slen = MAX_BL_SMALL[depth]; + dlen = MAX_BL_SMALL[depth + 1]; + llen = MAX_BL_LARGE[depth]; + + /* + * Fd and Gd are the F and G from the deeper level. Ft and Gt + * are the destination arrays for the unreduced F and G. + */ + Fd = tmp; + Gd = Fd + dlen * hn; + Ft = Gd + dlen * hn; + Gt = Ft + llen * n; + + /* + * We reduce Fd and Gd modulo all the small primes we will need, + * and store the values in Ft and Gt. + */ + for (u = 0; u < llen; u ++) { + uint p, p0i, R2, Rx; + int v; + int xs, ys; + int xd, yd; + + p = this.PRIMES[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + Rx = modp_Rx((uint)dlen, p, p0i, R2); + for (v = 0, xs = Fd, ys = Gd, xd = Ft + u, yd = Gt + u; + v < hn; + v ++, xs += dlen, ys += dlen, xd += llen, yd += llen) + { + tmpsrc[xd] = zint_mod_small_signed(tmpsrc, xs, dlen, p, p0i, R2, Rx); + tmpsrc[yd] = zint_mod_small_signed(tmpsrc, ys, dlen, p, p0i, R2, Rx); + } + } + + /* + * Now Fd and Gd are not needed anymore; we can squeeze them out. + */ + // memmove(tmp, Ft, llen * n * sizeof(uint)); + Array.Copy(tmpsrc, Ft, tmpsrc, tmp, llen * n); + Ft = tmp; + // memmove(Ft + llen * n, Gt, llen * n * sizeof(uint)); + Array.Copy(tmpsrc, Gt, tmpsrc, Ft + llen * n, llen * n); + Gt = Ft + llen * n; + ft = Gt + llen * n; + gt = ft + slen * n; + + t1 = gt + slen * n; + + /* + * Compute our F and G modulo sufficiently many small primes. + */ + for (u = 0; u < llen; u ++) { + uint p, p0i, R2; + int gm, igm; + int fx, gx; + int Fp, Gp; + uint e; + int v; + + /* + * All computations are done modulo p. + */ + p = this.PRIMES[u].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + /* + * We recompute things from the source f and g, of full + * degree. However, we will need only the n first elements + * of the inverse NTT table (igm); the call to modp_mkgm() + * below will fill n_top elements in igm[] (thus overflowing + * into fx[]) but later code will overwrite these extra + * elements. + */ + gm = t1; + igm = gm + n_top; + fx = igm + n; + gx = fx + n_top; + modp_mkgm2(tmpsrc, gm, tmpsrc, igm, logn_top, this.PRIMES[u].g, p, p0i); + + /* + * Set ft and gt to f and g modulo p, respectively. + */ + for (v = 0; v < n_top; v ++) { + tmpsrc[fx+v] = modp_set(fsrc[f+v], p); + tmpsrc[gx+v] = modp_set(gsrc[g+v], p); + } + + /* + * Convert to NTT and compute our f and g. + */ + modp_NTT2(tmpsrc, fx, tmpsrc, gm, logn_top, p, p0i); + modp_NTT2(tmpsrc, gx, tmpsrc, gm, logn_top, p, p0i); + for (e = logn_top; e > logn; e --) { + modp_poly_rec_res(tmpsrc, fx, e, p, p0i, R2); + modp_poly_rec_res(tmpsrc, gx, e, p, p0i, R2); + } + + /* + * From that point onward, we only need tables for + * degree n, so we can save some space. + */ + if (depth > 0) { /* always true */ + // memmove(gm + n, igm, n * sizeof *igm); + Array.Copy(tmpsrc, igm, tmpsrc, gm + n, n); + igm = gm + n; + // memmove(igm + n, fx, n * sizeof *ft); + Array.Copy(tmpsrc, fx, tmpsrc, igm + n, n); + fx = igm + n; + // memmove(fx + n, gx, n * sizeof *gt); + Array.Copy(tmpsrc, gx, tmpsrc, fx + n, n); + gx = fx + n; + } + + /* + * Get F' and G' modulo p and in NTT representation + * (they have degree n/2). These values were computed + * in a previous step, and stored in Ft and Gt. + */ + Fp = gx + n; + Gp = Fp + hn; + for (v = 0, x = Ft + u, y = Gt + u; + v < hn; v ++, x += llen, y += llen) + { + tmpsrc[Fp+v] = tmpsrc[x]; + tmpsrc[Gp+v] = tmpsrc[y]; + } + modp_NTT2(tmpsrc, Fp, tmpsrc, gm, logn - 1, p, p0i); + modp_NTT2(tmpsrc, Gp, tmpsrc, gm, logn - 1, p, p0i); + + /* + * Compute our F and G modulo p. + * + * Equations are: + * + * f'(x^2) = N(f)(x^2) = f * adj(f) + * g'(x^2) = N(g)(x^2) = g * adj(g) + * + * f'*G' - g'*F' = q + * + * F = F'(x^2) * adj(g) + * G = G'(x^2) * adj(f) + * + * The NTT representation of f is f(w) for all w which + * are roots of phi. In the binary case, as well as in + * the ternary case for all depth except the deepest, + * these roots can be grouped in pairs (w,-w), and we + * then have: + * + * f(w) = adj(f)(-w) + * f(-w) = adj(f)(w) + * + * and w^2 is then a root for phi at the half-degree. + * + * At the deepest level in the ternary case, this still + * holds, in the following sense: the roots of x^2-x+1 + * are (w,-w^2) (for w^3 = -1, and w != -1), and we + * have: + * + * f(w) = adj(f)(-w^2) + * f(-w^2) = adj(f)(w) + * + * In all case, we can thus compute F and G in NTT + * representation by a few simple multiplications. + * Moreover, the two roots for each pair are consecutive + * in our bit-reversal encoding. + */ + for (v = 0, x = Ft + u, y = Gt + u; + v < hn; v ++, x += (llen << 1), y += (llen << 1)) + { + uint ftA, ftB, gtA, gtB; + uint mFp, mGp; + + ftA = tmpsrc[fx + (v << 1) + 0]; + ftB = tmpsrc[fx + (v << 1) + 1]; + gtA = tmpsrc[gx + (v << 1) + 0]; + gtB = tmpsrc[gx + (v << 1) + 1]; + mFp = modp_montymul(tmpsrc[Fp+v], R2, p, p0i); + mGp = modp_montymul(tmpsrc[Gp+v], R2, p, p0i); + tmpsrc[x+0] = modp_montymul(gtB, mFp, p, p0i); + tmpsrc[x+llen] = modp_montymul(gtA, mFp, p, p0i); + tmpsrc[y+0] = modp_montymul(ftB, mGp, p, p0i); + tmpsrc[y+llen] = modp_montymul(ftA, mGp, p, p0i); + } + modp_iNTT2_ext(tmpsrc, Ft + u, llen, tmpsrc, igm, logn, p, p0i); + modp_iNTT2_ext(tmpsrc, Gt + u, llen, tmpsrc, igm, logn, p, p0i); + + /* + * Also save ft and gt (only up to size slen). + */ + if (u < slen) { + modp_iNTT2(tmpsrc, fx, tmpsrc, igm, logn, p, p0i); + modp_iNTT2(tmpsrc, gx, tmpsrc, igm, logn, p, p0i); + for (v = 0, x = ft + u, y = gt + u; + v < n; v ++, x += slen, y += slen) + { + tmpsrc[x] = tmpsrc[fx+v]; + tmpsrc[y] = tmpsrc[gx+v]; + } + } + } + + /* + * Rebuild f, g, F and G with the CRT. Note that the elements of F + * and G are consecutive, and thus can be rebuilt in a single + * loop; similarly, the elements of f and g are consecutive. + */ + zint_rebuild_CRT(tmpsrc, Ft, llen, llen, n << 1, this.PRIMES, 1, tmpsrc, t1); + zint_rebuild_CRT(tmpsrc, ft, slen, slen, n << 1, this.PRIMES, 1, tmpsrc, t1); + + /* + * Here starts the Babai reduction, specialized for depth = 1. + * + * Candidates F and G (from Ft and Gt), and base f and g (ft and gt), + * are converted to floating point. There is no scaling, and a + * single pass is sufficient. + */ + + /* + * Convert F and G into floating point (rt1 and rt2). + */ + rt1 = new FalconFPR[n]; + rt2 = new FalconFPR[n]; + poly_big_to_fp(rt1, 0, tmpsrc, Ft, llen, llen, logn); + poly_big_to_fp(rt2, 0, tmpsrc, Gt, llen, llen, logn); + + /* + * Integer representation of F and G is no longer needed, we + * can remove it. + */ + // memmove(tmp, ft, 2 * slen * n * sizeof *ft); + Array.Copy(tmpsrc, ft, tmpsrc, tmp, 2 * slen * n); + ft = tmp; + gt = ft + slen * n; + rt3 = new FalconFPR[n]; + rt4 = new FalconFPR[n]; + + /* + * Convert f and g into floating point (rt3 and rt4). + */ + poly_big_to_fp(rt3, 0, tmpsrc, ft, slen, slen, logn); + poly_big_to_fp(rt4, 0, tmpsrc, gt, slen, slen, logn); + + /* + * We now have: + * rt1 = F + * rt2 = G + * rt3 = f + * rt4 = g + * in that order in RAM. We convert all of them to FFT. + */ + this.ffte.FFT(rt1, 0, logn); + this.ffte.FFT(rt2, 0, logn); + this.ffte.FFT(rt3, 0, logn); + this.ffte.FFT(rt4, 0, logn); + + /* + * Compute: + * rt5 = F*adj(f) + G*adj(g) + * rt6 = 1 / (f*adj(f) + g*adj(g)) + * (Note that rt6 is half-length.) + */ + rt5 = new FalconFPR[n]; + rt6 = new FalconFPR[n]; + this.ffte.poly_add_muladj_fft(rt5, 0, rt1, 0, rt2, 0, rt3, 0, rt4, 0, logn); + this.ffte.poly_invnorm2_fft(rt6, 0, rt3, 0, rt4, 0, logn); + + /* + * Compute: + * rt5 = (F*adj(f)+G*adj(g)) / (f*adj(f)+g*adj(g)) + */ + this.ffte.poly_mul_autoadj_fft(rt5, 0, rt6, 0, logn); + + /* + * Compute k as the rounded version of rt5. Check that none of + * the values is larger than 2^63-1 (in absolute value) + * because that would make the this.fpre.fpr_rint() do something undefined; + * note that any out-of-bounds value here implies a failure and + * (f,g) will be discarded, so we can make a simple test. + */ + this.ffte.iFFT(rt5, 0, logn); + for (u = 0; u < n; u ++) { + FalconFPR z; + + z = rt5[u]; + if (!this.fpre.fpr_lt(z, this.fpre.fpr_ptwo63m1) || !this.fpre.fpr_lt(this.fpre.fpr_mtwo63m1, z)) { + return 0; + } + rt5[u] = this.fpre.fpr_of(this.fpre.fpr_rint(z)); + } + this.ffte.FFT(rt5, 0, logn); + + /* + * Subtract k*f from F, and k*g from G. + */ + this.ffte.poly_mul_fft(rt3, 0, rt5, 0, logn); + this.ffte.poly_mul_fft(rt4, 0, rt5, 0, logn); + this.ffte.poly_sub(rt1, 0, rt3, 0, logn); + this.ffte.poly_sub(rt2, 0, rt4, 0, logn); + this.ffte.iFFT(rt1, 0, logn); + this.ffte.iFFT(rt2, 0, logn); + + /* + * Convert back F and G to integers, and return. + */ + Ft = tmp; + Gt = Ft + n; + for (u = 0; u < n; u ++) { + tmpsrc[Ft+u] = (uint)this.fpre.fpr_rint(rt1[u]); + tmpsrc[Gt+u] = (uint)this.fpre.fpr_rint(rt2[u]); + } + + return 1; + } + + /* + * Solving the NTRU equation, top level. Upon entry, the F and G + * from the previous level should be in the tmp[] array. + * + * Returned value: 1 on success, 0 on error. + */ + int solve_NTRU_binary_depth0(uint logn, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, uint[] tmpsrc, int tmp) + { + int n, hn, u; + uint p, p0i, R2; + int Fp, Gp; + int t1, t2, t3, t4, t5; + int gm, igm, ft, gt; + int rt2, rt3; + + n = (int)1 << (int)logn; + hn = n >> 1; + + /* + * Equations are: + * + * f' = f0^2 - X^2*f1^2 + * g' = g0^2 - X^2*g1^2 + * F' and G' are a solution to f'G' - g'F' = q (from deeper levels) + * F = F'*(g0 - X*g1) + * G = G'*(f0 - X*f1) + * + * f0, f1, g0, g1, f', g', F' and G' are all "compressed" to + * degree N/2 (their odd-indexed coefficients are all zero). + * + * Everything should fit in 31-bit integers, hence we can just use + * the first small prime p = 2147473409. + */ + p = this.PRIMES[0].p; + p0i = modp_ninv31(p); + R2 = modp_R2(p, p0i); + + Fp = tmp; + Gp = Fp + hn; + ft = Gp + hn; + gt = ft + n; + gm = gt + n; + igm = gm + n; + + modp_mkgm2(tmpsrc, gm, tmpsrc, igm, logn, PRIMES[0].g, p, p0i); + + /* + * Convert F' anf G' in NTT representation. + */ + for (u = 0; u < hn; u ++) { + tmpsrc[Fp+u] = modp_set(zint_one_to_plain(tmpsrc, Fp + u), p); + tmpsrc[Gp+u] = modp_set(zint_one_to_plain(tmpsrc, Gp + u), p); + } + modp_NTT2(tmpsrc, Fp, tmpsrc, gm, logn - 1, p, p0i); + modp_NTT2(tmpsrc, Gp, tmpsrc, gm, logn - 1, p, p0i); + + /* + * Load f and g and convert them to NTT representation. + */ + for (u = 0; u < n; u ++) { + tmpsrc[ft+u] = modp_set(fsrc[f+u], p); + tmpsrc[gt+u] = modp_set(gsrc[g+u], p); + } + modp_NTT2(tmpsrc, ft, tmpsrc, gm, logn, p, p0i); + modp_NTT2(tmpsrc, gt, tmpsrc, gm, logn, p, p0i); + + /* + * Build the unreduced F,G in ft and gt. + */ + for (u = 0; u < n; u += 2) { + uint ftA, ftB, gtA, gtB; + uint mFp, mGp; + + ftA = tmpsrc[ft + u + 0]; + ftB = tmpsrc[ft + u + 1]; + gtA = tmpsrc[gt + u + 0]; + gtB = tmpsrc[gt + u + 1]; + mFp = modp_montymul(tmpsrc[Fp + (u >> 1)], R2, p, p0i); + mGp = modp_montymul(tmpsrc[Gp + (u >> 1)], R2, p, p0i); + tmpsrc[ft + u + 0] = modp_montymul(gtB, mFp, p, p0i); + tmpsrc[ft + u + 1] = modp_montymul(gtA, mFp, p, p0i); + tmpsrc[gt + u + 0] = modp_montymul(ftB, mGp, p, p0i); + tmpsrc[gt + u + 1] = modp_montymul(ftA, mGp, p, p0i); + } + modp_iNTT2(tmpsrc, ft, tmpsrc, igm, logn, p, p0i); + modp_iNTT2(tmpsrc, gt, tmpsrc, igm, logn, p, p0i); + + Gp = Fp + n; + t1 = Gp + n; + // memmove(Fp, ft, 2 * n * sizeof *ft); + Array.Copy(tmpsrc, ft, tmpsrc, Fp, 2 * n); + + /* + * We now need to apply the Babai reduction. At that point, + * we have F and G in two n-word arrays. + * + * We can compute F*adj(f)+G*adj(g) and f*adj(f)+g*adj(g) + * modulo p, using the NTT. We still move memory around in + * order to save RAM. + */ + t2 = t1 + n; + t3 = t2 + n; + t4 = t3 + n; + t5 = t4 + n; + + /* + * Compute the NTT tables in t1 and t2. We do not keep t2 + * (we'll recompute it later on). + */ + modp_mkgm2(tmpsrc, t1, tmpsrc, t2, logn, PRIMES[0].g, p, p0i); + + /* + * Convert F and G to NTT. + */ + modp_NTT2(tmpsrc, Fp, tmpsrc, t1, logn, p, p0i); + modp_NTT2(tmpsrc, Gp, tmpsrc, t1, logn, p, p0i); + + /* + * Load f and adj(f) in t4 and t5, and convert them to NTT + * representation. + */ + tmpsrc[t4+0] = tmpsrc[t5+0] = modp_set(fsrc[f + 0], p); + for (u = 1; u < n; u ++) { + tmpsrc[t4+u] = modp_set(fsrc[f + u], p); + tmpsrc[t5+n - u] = modp_set(-fsrc[f + u], p); + } + modp_NTT2(tmpsrc, t4, tmpsrc, t1, logn, p, p0i); + modp_NTT2(tmpsrc, t5, tmpsrc, t1, logn, p, p0i); + + /* + * Compute F*adj(f) in t2, and f*adj(f) in t3. + */ + for (u = 0; u < n; u ++) { + uint w; + + w = modp_montymul(tmpsrc[t5+u], R2, p, p0i); + tmpsrc[t2+u] = modp_montymul(w, tmpsrc[Fp+u], p, p0i); + tmpsrc[t3+u] = modp_montymul(w, tmpsrc[t4+u], p, p0i); + } + + /* + * Load g and adj(g) in t4 and t5, and convert them to NTT + * representation. + */ + tmpsrc[t4+0] = tmpsrc[t5+0] = modp_set(gsrc[g + 0], p); + for (u = 1; u < n; u ++) { + tmpsrc[t4+u] = modp_set(gsrc[g + u], p); + tmpsrc[t5+n - u] = modp_set(-gsrc[g + u], p); + } + modp_NTT2(tmpsrc, t4, tmpsrc, t1, logn, p, p0i); + modp_NTT2(tmpsrc, t5, tmpsrc, t1, logn, p, p0i); + + /* + * Add G*adj(g) to t2, and g*adj(g) to t3. + */ + for (u = 0; u < n; u ++) { + uint w; + + w = modp_montymul(tmpsrc[t5+u], R2, p, p0i); + tmpsrc[t2+u] = modp_add(tmpsrc[t2+u], + modp_montymul(w, tmpsrc[Gp+u], p, p0i), p); + tmpsrc[t3+u] = modp_add(tmpsrc[t3+u], + modp_montymul(w, tmpsrc[t4+u], p, p0i), p); + } + + /* + * Convert back t2 and t3 to normal representation (normalized + * around 0), and then + * move them to t1 and t2. We first need to recompute the + * inverse table for NTT. + */ + modp_mkgm2(tmpsrc, t1, tmpsrc, t4, logn, this.PRIMES[0].g, p, p0i); + modp_iNTT2(tmpsrc, t2, tmpsrc, t4, logn, p, p0i); + modp_iNTT2(tmpsrc, t3, tmpsrc, t4, logn, p, p0i); + for (u = 0; u < n; u ++) { + tmpsrc[t1+u] = (uint)modp_norm(tmpsrc[t2+u], p); + tmpsrc[t2+u] = (uint)modp_norm(tmpsrc[t3+u], p); + } + + /* + * At that point, array contents are: + * + * F (NTT representation) (Fp) + * G (NTT representation) (Gp) + * F*adj(f)+G*adj(g) (t1) + * f*adj(f)+g*adj(g) (t2) + * + * We want to divide t1 by t2. The result is not integral; it + * must be rounded. We thus need to use the FFT. + */ + + /* + * Get f*adj(f)+g*adj(g) in FFT representation. Since this + * polynomial is auto-adjoint, all its coordinates in FFT + * representation are actually real, so we can truncate off + * the imaginary parts. + */ + FalconFPR[] rtmp = new FalconFPR[2 * n]; + rt3 = n; + for (u = 0; u < n; u ++) { + rtmp[rt3+u] = this.fpre.fpr_of((int)tmpsrc[t2+u]); + } + this.ffte.FFT(rtmp, rt3, logn); + rt2 = 0; + // memmove(rt2, rt3, hn * sizeof *rt3); + Array.Copy(rtmp, rt3, rtmp, rt2, hn); + + /* + * Convert F*adj(f)+G*adj(g) in FFT representation. + */ + rt3 = rt2 + hn; + for (u = 0; u < n; u ++) { + rtmp[rt3+u] = this.fpre.fpr_of((int)tmpsrc[t1 + u]); + } + this.ffte.FFT(rtmp, rt3, logn); + + /* + * Compute (F*adj(f)+G*adj(g))/(f*adj(f)+g*adj(g)) and get + * its rounded normal representation in t1. + */ + this.ffte.poly_div_autoadj_fft(rtmp, rt3, rtmp, rt2, logn); + this.ffte.iFFT(rtmp, rt3, logn); + for (u = 0; u < n; u ++) { + tmpsrc[t1+u] = modp_set((int)this.fpre.fpr_rint(rtmp[rt3+u]), p); + } + + /* + * RAM contents are now: + * + * F (NTT representation) (Fp) + * G (NTT representation) (Gp) + * k (t1) + * + * We want to compute F-k*f, and G-k*g. + */ + t2 = t1 + n; + t3 = t2 + n; + t4 = t3 + n; + t5 = t4 + n; + modp_mkgm2(tmpsrc, t2, tmpsrc, t3, logn, this.PRIMES[0].g, p, p0i); + for (u = 0; u < n; u ++) { + tmpsrc[t4+u] = modp_set(fsrc[f+u], p); + tmpsrc[t5+u] = modp_set(gsrc[g+u], p); + } + modp_NTT2(tmpsrc, t1, tmpsrc, t2, logn, p, p0i); + modp_NTT2(tmpsrc, t4, tmpsrc, t2, logn, p, p0i); + modp_NTT2(tmpsrc, t5, tmpsrc, t2, logn, p, p0i); + for (u = 0; u < n; u ++) { + uint kw; + + kw = modp_montymul(tmpsrc[t1+u], R2, p, p0i); + tmpsrc[Fp+u] = modp_sub(tmpsrc[Fp+u], + modp_montymul(kw, tmpsrc[t4+u], p, p0i), p); + tmpsrc[Gp+u] = modp_sub(tmpsrc[Gp+u], + modp_montymul(kw, tmpsrc[t5+u], p, p0i), p); + } + modp_iNTT2(tmpsrc, Fp, tmpsrc, t3, logn, p, p0i); + modp_iNTT2(tmpsrc, Gp, tmpsrc, t3, logn, p, p0i); + for (u = 0; u < n; u ++) { + tmpsrc[Fp+u] = (uint)modp_norm(tmpsrc[Fp+u], p); + tmpsrc[Gp+u] = (uint)modp_norm(tmpsrc[Gp+u], p); + } + + return 1; + } + + /* + * Solve the NTRU equation. Returned value is 1 on success, 0 on error. + * G can be NULL, in which case that value is computed but not returned. + * If any of the coefficients of F and G exceeds lim (in absolute value), + * then 0 is returned. + */ + int solve_NTRU(uint logn, sbyte[] Fsrc, int F, sbyte[] Gsrc, int G, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, int lim, uint[] tmpsrc, int tmp) + { + int n, u; + int ft, gt, Ft, Gt, gm; + uint p, p0i, r; + FalconSmallPrime[] primes; + + n = (int)1 << (int)logn; + + if (solve_NTRU_deepest(logn, fsrc, f, gsrc, g, tmpsrc, tmp) == 0) { + return 0; + } + + /* + * For logn <= 2, we need to use solve_NTRU_intermediate() + * directly, because coefficients are a bit too large and + * do not fit the hypotheses in solve_NTRU_binary_depth0(). + */ + if (logn <= 2) { + uint depth; + + depth = logn; + while (depth -- > 0) { + if (solve_NTRU_intermediate(logn, fsrc, f, gsrc, g, depth, tmpsrc, tmp) == 0) { + return 0; + } + } + } else { + uint depth; + + depth = logn; + while (depth -- > 2) { + // TODO check what causes this to fail + if (solve_NTRU_intermediate(logn, fsrc, f, gsrc, g, depth, tmpsrc, tmp) == 0) { + return 0; + } + } + if (solve_NTRU_binary_depth1(logn, fsrc, f, gsrc, g, tmpsrc, tmp) == 0) { + return 0; + } + if (solve_NTRU_binary_depth0(logn, fsrc, f, gsrc, g, tmpsrc, tmp) == 0) { + return 0; + } + } + + /* + * If no buffer has been provided for G, use a temporary one. + */ + if (Gsrc == null) { + G = 0; + Gsrc = new sbyte[n]; + } + + /* + * Final F and G are in fk->tmp, one word per coefficient + * (signed value over 31 bits). + */ + if (poly_big_to_small(Fsrc, F, tmpsrc, tmp, lim, logn) == 0 + || poly_big_to_small(Gsrc, G, tmpsrc, tmp + n, lim, logn) == 0) + { + return 0; + } + + /* + * Verify that the NTRU equation is fulfilled. Since all elements + * have short lengths, verifying modulo a small prime p works, and + * allows using the NTT. + * + * We put Gt[] first in tmp[], and process it first, so that it does + * not overlap with G[] in case we allocated it ourselves. + */ + Gt = tmp; + ft = Gt + n; + gt = ft + n; + Ft = gt + n; + gm = Ft + n; + + primes = this.PRIMES; + p = primes[0].p; + p0i = modp_ninv31(p); + modp_mkgm2(tmpsrc, gm, tmpsrc, tmp, logn, primes[0].g, p, p0i); + for (u = 0; u < n; u ++) { + tmpsrc[Gt+u] = modp_set(Gsrc[G+u], p); + } + for (u = 0; u < n; u ++) { + tmpsrc[ft+u] = modp_set(fsrc[f+u], p); + tmpsrc[gt+u] = modp_set(gsrc[g+u], p); + tmpsrc[Ft+u] = modp_set(Fsrc[F+u], p); + } + modp_NTT2(tmpsrc, ft, tmpsrc, gm, logn, p, p0i); + modp_NTT2(tmpsrc, gt, tmpsrc, gm, logn, p, p0i); + modp_NTT2(tmpsrc, Ft, tmpsrc, gm, logn, p, p0i); + modp_NTT2(tmpsrc, Gt, tmpsrc, gm, logn, p, p0i); + r = modp_montymul(12289, 1, p, p0i); + for (u = 0; u < n; u ++) { + uint z; + + z = modp_sub(modp_montymul(tmpsrc[ft+u], tmpsrc[Gt+u], p, p0i), + modp_montymul(tmpsrc[gt+u], tmpsrc[Ft+u], p, p0i), p); + if (z != r) { + return 0; + } + } + + return 1; + } + + /* + * Generate a random polynomial with a Gaussian distribution. This function + * also makes sure that the resultant of the polynomial with phi is odd. + */ + void poly_small_mkgauss(SHAKE256 rng, sbyte[] fsrc, int f, uint logn) + { + int n, u; + uint mod2; + + n = (int)1 << (int)logn; + mod2 = 0; + for (u = 0; u < n; u ++) { + int s; + + for(;;) { + s = mkgauss(rng, logn); + + /* + * We need the coefficient to fit within -127..+127; + * realistically, this is always the case except for + * the very low degrees (N = 2 or 4), for which there + * is no real security anyway. + */ + if (s < -127 || s > 127) { + continue; // restart + } + + /* + * We need the sum of all coefficients to be 1; otherwise, + * the resultant of the polynomial with X^N+1 will be even, + * and the binary GCD will fail. + */ + if (u == n - 1) { + if ((mod2 ^ (uint)(s & 1)) == 0) { + continue; // restart + } + } else { + mod2 ^= (uint)(s & 1); + } + fsrc[f+u] = (sbyte)s; + break; // end + } + } + } + + internal void keygen(SHAKE256 rng, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, sbyte[] Fsrc, int F, sbyte[] Gsrc, int G, ushort[] hsrc, int h, + uint logn) + { + /* + * Algorithm is the following: + * + * - Generate f and g with the Gaussian distribution. + * + * - If either Res(f,phi) or Res(g,phi) is even, try again. + * + * - If ||(f,g)|| is too large, try again. + * + * - If ||B~_{f,g}|| is too large, try again. + * + * - If f is not invertible mod phi mod q, try again. + * + * - Compute h = g/f mod phi mod q. + * + * - Solve the NTRU equation fG - gF = q; if the solving fails, + * try again. Usual failure condition is when Res(f,phi) + * and Res(g,phi) are not prime to each other. + */ + int n, u; + int h2, tmp2; + SHAKE256 rc; + + n = (int)1 << (int)logn; + rc = rng; + + /* + * We need to generate f and g randomly, until we find values + * such that the norm of (g,-f), and of the orthogonalized + * vector, are satisfying. The orthogonalized vector is: + * (q*adj(f)/(f*adj(f)+g*adj(g)), q*adj(g)/(f*adj(f)+g*adj(g))) + * (it is actually the (N+1)-th row of the Gram-Schmidt basis). + * + * In the binary case, coefficients of f and g are generated + * independently of each other, with a discrete Gaussian + * distribution of standard deviation 1.17*sqrt(q/(2*N)). Then, + * the two vectors have expected norm 1.17*sqrt(q), which is + * also our acceptance bound: we require both vectors to be no + * larger than that (this will be satisfied about 1/4th of the + * time, thus we expect sampling new (f,g) about 4 times for that + * step). + * + * We require that Res(f,phi) and Res(g,phi) are both odd (the + * NTRU equation solver requires it). + */ + for (;;) { + int rt1, rt2, rt3; + FalconFPR bnorm; + uint normf, normg, norm; + int lim; + + /* + * The poly_small_mkgauss() function makes sure + * that the sum of coefficients is 1 modulo 2 + * (i.e. the resultant of the polynomial with phi + * will be odd). + */ + poly_small_mkgauss(rc, fsrc, f, logn); + poly_small_mkgauss(rc, gsrc, g, logn); + + /* + * Verify that all coefficients are within the bounds + * defined in max_fg_bits. This is the case with + * overwhelming probability; this guarantees that the + * key will be encodable with FALCON_COMP_TRIM. + */ + lim = 1 << (this.codec.max_fg_bits[logn] - 1); + for (u = 0; u < n; u ++) { + /* + * We can use non-CT tests since on any failure + * we will discard f and g. + */ + if (fsrc[f+u] >= lim || fsrc[f+u] <= -lim + || gsrc[g+u] >= lim || gsrc[g+u] <= -lim) + { + lim = -1; + break; + } + } + if (lim < 0) { + continue; + } + + /* + * Bound is 1.17*sqrt(q). We compute the squared + * norms. With q = 12289, the squared bound is: + * (1.17^2)* 12289 = 16822.4121 + * Since f and g are integral, the squared norm + * of (g,-f) is an integer. + */ + normf = poly_small_sqnorm(fsrc, f, logn); + normg = poly_small_sqnorm(gsrc, g, logn); + norm = (uint)((normf + normg) | -((normf | normg) >> 31)); + if (norm >= 16823) { + continue; + } + + /* + * We compute the orthogonalized vector norm. + */ + FalconFPR[] rtmp = new FalconFPR[3 * n]; + rt1 = 0; + rt2 = rt1 + n; + rt3 = rt2 + n; + poly_small_to_fp(rtmp, rt1, fsrc, f, logn); + poly_small_to_fp(rtmp, rt2, gsrc, g, logn); + this.ffte.FFT(rtmp, rt1, logn); + this.ffte.FFT(rtmp, rt2, logn); + this.ffte.poly_invnorm2_fft(rtmp, rt3, rtmp, rt1, rtmp, rt2, logn); + this.ffte.poly_adj_fft(rtmp, rt1, logn); + this.ffte.poly_adj_fft(rtmp, rt2, logn); + this.ffte.poly_mulconst(rtmp, rt1, this.fpre.fpr_q, logn); + this.ffte.poly_mulconst(rtmp, rt2, this.fpre.fpr_q, logn); + this.ffte.poly_mul_autoadj_fft(rtmp, rt1, rtmp, rt3, logn); + this.ffte.poly_mul_autoadj_fft(rtmp, rt2, rtmp, rt3, logn); + this.ffte.iFFT(rtmp, rt1, logn); + this.ffte.iFFT(rtmp, rt2, logn); + bnorm = this.fpre.fpr_zero; + for (u = 0; u < n; u ++) { + bnorm = this.fpre.fpr_add(bnorm, this.fpre.fpr_sqr(rtmp[rt1+u])); + bnorm = this.fpre.fpr_add(bnorm, this.fpre.fpr_sqr(rtmp[rt2+u])); + } + if (!this.fpre.fpr_lt(bnorm, this.fpre.fpr_bnorm_max)) { + continue; + } + + /* + * Compute public key h = g/f mod X^N+1 mod q. If this + * fails, we must restart. + */ + ushort[] htmp; + ushort[] h2src; + if (hsrc == null) { + htmp = new ushort[2 * n]; + h2 = 0; + h2src = htmp; + tmp2 = h2 + n; + } else { + htmp = new ushort[n]; + h2 = h; + h2src = hsrc; + tmp2 = 0; + } + if (vrfy.compute_public(h2src, h2, fsrc, f, gsrc, g, logn, htmp, tmp2) == 0) { + continue; + } + + /* + * Solve the NTRU equation to get F and G. + */ + uint[] itmp = logn > 2 ? new uint[28 * n] : new uint[28 * n * 3]; + lim = (1 << (this.codec.max_FG_bits[logn] - 1)) - 1; + if (solve_NTRU(logn, Fsrc, F, Gsrc, G, fsrc, f, gsrc, g, lim, itmp, 0) == 0) { + continue; + } + + /* + * Key pair is generated. + */ + break; + } + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconNIST.cs b/crypto/src/pqc/crypto/falcon/FalconNIST.cs new file mode 100644 index 000000000..50459532f --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconNIST.cs @@ -0,0 +1,303 @@ +using System; +using Org.BouncyCastle.Security; +using Org.BouncyCastle.Utilities; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconNIST + { + private FalconCodec codec; + private FalconVrfy vrfy; + private FalconCommon common; + private SecureRandom random; + private uint logn; + private uint noncelen; + private int CRYPTO_BYTES; + private int CRYPTO_PUBLICKEYBYTES; + private int CRYPTO_SECRETKEYBYTES; + + internal uint GetNonceLength() { + return this.noncelen; + } + internal uint GetLogn() { + return this.logn; + } + internal int GetCryptoBytes() { + return this.CRYPTO_BYTES; + } + + internal FalconNIST(SecureRandom random, uint logn, uint noncelen) { + this.logn = logn; + this.codec = new FalconCodec(); + this.common = new FalconCommon(); + this.vrfy = new FalconVrfy(this.common); + this.random = random; + this.noncelen = noncelen; + int n = (int)1 << (int)logn; + this.CRYPTO_PUBLICKEYBYTES = 1 + (14 * n / 8); + if (logn == 10) + { + this.CRYPTO_SECRETKEYBYTES = 2305; + this.CRYPTO_BYTES = 1330; + } + else if (logn == 9 || logn == 8) + { + this.CRYPTO_SECRETKEYBYTES = 1 + (6 * n * 2 / 8) + n; + this.CRYPTO_BYTES = 690; // TODO find what the byte length is here when not at degree 9 or 10 + } + else if (logn == 7 || logn == 6) + { + this.CRYPTO_SECRETKEYBYTES = 1 + (7 * n * 2 / 8) + n; + this.CRYPTO_BYTES = 690; + } + else + { + this.CRYPTO_SECRETKEYBYTES = 1 + (n * 2) + n; + this.CRYPTO_BYTES = 690; + } + } + + internal int crypto_sign_keypair(byte[] pksrc, int pk, byte[] sksrc, int sk) + { + int n = (int)1 << (int)this.logn; + SHAKE256 rng = new SHAKE256(); + sbyte[] f = new sbyte[n], + g = new sbyte[n], + F = new sbyte[n]; + ushort[] h = new ushort[n]; + byte[] seed = new byte[48]; + int u, v; + FalconKeygen keygen = new FalconKeygen(this.codec, this.vrfy); + + /* + * Generate key pair. + */ + this.random.NextBytes(seed); + rng.i_shake256_init(); + rng.i_shake256_inject(seed, 0, seed.Length); + rng.i_shake256_flip(); + keygen.keygen(rng, f, 0, g, 0, F, 0, null, 0, h, 0, this.logn); + + /* + * Encode private key. + */ + sksrc[sk+0] = (byte)(0x50 + this.logn); + u = 1; + v = this.codec.trim_i8_encode(sksrc, sk + u, CRYPTO_SECRETKEYBYTES - u, + f, 0, this.logn, this.codec.max_fg_bits[this.logn]); + if (v == 0) { + // TODO check which exception types to use here + throw new InvalidOperationException("f encode failed"); + } + u += v; + v = this.codec.trim_i8_encode(sksrc, sk + u, CRYPTO_SECRETKEYBYTES - u, + g, 0, this.logn, this.codec.max_fg_bits[this.logn]); + if (v == 0) { + throw new InvalidOperationException("g encode failed"); + } + u += v; + v = this.codec.trim_i8_encode(sksrc, sk + u, CRYPTO_SECRETKEYBYTES - u, + F, 0, this.logn, this.codec.max_FG_bits[this.logn]); + if (v == 0) { + throw new InvalidOperationException("F encode failed"); + } + u += v; + if (u != CRYPTO_SECRETKEYBYTES) { + throw new InvalidOperationException("secret key encoding failed"); + } + + /* + * Encode public key. + */ + pksrc[pk+0] = (byte)(0x00 + this.logn); + v = this.codec.modq_encode(pksrc, pk + 1, CRYPTO_PUBLICKEYBYTES - 1, h, 0, this.logn); + if (v != CRYPTO_PUBLICKEYBYTES - 1) { + throw new InvalidOperationException("public key encoding failed"); + } + + return 0; + } + + internal byte[] crypto_sign(byte[] sm, + byte[] msrc, int m, uint mlen, + byte[] sksrc, int sk) + { + // TEMPALLOC union { + // uint8_t b[72 * 1024]; + // uint64_t dummy_u64; + // fpr dummy_fpr; + // } tmp; + int u, v, sig_len; + int n = (int)1 << (int)this.logn; + sbyte[] f = new sbyte[n], + g = new sbyte[n], + F = new sbyte[n], + G = new sbyte[n]; + short[] sig = new short[n]; + ushort[] hm = new ushort[n]; + byte[] seed = new byte[48], + nonce = new byte[this.noncelen]; + byte[] esig = new byte[this.CRYPTO_BYTES - 2 - this.noncelen]; + SHAKE256 sc = new SHAKE256(); + FalconSign signer = new FalconSign(this.common); + + /* + * Decode the private key. + */ + if (sksrc[sk+0] != 0x50 + this.logn) { + throw new ArgumentException("private key header incorrect"); + } + u = 1; + v = this.codec.trim_i8_decode(f, 0, this.logn, this.codec.max_fg_bits[this.logn], + sksrc, sk + u, CRYPTO_SECRETKEYBYTES - u); + if (v == 0) { + throw new InvalidOperationException("f decode failed"); + } + u += v; + v = this.codec.trim_i8_decode(g, 0, this.logn, this.codec.max_fg_bits[this.logn], + sksrc, sk + u, CRYPTO_SECRETKEYBYTES - u); + if (v == 0) { + throw new InvalidOperationException("g decode failed"); + } + u += v; + v = this.codec.trim_i8_decode(F, 0, this.logn, this.codec.max_FG_bits[this.logn], + sksrc, sk + u, CRYPTO_SECRETKEYBYTES - u); + if (v == 0) { + throw new InvalidOperationException("F decode failed"); + } + u += v; + if (u != CRYPTO_SECRETKEYBYTES) { + throw new InvalidOperationException("full Key not used"); + } + if (this.vrfy.complete_private(G, 0, f, 0, g, 0, F, 0, this.logn, new ushort[2 * n],0) == 0) { + throw new InvalidOperationException("complete private failed"); + } + + /* + * Create a random nonce (40 bytes). + */ + this.random.NextBytes(nonce); + + /* + * Hash message nonce + message into a vector. + */ + sc.i_shake256_init(); + sc.i_shake256_inject(nonce,0,nonce.Length); + sc.i_shake256_inject(msrc,m, (int)mlen); + sc.i_shake256_flip(); + this.common.hash_to_point_vartime(sc, hm, 0, this.logn); + + /* + * Initialize a RNG. + */ + this.random.NextBytes(seed); + sc.i_shake256_init(); + sc.i_shake256_inject(seed, 0, seed.Length); + sc.i_shake256_flip(); + + /* + * Compute the signature. + */ + signer.sign_dyn(sig, 0, sc, f, 0, g, 0, F, 0, G, 0, hm, 0, this.logn, new FalconFPR[10 * n], 0); + + /* + * Encode the signature. Format is: + * signature header 1 bytes + * nonce 40 bytes + * signature slen bytes + */ + esig[0] = (byte)(0x20 + logn); + sig_len = codec.comp_encode(esig, 1, esig.Length - 1, sig, 0, logn); + if (sig_len == 0) + { + throw new InvalidOperationException("signature failed to generate"); + } + sig_len++; + + // header + sm[0] = (byte)(0x30 + logn); + // nonce + Array.Copy(nonce, 0, sm, 1, noncelen); + + // signature + Array.Copy(esig, 0, sm, 1 + noncelen, sig_len); + + return Arrays.CopyOfRange(sm, 0, 1 + (int)noncelen + sig_len); + } + + internal int crypto_sign_open(byte[] sig_encoded, byte[] nonce, byte[] m, + byte[] pksrc, int pk) + { + int sig_len, msg_len; + int n = (int)1 << (int)this.logn; + ushort[] h = new ushort[n], + hm = new ushort[n]; + short[] sig = new short[n]; + SHAKE256 sc = new SHAKE256(); + + /* + * Decode public key. + */ + if (pksrc[pk+0] != 0x00 + this.logn) { + return -1; + } + if (this.codec.modq_decode(h, 0, this.logn, pksrc, pk + 1, CRYPTO_PUBLICKEYBYTES - 1) + != CRYPTO_PUBLICKEYBYTES - 1) + { + return -1; + } + this.vrfy.to_ntt_monty(h, 0, this.logn); + + /* + * Find nonce, signature, message length. + */ + // if (smlen < 2 + this.noncelen) { + // return -1; + // } + // sig_len = ((int)sm[0] << 8) | (int)sm[1]; + sig_len = sig_encoded.Length; + // if (sig_len > (smlen - 2 - this.noncelen)) { + // return -1; + // } + // msg_len = smlen - 2 - this.noncelen - sig_len; + msg_len = m.Length; + + /* + * Decode signature. + */ + // esig = sm + 2 + this.noncelen + msg_len; + if (sig_len < 1 || sig_encoded[0] != (byte)(0x20 + this.logn)) { + return -1; + } + if (this.codec.comp_decode(sig, 0, this.logn, sig_encoded, + 1, sig_len - 1) != sig_len - 1) + { + return -1; + } + + /* + * Hash nonce + message into a vector. + */ + sc.i_shake256_init(); + // sc.i_shake256_inject(sm + 2, this.noncelen + msg_len); + sc.i_shake256_inject(nonce, 0, (int)this.noncelen); + sc.i_shake256_inject(m, 0, m.Length); + sc.i_shake256_flip(); + this.common.hash_to_point_vartime(sc, hm, 0, this.logn); + + /* + * Verify signature. + */ + if (!this.vrfy.verify_raw(hm, 0, sig, 0, h, 0, this.logn, new ushort[n], 0)) { + return -1; + } + + /* + * Return plaintext. - not in use + */ + // Array.Copy(sm + 2 + this.noncelen, m, msg_len); + // *mlen = msg_len; + return 0; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconParameters.cs b/crypto/src/pqc/crypto/falcon/FalconParameters.cs new file mode 100644 index 000000000..313d25709 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconParameters.cs @@ -0,0 +1,38 @@ +using System; +using Org.BouncyCastle.Crypto; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + public class FalconParameters + : ICipherParameters + { + public static FalconParameters falcon_512 = new FalconParameters("falcon512", 9, 40); + public static FalconParameters falcon_1024 = new FalconParameters("falcon1024", 10, 40); + + private String name; + private uint logn; + private uint nonce_length; + + public FalconParameters(String name, uint logn, uint nonce_length) + { + this.name = name; + this.logn = logn; + this.nonce_length = nonce_length; + } + + public uint GetLogN() + { + return logn; + } + + public uint GetNonceLength() + { + return nonce_length; + } + + public String GetName() + { + return name; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconPrivateKeyParameters.cs b/crypto/src/pqc/crypto/falcon/FalconPrivateKeyParameters.cs new file mode 100644 index 000000000..448ba7275 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconPrivateKeyParameters.cs @@ -0,0 +1,24 @@ +using Org.BouncyCastle.Utilities; + + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + public class FalconPrivateKeyParameters + : FalconKeyParameters + { + private byte[] privateKey; + + public byte[] PrivateKey => Arrays.Clone(privateKey); + + public FalconPrivateKeyParameters(FalconParameters parameters, byte[] sk_encoded) + : base(true, parameters) + { + this.privateKey = Arrays.Clone(sk_encoded); + } + + public byte[] GetEncoded() + { + return Arrays.Clone(privateKey); + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconPublicKeyParameters.cs b/crypto/src/pqc/crypto/falcon/FalconPublicKeyParameters.cs new file mode 100644 index 000000000..dace2e60f --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconPublicKeyParameters.cs @@ -0,0 +1,23 @@ +using Org.BouncyCastle.Utilities; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + public class FalconPublicKeyParameters + : FalconKeyParameters + { + private byte[] publicKey; + + public byte[] PublicKey => Arrays.Clone(publicKey); + + public FalconPublicKeyParameters(FalconParameters parameters, byte[] pk_encoded) + : base(false, parameters) + { + this.publicKey = Arrays.Clone(pk_encoded); + } + + public byte[] GetEncoded() + { + return Arrays.Clone(publicKey); + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconRNG.cs b/crypto/src/pqc/crypto/falcon/FalconRNG.cs new file mode 100644 index 000000000..31f04d5d7 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconRNG.cs @@ -0,0 +1,261 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconRNG + { + byte[] bd; + //ulong bdummy_u64; + byte[] sd; + //ulong sdummy_u64; + //int type; + int ptr; + + FalconConversions convertor; + + internal FalconRNG() { + this.bd = new byte[512]; + this.sd = new byte[256]; + this.convertor = new FalconConversions(); + } + + /* + * License from the reference C code (the code was copied then modified + * to function in C#): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + + internal void prng_init(SHAKE256 src) + { + /* + * To ensure reproducibility for a given seed, we + * must enforce little-endian interpretation of + * the state words. + */ + byte[] tmp = new byte[56]; + ulong th, tl; + int i; + + src.i_shake256_extract(tmp,0, 56); + for (i = 0; i < 14; i ++) { + uint w; + + w = (uint)tmp[(i << 2) + 0] + | ((uint)tmp[(i << 2) + 1] << 8) + | ((uint)tmp[(i << 2) + 2] << 16) + | ((uint)tmp[(i << 2) + 3] << 24); + //*(uint *)(this.sd + (i << 2)) = w; + Array.Copy(convertor.int_to_bytes((int)w), 0, this.sd, i << 2, 4); + } + // tl = *(uint32_t *)(p->state.d + 48); + tl = convertor.bytes_to_uint(this.sd, 48); + // th = *(uint32_t *)(p->state.d + 52); + th = convertor.bytes_to_uint(this.sd, 52); + Array.Copy(convertor.ulong_to_bytes(tl + (th << 32)), 0, this.sd, 48, 8); + this.prng_refill(); + } + + /* + * PRNG based on ChaCha20. + * + * State consists in key (32 bytes) then IV (16 bytes) and block counter + * (8 bytes). Normally, we should not care about local endianness (this + * is for a PRNG), but for the NIST competition we need reproducible KAT + * vectors that work across architectures, so we enforce little-endian + * interpretation where applicable. Moreover, output words are "spread + * out" over the output buffer with the interleaving pattern that is + * naturally obtained from the AVX2 implementation that runs eight + * ChaCha20 instances in parallel. + * + * The block counter is XORed into the first 8 bytes of the IV. + */ + private void QROUND(uint[] state, int a, int b, int c, int d) { + state[a] += state[b]; + state[d] ^= state[a]; + state[d] = (state[d] << 16) | (state[d] >> 16); + state[c] += state[d]; + state[b] ^= state[c]; + state[b] = (state[b] << 12) | (state[b] >> 20); + state[a] += state[b]; + state[d] ^= state[a]; + state[d] = (state[d] << 8) | (state[d] >> 24); + state[c] += state[d]; + state[b] ^= state[c]; + state[b] = (state[b] << 7) | (state[b] >> 25); + } + void prng_refill() + { + + uint[] CW = { + 0x61707865, 0x3320646e, 0x79622d32, 0x6b206574 + }; + + ulong cc; + int u; + + /* + * State uses local endianness. Only the output bytes must be + * converted to little endian (if used on a big-endian machine). + */ + //cc = *(ulong *)(this.sd + 48); + cc = convertor.bytes_to_ulong(this.sd, 48); + for (u = 0; u < 8; u ++) { + uint[] state = new uint[16]; + int v; + int i; + + // memcpy(&state[0], CW, sizeof CW); + Array.Copy(CW, 0, state, 0, 4); + // memcpy(&state[4], this.sd, 48); + Array.Copy(convertor.bytes_to_uint_array(this.sd, 0, 12), 0, state, 4, 12); + + state[14] ^= (uint)cc; + state[15] ^= (uint)(cc >> 32); + for (i = 0; i < 10; i ++) { + + QROUND(state, 0, 4, 8, 12); + QROUND(state, 1, 5, 9, 13); + QROUND(state, 2, 6, 10, 14); + QROUND(state, 3, 7, 11, 15); + QROUND(state, 0, 5, 10, 15); + QROUND(state, 1, 6, 11, 12); + QROUND(state, 2, 7, 8, 13); + QROUND(state, 3, 4, 9, 14); + + } + + for (v = 0; v < 4; v++) + { + state[v] += CW[v]; + } + for (v = 4; v < 14; v++) + { + // state[v] += ((uint32_t *)p->state.d)[v - 4]; + // we multiply the -4 by 4 to account for 4 bytes per int + state[v] += convertor.bytes_to_uint(sd, (4 * v) - 16); + } + // state[14] += ((uint32_t *)p->state.d)[10] + // ^ (uint32_t)cc; + state[14] += (uint)(convertor.bytes_to_uint(sd, 40) ^ ((int)cc)); + // state[15] += ((uint32_t *)p->state.d)[11] + // ^ (uint32_t)(cc >> 32); + state[15] += (uint)(convertor.bytes_to_uint(sd, 44) ^ ((int)(cc >> 32))); + cc ++; + + /* + * We mimic the interleaving that is used in the AVX2 + * implementation. + */ + for (v = 0; v < 16; v ++) { + this.bd[(u << 2) + (v << 5) + 0] = + (byte)state[v]; + this.bd[(u << 2) + (v << 5) + 1] = + (byte)(state[v] >> 8); + this.bd[(u << 2) + (v << 5) + 2] = + (byte)(state[v] >> 16); + this.bd[(u << 2) + (v << 5) + 3] = + (byte)(state[v] >> 24); + } + } + //*(ulong *)(this.sd + 48) = cc; + Array.Copy(convertor.ulong_to_bytes(cc), 0, sd, 48, 8); + + + this.ptr = 0; + } + + internal void prng_get_bytes( byte[] dstsrc, int dst, int len) + { + int buf; + + buf = dst; + while (len > 0) { + int clen; + + clen = (this.bd.Length) - this.ptr; + if (clen > len) { + clen = len; + } + // memcpy(buf, this.bd, clen); + Array.Copy(this.bd, 0, dstsrc, buf, clen); + buf += clen; + len -= clen; + this.ptr += clen; + if (this.ptr == this.bd.Length) { + this.prng_refill(); + } + } + } + + /* + * Get a 64-bit random value from a PRNG. + */ + internal ulong prng_get_u64() + { + int u; + + /* + * If there are less than 9 bytes in the buffer, we refill it. + * This means that we may drop the last few bytes, but this allows + * for faster extraction code. Also, it means that we never leave + * an empty buffer. + */ + u = this.ptr; + if (u >= (this.bd.Length) - 9) { + this.prng_refill(); + u = 0; + } + this.ptr = u + 8; + + /* + * On systems that use little-endian encoding and allow + * unaligned accesses, we can simply read the data where it is. + */ + return (ulong)this.bd[u + 0] + | ((ulong)this.bd[u + 1] << 8) + | ((ulong)this.bd[u + 2] << 16) + | ((ulong)this.bd[u + 3] << 24) + | ((ulong)this.bd[u + 4] << 32) + | ((ulong)this.bd[u + 5] << 40) + | ((ulong)this.bd[u + 6] << 48) + | ((ulong)this.bd[u + 7] << 56); + } + + /* + * Get an 8-bit random value from a PRNG. + */ + internal uint prng_get_u8() + { + uint v; + + v = this.bd[this.ptr ++]; + if (this.ptr == this.bd.Length) { + this.prng_refill(); + } + return v; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconSign.cs b/crypto/src/pqc/crypto/falcon/FalconSign.cs new file mode 100644 index 000000000..613ef498b --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconSign.cs @@ -0,0 +1,974 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconSign + { + + FalconFFT ffte; + FPREngine fpre; + FalconCommon common; + + internal FalconSign(FalconCommon common) { + this.ffte = new FalconFFT(); + this.fpre = new FPREngine(); + this.common = common; + } + + /* + * License from the reference C code (the code was copied then modified + * to function in C#): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + + /* + * Binary case: + * N = 2^logn + * phi = X^N+1 + */ + + /* + * Get the size of the LDL tree for an input with polynomials of size + * 2^logn. The size is expressed in the number of elements. + */ + internal uint ffLDL_treesize(uint logn) + { + /* + * For logn = 0 (polynomials are constant), the "tree" is a + * single element. Otherwise, the tree node has size 2^logn, and + * has two child trees for size logn-1 each. Thus, treesize s() + * must fulfill these two relations: + * + * s(0) = 1 + * s(logn) = (2^logn) + 2*s(logn-1) + */ + return (logn + 1) << (int)logn; + } + + /* + * Inner function for ffLDL_fft(). It expects the matrix to be both + * auto-adjoint and quasicyclic; also, it uses the source operands + * as modifiable temporaries. + * + * tmp[] must have room for at least one polynomial. + */ + internal void ffLDL_fft_inner(FalconFPR[] treesrc, int tree, + FalconFPR[] g0src, int g0, FalconFPR[] g1src, int g1, uint logn, FalconFPR[] tmpsrc, int tmp) + { + int n, hn; + + n = (int)1 << (int)logn; + if (n == 1) { + treesrc[tree+0] = g0src[g0 + 0]; + return; + } + hn = n >> 1; + + /* + * The LDL decomposition yields L (which is written in the tree) + * and the diagonal of D. Since d00 = g0, we just write d11 + * into tmp. + */ + this.ffte.poly_LDLmv_fft(tmpsrc, tmp, treesrc, tree, g0src, g0, g1src, g1, g0src, g0, logn); + + /* + * Split d00 (currently in g0) and d11 (currently in tmp). We + * reuse g0 and g1 as temporary storage spaces: + * d00 splits into g1, g1+hn + * d11 splits into g0, g0+hn + */ + this.ffte.poly_split_fft(g1src, g1, g1src, g1 + hn, g0src, g0, logn); + this.ffte.poly_split_fft(g0src, g0, g0src, g0 + hn, tmpsrc, tmp, logn); + + /* + * Each split result is the first row of a new auto-adjoint + * quasicyclic matrix for the next recursive step. + */ + ffLDL_fft_inner(treesrc, tree + n, + g1src, g1, g1src, g1 + hn, logn - 1, tmpsrc, tmp); + ffLDL_fft_inner(treesrc, tree + n + (int)ffLDL_treesize(logn - 1), + g0src, g0, g0src, g0 + hn, logn - 1, tmpsrc, tmp); + } + + /* + * Compute the ffLDL tree of an auto-adjoint matrix G. The matrix + * is provided as three polynomials (FFT representation). + * + * The "tree" array is filled with the computed tree, of size + * (logn+1)*(2^logn) elements (see ffLDL_treesize()). + * + * Input arrays MUST NOT overlap, except possibly the three unmodified + * arrays g00, g01 and g11. tmp[] should have room for at least three + * polynomials of 2^logn elements each. + */ + internal void ffLDL_fft(FalconFPR[] treesrc, int tree, FalconFPR[] g00src, int g00, + FalconFPR[] g01src, int g01, FalconFPR[] g11src, int g11, + uint logn, FalconFPR[] tmpsrc, int tmp) + { + int n, hn; + int d00, d11; + + n = (int)1 << (int)logn; + if (n == 1) { + treesrc[tree+0] = g00src[g00+0]; + return; + } + hn = n >> 1; + d00 = tmp; + d11 = tmp + n; + tmp += n << 1; + + // memcpy(d00, g00, n * sizeof *g00); + Array.Copy(g00src, g00, tmpsrc, d00, n); + this.ffte.poly_LDLmv_fft(tmpsrc, d11, treesrc, tree, g00src, g00, g01src, g01, g11src, g11, logn); + + this.ffte.poly_split_fft(tmpsrc, tmp, tmpsrc, tmp + hn, tmpsrc, d00, logn); + this.ffte.poly_split_fft(tmpsrc, d00, tmpsrc, d00 + hn, tmpsrc, d11, logn); + // memcpy(d11, tmp, n * sizeof *tmp); + Array.Copy(tmpsrc, tmp, tmpsrc, d11, n); + ffLDL_fft_inner(treesrc, tree + n, + tmpsrc, d11, tmpsrc, d11 + hn, logn - 1, tmpsrc, tmp); + ffLDL_fft_inner(treesrc, tree + n + (int)ffLDL_treesize(logn - 1), + tmpsrc, d00, tmpsrc, d00 + hn, logn - 1, tmpsrc, tmp); + } + + /* + * Normalize an ffLDL tree: each leaf of value x is replaced with + * sigma / sqrt(x). + */ + internal void ffLDL_binary_normalize(FalconFPR[] treesrc, int tree, uint orig_logn, uint logn) + { + /* + * TODO: make an iterative version. + */ + int n; + + n = (int)1 << (int)logn; + if (n == 1) { + /* + * We actually store in the tree leaf the inverse of + * the value mandated by the specification: this + * saves a division both here and in the sampler. + */ + treesrc[tree+0] = this.fpre.fpr_mul(this.fpre.fpr_sqrt(treesrc[tree+0]), this.fpre.fpr_inv_sigma[orig_logn]); + } else { + ffLDL_binary_normalize(treesrc, tree + n, orig_logn, logn - 1); + ffLDL_binary_normalize(treesrc, tree + n + (int)ffLDL_treesize(logn - 1), + orig_logn, logn - 1); + } + } + + /* =================================================================== */ + + /* + * Convert an integer polynomial (with small values) into the + * representation with complex numbers. + */ + internal void smallints_to_fpr(FalconFPR[] rsrc, int r, sbyte[] tsrc, int t, uint logn) + { + int n, u; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + rsrc[r+u] = this.fpre.fpr_of(tsrc[t+u]); + } + } + + /* + * The expanded private key contains: + * - The B0 matrix (four elements) + * - The ffLDL tree + */ + + int skoff_b00(uint logn) + { + return 0; + } + + int skoff_b01(uint logn) + { + return (int)1 << (int)logn; + } + + int skoff_b10(uint logn) + { + return 2 * (int)1 << (int)logn; + } + + int skoff_b11(uint logn) + { + return 3 * (int)1 << (int)logn; + } + + int skoff_tree(uint logn) + { + return 4 * (int)1 << (int)logn; + } + + /* + * Perform Fast Fourier Sampling for target vector t. The Gram matrix + * is provided (G = [[g00, g01], [adj(g01), g11]]). The sampled vector + * is written over (t0,t1). The Gram matrix is modified as well. The + * tmp[] buffer must have room for four polynomials. + */ + internal void ffSampling_fft_dyntree(SamplerZ samp, + FalconFPR[] t0src, int t0, FalconFPR[] t1src, int t1, + FalconFPR[] g00src, int g00, FalconFPR[] g01src, int g01, FalconFPR[] g11src, int g11, + uint orig_logn, uint logn, FalconFPR[] tmpsrc, int tmp) + { + int n, hn; + int z0, z1; + + /* + * Deepest level: the LDL tree leaf value is just g00 (the + * array has length only 1 at this point); we normalize it + * with regards to sigma, then use it for sampling. + */ + if (logn == 0) { + FalconFPR leaf; + + leaf = g00src[g00+0]; + leaf = this.fpre.fpr_mul(this.fpre.fpr_sqrt(leaf), this.fpre.fpr_inv_sigma[orig_logn]); + t0src[t0+0] = this.fpre.fpr_of(samp.Sample(t0src[t0+0], leaf)); + t1src[t1+0] = this.fpre.fpr_of(samp.Sample(t1src[t1+0], leaf)); + return; + } + + n = (int)1 << (int)logn; + hn = n >> 1; + + /* + * Decompose G into LDL. We only need d00 (identical to g00), + * d11, and l10; we do that in place. + */ + this.ffte.poly_LDL_fft(g00src, g00, g01src, g01, g11src, g11, logn); + + /* + * Split d00 and d11 and expand them into half-size quasi-cyclic + * Gram matrices. We also save l10 in tmp[]. + */ + this.ffte.poly_split_fft(tmpsrc, tmp, tmpsrc, tmp + hn, g00src, g00, logn); + // memcpy(g00, tmp, n * sizeof *tmp); + Array.Copy(tmpsrc, tmp, g00src, g00, n); + this.ffte.poly_split_fft(tmpsrc, tmp, tmpsrc, tmp + hn, g11src, g11, logn); + // memcpy(g11, tmp, n * sizeof *tmp); + // memcpy(tmp, g01, n * sizeof *g01); + // memcpy(g01, g00, hn * sizeof *g00); + // memcpy(g01 + hn, g11, hn * sizeof *g00); + Array.Copy(tmpsrc, tmp, g11src, g11, n); + Array.Copy(g01src, g01, tmpsrc, tmp, n); + Array.Copy(g00src, g00,g01src, g01, hn); + Array.Copy(g11src, g11, g01src, g01 + hn, hn); + /* + * The half-size Gram matrices for the recursive LDL tree + * building are now: + * - left sub-tree: g00, g00+hn, g01 + * - right sub-tree: g11, g11+hn, g01+hn + * l10 is in tmp[]. + */ + + /* + * We split t1 and use the first recursive call on the two + * halves, using the right sub-tree. The result is merged + * back into tmp + 2*n. + */ + z1 = tmp + n; + this.ffte.poly_split_fft(tmpsrc, z1, tmpsrc, z1 + hn, tmpsrc, t1, logn); + ffSampling_fft_dyntree(samp, tmpsrc, z1, tmpsrc, z1 + hn, + g11src, g11, g11src, g11 + hn, g01src, g01 + hn, orig_logn, logn - 1, tmpsrc, z1 + n); + this.ffte.poly_merge_fft(tmpsrc, tmp + (n << 1), tmpsrc, z1, tmpsrc, z1 + hn, logn); + + /* + * Compute tb0 = t0 + (t1 - z1) * l10. + * At that point, l10 is in tmp, t1 is unmodified, and z1 is + * in tmp + (n << 1). The buffer in z1 is free. + * + * In the end, z1 is written over t1, and tb0 is in t0. + */ + // memcpy(z1, t1, n * sizeof *t1); + Array.Copy(tmpsrc, t1, tmpsrc, z1, n); + this.ffte.poly_sub(tmpsrc, z1, tmpsrc, tmp + (n << 1), logn); + // memcpy(t1, tmp + (n << 1), n * sizeof *tmp); + Array.Copy(tmpsrc, tmp + (n << 1), tmpsrc, t1, n); + this.ffte.poly_mul_fft(tmpsrc, tmp, tmpsrc, z1, logn); + this.ffte.poly_add(tmpsrc, t0, tmpsrc, tmp, logn); + + /* + * Second recursive invocation, on the split tb0 (currently in t0) + * and the left sub-tree. + */ + z0 = tmp; + this.ffte.poly_split_fft(tmpsrc, z0, tmpsrc, z0 + hn, tmpsrc, t0, logn); + ffSampling_fft_dyntree(samp, tmpsrc, z0, tmpsrc, z0 + hn, + g00src, g00, g00src, g00 + hn, g01src, g01, orig_logn, logn - 1, tmpsrc, z0 + n); + this.ffte.poly_merge_fft(tmpsrc, t0, tmpsrc, z0, tmpsrc, z0 + hn, logn); + } + + /* + * Perform Fast Fourier Sampling for target vector t and LDL tree T. + * tmp[] must have size for at least two polynomials of size 2^logn. + */ + internal void ffSampling_fft(SamplerZ samp, + FalconFPR[] z0src, int z0, FalconFPR[] z1src, int z1, + FalconFPR[] treesrc, int tree, + FalconFPR[] t0src, int t0, FalconFPR[] t1src, int t1, uint logn, + FalconFPR[] tmpsrc, int tmp) + { + int n, hn; + int tree0, tree1; + + /* + * When logn == 2, we inline the last two recursion levels. + */ + if (logn == 2) { + FalconFPR x0, x1, y0, y1, w0, w1, w2, w3, sigma; + FalconFPR a_re, a_im, b_re, b_im, c_re, c_im; + + tree0 = tree + 4; + tree1 = tree + 8; + + /* + * We split t1 into w*, then do the recursive invocation, + * with output in w*. We finally merge back into z1. + */ + a_re = t1src[t1+0]; + a_im = t1src[t1 + 2]; + b_re = t1src[t1 + 1]; + b_im = t1src[t1 + 3]; + c_re = this.fpre.fpr_add(a_re, b_re); + c_im = this.fpre.fpr_add(a_im, b_im); + w0 = this.fpre.fpr_half(c_re); + w1 = this.fpre.fpr_half(c_im); + c_re = this.fpre.fpr_sub(a_re, b_re); + c_im = this.fpre.fpr_sub(a_im, b_im); + w2 = this.fpre.fpr_mul(this.fpre.fpr_add(c_re, c_im), this.fpre.fpr_invsqrt8); + w3 = this.fpre.fpr_mul(this.fpre.fpr_sub(c_im, c_re), this.fpre.fpr_invsqrt8); + + x0 = w2; + x1 = w3; + sigma = treesrc[tree1 + 3]; + w2 = this.fpre.fpr_of(samp.Sample(x0, sigma)); + w3 = this.fpre.fpr_of(samp.Sample(x1, sigma)); + a_re = this.fpre.fpr_sub(x0, w2); + a_im = this.fpre.fpr_sub(x1, w3); + b_re = treesrc[tree1 + 0]; + b_im = treesrc[tree1 + 1]; + c_re = this.fpre.fpr_sub(this.fpre.fpr_mul(a_re, b_re), this.fpre.fpr_mul(a_im, b_im)); + c_im = this.fpre.fpr_add(this.fpre.fpr_mul(a_re, b_im), this.fpre.fpr_mul(a_im, b_re)); + x0 = this.fpre.fpr_add(c_re, w0); + x1 = this.fpre.fpr_add(c_im, w1); + sigma = treesrc[tree1 + 2]; + w0 = this.fpre.fpr_of(samp.Sample(x0, sigma)); + w1 = this.fpre.fpr_of(samp.Sample(x1, sigma)); + + a_re = w0; + a_im = w1; + b_re = w2; + b_im = w3; + c_re = this.fpre.fpr_mul(this.fpre.fpr_sub(b_re, b_im), this.fpre.fpr_invsqrt2); + c_im = this.fpre.fpr_mul(this.fpre.fpr_add(b_re, b_im), this.fpre.fpr_invsqrt2); + z1src[z1 + 0] = w0 = this.fpre.fpr_add(a_re, c_re); + z1src[z1 + 2] = w2 = this.fpre.fpr_add(a_im, c_im); + z1src[z1 + 1] = w1 = this.fpre.fpr_sub(a_re, c_re); + z1src[z1 + 3] = w3 = this.fpre.fpr_sub(a_im, c_im); + + /* + * Compute tb0 = t0 + (t1 - z1) * L. Value tb0 ends up in w*. + */ + w0 = this.fpre.fpr_sub(t1src[t1+0], w0); + w1 = this.fpre.fpr_sub(t1src[t1 + 1], w1); + w2 = this.fpre.fpr_sub(t1src[t1 + 2], w2); + w3 = this.fpre.fpr_sub(t1src[t1 + 3], w3); + + a_re = w0; + a_im = w2; + b_re = treesrc[tree+0]; + b_im = treesrc[tree + 2]; + w0 = this.fpre.fpr_sub(this.fpre.fpr_mul(a_re, b_re), this.fpre.fpr_mul(a_im, b_im)); + w2 = this.fpre.fpr_add(this.fpre.fpr_mul(a_re, b_im), this.fpre.fpr_mul(a_im, b_re)); + a_re = w1; + a_im = w3; + b_re = treesrc[tree + 1]; + b_im = treesrc[tree + 3]; + w1 = this.fpre.fpr_sub(this.fpre.fpr_mul(a_re, b_re), this.fpre.fpr_mul(a_im, b_im)); + w3 = this.fpre.fpr_add(this.fpre.fpr_mul(a_re, b_im), this.fpre.fpr_mul(a_im, b_re)); + + w0 = this.fpre.fpr_add(w0, t0src[t0+0]); + w1 = this.fpre.fpr_add(w1, t0src[t0 + 1]); + w2 = this.fpre.fpr_add(w2, t0src[t0 + 2]); + w3 = this.fpre.fpr_add(w3, t0src[t0 + 3]); + + /* + * Second recursive invocation. + */ + a_re = w0; + a_im = w2; + b_re = w1; + b_im = w3; + c_re = this.fpre.fpr_add(a_re, b_re); + c_im = this.fpre.fpr_add(a_im, b_im); + w0 = this.fpre.fpr_half(c_re); + w1 = this.fpre.fpr_half(c_im); + c_re = this.fpre.fpr_sub(a_re, b_re); + c_im = this.fpre.fpr_sub(a_im, b_im); + w2 = this.fpre.fpr_mul(this.fpre.fpr_add(c_re, c_im), this.fpre.fpr_invsqrt8); + w3 = this.fpre.fpr_mul(this.fpre.fpr_sub(c_im, c_re), this.fpre.fpr_invsqrt8); + + x0 = w2; + x1 = w3; + sigma = treesrc[tree0 + 3]; + w2 = y0 = this.fpre.fpr_of(samp.Sample(x0, sigma)); + w3 = y1 = this.fpre.fpr_of(samp.Sample(x1, sigma)); + a_re = this.fpre.fpr_sub(x0, y0); + a_im = this.fpre.fpr_sub(x1, y1); + b_re = treesrc[tree0 + 0]; + b_im = treesrc[tree0 + 1]; + c_re = this.fpre.fpr_sub(this.fpre.fpr_mul(a_re, b_re), this.fpre.fpr_mul(a_im, b_im)); + c_im = this.fpre.fpr_add(this.fpre.fpr_mul(a_re, b_im), this.fpre.fpr_mul(a_im, b_re)); + x0 = this.fpre.fpr_add(c_re, w0); + x1 = this.fpre.fpr_add(c_im, w1); + sigma = treesrc[tree0 + 2]; + w0 = this.fpre.fpr_of(samp.Sample(x0, sigma)); + w1 = this.fpre.fpr_of(samp.Sample(x1, sigma)); + + a_re = w0; + a_im = w1; + b_re = w2; + b_im = w3; + c_re = this.fpre.fpr_mul(this.fpre.fpr_sub(b_re, b_im), this.fpre.fpr_invsqrt2); + c_im = this.fpre.fpr_mul(this.fpre.fpr_add(b_re, b_im), this.fpre.fpr_invsqrt2); + z0src[z0 + 0] = this.fpre.fpr_add(a_re, c_re); + z0src[z0 + 2] = this.fpre.fpr_add(a_im, c_im); + z0src[z0 + 1] = this.fpre.fpr_sub(a_re, c_re); + z0src[z0 + 3] = this.fpre.fpr_sub(a_im, c_im); + + return; + } + + /* + * Case logn == 1 is reachable only when using Falcon-2 (the + * smallest size for which Falcon is mathematically defined, but + * of course way too insecure to be of any use). + */ + if (logn == 1) { + FalconFPR x0, x1, y0, y1, sigma; + FalconFPR a_re, a_im, b_re, b_im, c_re, c_im; + + x0 = t1src[t1+0]; + x1 = t1src[t1 + 1]; + sigma = treesrc[tree + 3]; + z1src[z1 + 0] = y0 = this.fpre.fpr_of(samp.Sample(x0, sigma)); + z1src[z1 + 1] = y1 = this.fpre.fpr_of(samp.Sample(x1, sigma)); + a_re = this.fpre.fpr_sub(x0, y0); + a_im = this.fpre.fpr_sub(x1, y1); + b_re = treesrc[tree+0]; + b_im = treesrc[tree + 1]; + c_re = this.fpre.fpr_sub(this.fpre.fpr_mul(a_re, b_re), this.fpre.fpr_mul(a_im, b_im)); + c_im = this.fpre.fpr_add(this.fpre.fpr_mul(a_re, b_im), this.fpre.fpr_mul(a_im, b_re)); + x0 = this.fpre.fpr_add(c_re, t0src[t0+0]); + x1 = this.fpre.fpr_add(c_im, t0src[t0 + 1]); + sigma = treesrc[tree + 2]; + z0src[z0 + 0] = this.fpre.fpr_of(samp.Sample(x0, sigma)); + z0src[z0 + 1] = this.fpre.fpr_of(samp.Sample(x1, sigma)); + + return; + } + + /* + * Normal end of recursion is for logn == 0. Since the last + * steps of the recursions were inlined in the blocks above + * (when logn == 1 or 2), this case is not reachable, and is + * retained here only for documentation purposes. + + if (logn == 0) { + fpr x0, x1, sigma; + + x0 = t0src[t0+0]; + x1 = t1src[t1+0]; + sigma = treesrc[tree+0]; + z0[0] = this.fpre.fpr_of(samp.sample(x0, sigma)); + z1src[z1 + 0] = this.fpre.fpr_of(samp.sample(x1, sigma)); + return; + } + + */ + + /* + * General recursive case (logn >= 3). + */ + + n = (int)1 << (int)logn; + hn = n >> 1; + tree0 = tree + n; + tree1 = tree + n + (int)ffLDL_treesize(logn - 1); + + /* + * We split t1 into z1 (reused as temporary storage), then do + * the recursive invocation, with output in tmp. We finally + * merge back into z1. + */ + this.ffte.poly_split_fft(z1src, z1, z1src, z1 + hn, t1src, t1, logn); + ffSampling_fft(samp, tmpsrc, tmp, tmpsrc, tmp + hn, + treesrc, tree1, z1src, z1, z1src, z1 + hn, logn - 1, tmpsrc, tmp + n); + this.ffte.poly_merge_fft(z1src, z1, tmpsrc, tmp, tmpsrc, tmp + hn, logn); + + /* + * Compute tb0 = t0 + (t1 - z1) * L. Value tb0 ends up in tmp[]. + */ + // memcpy(tmp, t1, n * sizeof *t1); + Array.Copy(t1src, t1, tmpsrc, tmp, n); + this.ffte.poly_sub(tmpsrc, tmp, z1src, z1, logn); + this.ffte.poly_mul_fft(tmpsrc, tmp, treesrc, tree, logn); + this.ffte.poly_add(tmpsrc, tmp, t0src, t0, logn); + + /* + * Second recursive invocation. + */ + this.ffte.poly_split_fft(z0src, z0, z0src, z0 + hn, tmpsrc, tmp, logn); + ffSampling_fft(samp, tmpsrc, tmp, tmpsrc, tmp + hn, + treesrc, tree0, z0src, z0, z0src, z0 + hn, logn - 1, tmpsrc, tmp + n); + this.ffte.poly_merge_fft(z0src, z0, tmpsrc, tmp, tmpsrc, tmp + hn, logn); + } + + /* + * Compute a signature: the signature contains two vectors, s1 and s2. + * The s1 vector is not returned. The squared norm of (s1,s2) is + * computed, and if it is short enough, then s2 is returned into the + * s2[] buffer, and 1 is returned; otherwise, s2[] is untouched and 0 is + * returned; the caller should then try again. This function uses an + * expanded key. + * + * tmp[] must have room for at least six polynomials. + */ + internal int do_sign_tree(SamplerZ samp, short[] s2src, int s2, + FalconFPR[] ex_keysrc, int expanded_key, + ushort[] hmsrc, int hm, + uint logn, FalconFPR[] tmpsrc, int tmp) + { + int n, u; + int t0, t1, tx, ty; + int b00, b01, b10, b11, tree; + FalconFPR ni; + uint sqn, ng; + short[] s1tmp, s2tmp; + + n = (int)1 << (int)logn; + t0 = tmp; + t1 = t0 + n; + b00 = expanded_key + skoff_b00(logn); + b01 = expanded_key + skoff_b01(logn); + b10 = expanded_key + skoff_b10(logn); + b11 = expanded_key + skoff_b11(logn); + tree = expanded_key + skoff_tree(logn); + + /* + * Set the target vector to [hm, 0] (hm is the hashed message). + */ + for (u = 0; u < n; u ++) { + tmpsrc[t0+u] = this.fpre.fpr_of(hmsrc[hm + u]); + /* This is implicit. + t1src[t1 + u] = fpr_zero; + */ + } + + /* + * Apply the lattice basis to obtain the real target + * vector (after normalization with regards to modulus). + */ + this.ffte.FFT(tmpsrc, t0, logn); + ni = this.fpre.fpr_inverse_of_q; + // memcpy(t1, t0, n * sizeof *t0); + Array.Copy(tmpsrc, t0, tmpsrc, t1, n); + this.ffte.poly_mul_fft(tmpsrc, t1, ex_keysrc, b01, logn); + this.ffte.poly_mulconst(tmpsrc, t1, this.fpre.fpr_neg(ni), logn); + this.ffte.poly_mul_fft(tmpsrc, t0, ex_keysrc, b11, logn); + this.ffte.poly_mulconst(tmpsrc, t0, ni, logn); + + tx = t1 + n; + ty = tx + n; + + /* + * Apply sampling. Output is written back in [tx, ty]. + */ + ffSampling_fft(samp, tmpsrc, tx, tmpsrc, ty, ex_keysrc, tree, tmpsrc, t0, tmpsrc, t1, logn, tmpsrc, ty + n); + + /* + * Get the lattice point corresponding to that tiny vector. + */ + // memcpy(t0, tx, n * sizeof *tx); + Array.Copy(tmpsrc, tx, tmpsrc, t0, n); + // memcpy(t1, ty, n * sizeof *ty); + Array.Copy(tmpsrc, ty, tmpsrc, t1, n); + this.ffte.poly_mul_fft(tmpsrc, tx, ex_keysrc, b00, logn); + this.ffte.poly_mul_fft(tmpsrc, ty, ex_keysrc, b10, logn); + this.ffte.poly_add(tmpsrc, tx, tmpsrc, ty, logn); + // memcpy(ty, t0, n * sizeof *t0); + Array.Copy(tmpsrc, t0, tmpsrc, ty, n); + this.ffte.poly_mul_fft(tmpsrc, ty, ex_keysrc, b01, logn); + + // memcpy(t0, tx, n * sizeof *tx); + Array.Copy(tmpsrc, tx, tmpsrc, t0, n); + this.ffte.poly_mul_fft(tmpsrc, t1, ex_keysrc, b11, logn); + this.ffte.poly_add(tmpsrc, t1, tmpsrc, ty, logn); + + this.ffte.iFFT(tmpsrc, t0, logn); + this.ffte.iFFT(tmpsrc, t1, logn); + + /* + * Compute the signature. + */ + s1tmp = new short[n]; + s2tmp = new short[n]; + sqn = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int z; + + z = (int)hmsrc[hm + u] - (int)this.fpre.fpr_rint(tmpsrc[t0+u]); + sqn += (uint)(z * z); + ng |= sqn; + s1tmp[u] = (short)z; + } + sqn |= (uint)(-(ng >> 31)); + + /* + * With "normal" degrees (e.g. 512 or 1024), it is very + * improbable that the computed vector is not short enough; + * however, it may happen in practice for the very reduced + * versions (e.g. degree 16 or below). In that case, the caller + * will loop, and we must not write anything into s2[] because + * s2[] may overlap with the hashed message hm[] and we need + * hm[] for the next iteration. + */ + for (u = 0; u < n; u ++) { + s2tmp[u] = (short)-this.fpre.fpr_rint(tmpsrc[t1 + u]); + } + if (this.common.is_short_half(sqn, s2tmp, 0, logn)) { + // memcpy(s2, s2tmp, n * sizeof *s2); + Array.Copy(s2tmp, 0, s2src, s2, n); + // memcpy(tmp, s1tmp, n * sizeof *s1tmp); + Array.Copy(s1tmp, 0, tmpsrc, tmp, n); + return 1; + } + return 0; + } + + /* + * Compute a signature: the signature contains two vectors, s1 and s2. + * The s1 vector is not returned. The squared norm of (s1,s2) is + * computed, and if it is short enough, then s2 is returned into the + * s2[] buffer, and 1 is returned; otherwise, s2[] is untouched and 0 is + * returned; the caller should then try again. + * + * tmp[] must have room for at least nine polynomials. + */ + internal int do_sign_dyn(SamplerZ samp, short[] s2src, int s2, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, + sbyte[] Fsrc, int F, sbyte[] Gsrc, int G, + ushort[] hmsrc, int hm, uint logn, FalconFPR[] tmpsrc, int tmp) + { + int n, u; + int t0, t1, tx, ty; + int b00, b01, b10, b11; + int g00, g01, g11; + FalconFPR ni; + uint sqn, ng; + short[] s1tmp, s2tmp; + + n = (int)1 << (int)logn; + + /* + * Lattice basis is B = [[g, -f], [G, -F]]. We convert it to FFT. + */ + b00 = tmp; + b01 = b00 + n; + b10 = b01 + n; + b11 = b10 + n; + smallints_to_fpr(tmpsrc, b01, fsrc, f, logn); + smallints_to_fpr(tmpsrc, b00, gsrc, g, logn); + smallints_to_fpr(tmpsrc, b11, Fsrc, F, logn); + smallints_to_fpr(tmpsrc, b10, Gsrc, G, logn); + this.ffte.FFT(tmpsrc, b01, logn); + this.ffte.FFT(tmpsrc, b00, logn); + this.ffte.FFT(tmpsrc, b11, logn); + this.ffte.FFT(tmpsrc, b10, logn); + this.ffte.poly_neg(tmpsrc, b01, logn); + this.ffte.poly_neg(tmpsrc, b11, logn); + + /* + * Compute the Gram matrix G = B·B*. Formulas are: + * g00 = b00*adj(b00) + b01*adj(b01) + * g01 = b00*adj(b10) + b01*adj(b11) + * g10 = b10*adj(b00) + b11*adj(b01) + * g11 = b10*adj(b10) + b11*adj(b11) + * + * For historical reasons, this implementation uses + * g00, g01 and g11 (upper triangle). g10 is not kept + * since it is equal to adj(g01). + * + * We _replace_ the matrix B with the Gram matrix, but we + * must keep b01 and b11 for computing the target vector. + */ + t0 = b11 + n; + t1 = t0 + n; + + // memcpy(t0, b01, n * sizeof *b01); + Array.Copy(tmpsrc, b01, tmpsrc, t0, n); + this.ffte.poly_mulselfadj_fft(tmpsrc, t0, logn); // t0 <- b01*adj(b01) + + // memcpy(t1, b00, n * sizeof *b00); + Array.Copy(tmpsrc, b00, tmpsrc, t1, n); + this.ffte.poly_muladj_fft(tmpsrc, t1, tmpsrc, b10, logn); // t1 <- b00*adj(b10) + this.ffte.poly_mulselfadj_fft(tmpsrc, b00, logn); // b00 <- b00*adj(b00) + this.ffte.poly_add(tmpsrc, b00, tmpsrc, t0, logn); // b00 <- g00 + // memcpy(t0, b01, n * sizeof *b01); + Array.Copy(tmpsrc, b01, tmpsrc, t0, n); + this.ffte.poly_muladj_fft(tmpsrc, b01, tmpsrc, b11, logn); // b01 <- b01*adj(b11) + this.ffte.poly_add(tmpsrc, b01, tmpsrc, t1, logn); // b01 <- g01 + + this.ffte.poly_mulselfadj_fft(tmpsrc, b10, logn); // b10 <- b10*adj(b10) + // memcpy(t1, b11, n * sizeof *b11); + Array.Copy(tmpsrc, b11, tmpsrc, t1, n); + this.ffte.poly_mulselfadj_fft(tmpsrc, t1, logn); // t1 <- b11*adj(b11) + this.ffte.poly_add(tmpsrc, b10, tmpsrc, t1, logn); // b10 <- g11 + + /* + * We rename variables to make things clearer. The three elements + * of the Gram matrix uses the first 3*n slots of tmp[], followed + * by b11 and b01 (in that order). + */ + g00 = b00; + g01 = b01; + g11 = b10; + b01 = t0; + t0 = b01 + n; + t1 = t0 + n; + + /* + * Memory layout at that point: + * g00 g01 g11 b11 b01 t0 t1 + */ + + /* + * Set the target vector to [hm, 0] (hm is the hashed message). + */ + for (u = 0; u < n; u ++) { + tmpsrc[t0+u] = this.fpre.fpr_of((short)hmsrc[hm + u]); + /* This is implicit. + t1src[t1 + u] = fpr_zero; + */ + } + + /* + * Apply the lattice basis to obtain the real target + * vector (after normalization with regards to modulus). + */ + this.ffte.FFT(tmpsrc, t0, logn); + ni = this.fpre.fpr_inverse_of_q; + // memcpy(t1, t0, n * sizeof *t0); + Array.Copy(tmpsrc, t0, tmpsrc, t1, n); + this.ffte.poly_mul_fft(tmpsrc, t1, tmpsrc, b01, logn); + this.ffte.poly_mulconst(tmpsrc, t1, this.fpre.fpr_neg(ni), logn); + this.ffte.poly_mul_fft(tmpsrc, t0, tmpsrc, b11, logn); + this.ffte.poly_mulconst(tmpsrc, t0, ni, logn); + + /* + * b01 and b11 can be discarded, so we move back (t0,t1). + * Memory layout is now: + * g00 g01 g11 t0 t1 + */ + // memcpy(b11, t0, n * 2 * sizeof *t0); + Array.Copy(tmpsrc, t0, tmpsrc, b11, n * 2); + t0 = g11 + n; + t1 = t0 + n; + + /* + * Apply sampling; result is written over (t0,t1). + */ + ffSampling_fft_dyntree(samp, + tmpsrc, t0, tmpsrc, t1, tmpsrc, g00, tmpsrc, g01, tmpsrc, g11, logn, logn, tmpsrc, t1 + n); + + /* + * We arrange the layout back to: + * b00 b01 b10 b11 t0 t1 + * + * We did not conserve the matrix basis, so we must recompute + * it now. + */ + b00 = tmp; + b01 = b00 + n; + b10 = b01 + n; + b11 = b10 + n; + // memmove(b11 + n, t0, n * 2 * sizeof *t0); + Array.Copy(tmpsrc, t0, tmpsrc, b11 + n, n * 2); + t0 = b11 + n; + t1 = t0 + n; + smallints_to_fpr(tmpsrc, b01, fsrc, f, logn); + smallints_to_fpr(tmpsrc, b00, gsrc, g, logn); + smallints_to_fpr(tmpsrc, b11, Fsrc, F, logn); + smallints_to_fpr(tmpsrc, b10, Gsrc, G, logn); + this.ffte.FFT(tmpsrc, b01, logn); + this.ffte.FFT(tmpsrc, b00, logn); + this.ffte.FFT(tmpsrc, b11, logn); + this.ffte.FFT(tmpsrc, b10, logn); + this.ffte.poly_neg(tmpsrc, b01, logn); + this.ffte.poly_neg(tmpsrc, b11, logn); + tx = t1 + n; + ty = tx + n; + + /* + * Get the lattice point corresponding to that tiny vector. + */ + // memcpy(tx, t0, n * sizeof *t0); + Array.Copy(tmpsrc, t0, tmpsrc, tx, n); + // memcpy(ty, t1, n * sizeof *t1); + Array.Copy(tmpsrc, t1, tmpsrc, ty, n); + this.ffte.poly_mul_fft(tmpsrc, tx, tmpsrc, b00, logn); + this.ffte.poly_mul_fft(tmpsrc, ty, tmpsrc, b10, logn); + this.ffte.poly_add(tmpsrc, tx, tmpsrc, ty, logn); + // memcpy(ty, t0, n * sizeof *t0); + Array.Copy(tmpsrc, t0, tmpsrc, ty, n); + this.ffte.poly_mul_fft(tmpsrc, ty, tmpsrc, b01, logn); + + // memcpy(t0, tx, n * sizeof *tx); + Array.Copy(tmpsrc, tx, tmpsrc, t0, n); + this.ffte.poly_mul_fft(tmpsrc, t1, tmpsrc, b11, logn); + this.ffte.poly_add(tmpsrc, t1, tmpsrc, ty, logn); + this.ffte.iFFT(tmpsrc, t0, logn); + this.ffte.iFFT(tmpsrc, t1, logn); + + s1tmp = new short[n]; + sqn = 0; + ng = 0; + for (u = 0; u < n; u ++) { + int z; + + z = (int)hmsrc[hm + u] - (int)this.fpre.fpr_rint(tmpsrc[t0+u]); + sqn += (uint)(z * z); + ng |= sqn; + s1tmp[u] = (short)z; + } + sqn |= (uint)(-(ng >> 31)); + + /* + * With "normal" degrees (e.g. 512 or 1024), it is very + * improbable that the computed vector is not short enough; + * however, it may happen in practice for the very reduced + * versions (e.g. degree 16 or below). In that case, the caller + * will loop, and we must not write anything into s2[] because + * s2[] may overlap with the hashed message hm[] and we need + * hm[] for the next iteration. + */ + s2tmp = new short[n]; + for (u = 0; u < n; u ++) { + s2tmp[u] = (short)-this.fpre.fpr_rint(tmpsrc[t1 + u]); + } + if (this.common.is_short_half(sqn, s2tmp, 0, logn)) { + // memcpy(s2, s2tmp, n * sizeof *s2); + Array.Copy(s2tmp, 0, s2src, s2, n); + // memcpy(tmp, s1tmp, n * sizeof *s1tmp); + //Array.Copy(s1tmp, 0, tmpsrc, tmp, n); + return 1; + } + return 0; + } + + internal void sign_tree(short[] sigsrc, int sig, SHAKE256 rng, + FalconFPR[] ex_keysrc, int expanded_key, + ushort[] hmsrc, int hm, uint logn, FalconFPR[] tmpsrc, int tmp) + { + + int ftmp = tmp; + for (;;) { + /* + * Signature produces short vectors s1 and s2. The + * signature is acceptable only if the aggregate vector + * s1,s2 is short; we must use the same bound as the + * verifier. + * + * If the signature is acceptable, then we return only s2 + * (the verifier recomputes s1 from s2, the hashed message, + * and the public key). + */ + + /* + * Normal sampling. We use a fast PRNG seeded from our + * SHAKE context ('rng'). + */ + FalconRNG prng = new FalconRNG(); + prng.prng_init(rng); + SamplerZ samp = new SamplerZ(prng, this.fpre.fpr_sigma_min[logn], this.fpre); + + + /* + * Do the actual signature. + */ + if (do_sign_tree(samp, sigsrc, sig, + ex_keysrc, expanded_key, hmsrc, hm, logn, tmpsrc, ftmp) != 0) + { + break; + } + } + } + + internal void sign_dyn(short[] sigsrc, int sig, SHAKE256 rng, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, + sbyte[] Fsrc, int F, sbyte[] Gsrc, int G, + ushort[] hmsrc, int hm, uint logn, FalconFPR[] tmpsrc, int tmp) + { + for (;;) { + /* + * Signature produces short vectors s1 and s2. The + * signature is acceptable only if the aggregate vector + * s1,s2 is short; we must use the same bound as the + * verifier. + * + * If the signature is acceptable, then we return only s2 + * (the verifier recomputes s1 from s2, the hashed message, + * and the public key). + */ + + /* + * Normal sampling. We use a fast PRNG seeded from our + * SHAKE context ('rng'). + */ + + FalconRNG prng = new FalconRNG(); + prng.prng_init(rng); + SamplerZ samp = new SamplerZ(prng, this.fpre.fpr_sigma_min[logn], this.fpre); + + /* + * Do the actual signature. + */ + if (do_sign_dyn(samp, sigsrc, sig, + fsrc, f, gsrc, g, Fsrc, F, Gsrc, G, hmsrc, hm, logn, tmpsrc, tmp) != 0) + { + break; + } + } + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconSigner.cs b/crypto/src/pqc/crypto/falcon/FalconSigner.cs new file mode 100644 index 000000000..8af2f4c93 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconSigner.cs @@ -0,0 +1,76 @@ +using System; +using Org.BouncyCastle.Crypto; +using Org.BouncyCastle.Pqc.Crypto; +using Org.BouncyCastle.Security; +using Org.BouncyCastle.Crypto.Parameters; +using Org.BouncyCastle.Utilities; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + public class FalconSigner + : IMessageSigner + { + private byte[] encodedkey; + private FalconNIST nist; + + public void Init(bool forSigning, ICipherParameters param) + { + if (forSigning) + { + if (param is ParametersWithRandom) + { + FalconPrivateKeyParameters skparam = ((FalconPrivateKeyParameters)((ParametersWithRandom)param).Parameters); + encodedkey = skparam.GetEncoded(); + nist = new FalconNIST( + ((ParametersWithRandom)param).Random, + skparam.GetParameters().GetLogN(), + skparam.GetParameters().GetNonceLength()); + } + else + { + FalconPrivateKeyParameters skparam = (FalconPrivateKeyParameters)param; + encodedkey = ((FalconPrivateKeyParameters)param).GetEncoded(); + nist = new FalconNIST( + new SecureRandom(), + // CryptoServicesRegistrar.GetSecureRandom(), + skparam.GetParameters().GetLogN(), + skparam.GetParameters().GetNonceLength() + ); + // TODO when CryptoServicesRegistrar has been implemented, use that instead + + } + } + else + { + FalconPublicKeyParameters pkparam = (FalconPublicKeyParameters)param; + encodedkey = pkparam.GetEncoded(); + nist = new FalconNIST( + new SecureRandom(), + // CryptoServicesRegistrar.GetSecureRandom() + pkparam.GetParameters().GetLogN(), + pkparam.GetParameters().GetNonceLength()); + } + } + + public byte[] GenerateSignature(byte[] message) + { + byte[] sm = new byte[nist.GetCryptoBytes()]; + + return nist.crypto_sign(sm, message, 0, (uint)message.Length, encodedkey, 0); + } + + public bool VerifySignature(byte[] message, byte[] signature) + { + if (signature[0] != (byte)(0x30 + nist.GetLogn())) + { + return false; + } + byte[] nonce = new byte[nist.GetNonceLength()]; + byte[] sig = new byte[signature.Length - nist.GetNonceLength() - 1]; + Array.Copy(signature, 1, nonce, 0, nist.GetNonceLength()); + Array.Copy(signature, nist.GetNonceLength() + 1, sig, 0, signature.Length - nist.GetNonceLength() - 1); + bool res = nist.crypto_sign_open(sig,nonce,message,encodedkey,0) == 0; + return res; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconSmallPrime.cs b/crypto/src/pqc/crypto/falcon/FalconSmallPrime.cs new file mode 100644 index 000000000..83a7cdfaf --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconSmallPrime.cs @@ -0,0 +1,46 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconSmallPrime + { + /* + * License from the reference C code (the code was copied then modified + * to function in C#, this file corresponds to the small_prime type defined + * in keygen.c): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + internal uint p; + internal uint g; + internal uint s; + + internal FalconSmallPrime(uint p, uint g, uint s) { + this.p = p; + this.g = g; + this.s = s; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconSmallPrimes.cs b/crypto/src/pqc/crypto/falcon/FalconSmallPrimes.cs new file mode 100644 index 000000000..dcefa7f05 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconSmallPrimes.cs @@ -0,0 +1,536 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Threading.Tasks; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconSmallPrimes + { + internal FalconSmallPrimes() {} + internal FalconSmallPrime[] PRIMES = { + new FalconSmallPrime( 2147473409, 383167813, 10239 ), + new FalconSmallPrime( 2147389441, 211808905, 471403745 ), + new FalconSmallPrime( 2147387393, 37672282, 1329335065 ), + new FalconSmallPrime( 2147377153, 1977035326, 968223422 ), + new FalconSmallPrime( 2147358721, 1067163706, 132460015 ), + new FalconSmallPrime( 2147352577, 1606082042, 598693809 ), + new FalconSmallPrime( 2147346433, 2033915641, 1056257184 ), + new FalconSmallPrime( 2147338241, 1653770625, 421286710 ), + new FalconSmallPrime( 2147309569, 631200819, 1111201074 ), + new FalconSmallPrime( 2147297281, 2038364663, 1042003613 ), + new FalconSmallPrime( 2147295233, 1962540515, 19440033 ), + new FalconSmallPrime( 2147239937, 2100082663, 353296760 ), + new FalconSmallPrime( 2147235841, 1991153006, 1703918027 ), + new FalconSmallPrime( 2147217409, 516405114, 1258919613 ), + new FalconSmallPrime( 2147205121, 409347988, 1089726929 ), + new FalconSmallPrime( 2147196929, 927788991, 1946238668 ), + new FalconSmallPrime( 2147178497, 1136922411, 1347028164 ), + new FalconSmallPrime( 2147100673, 868626236, 701164723 ), + new FalconSmallPrime( 2147082241, 1897279176, 617820870 ), + new FalconSmallPrime( 2147074049, 1888819123, 158382189 ), + new FalconSmallPrime( 2147051521, 25006327, 522758543 ), + new FalconSmallPrime( 2147043329, 327546255, 37227845 ), + new FalconSmallPrime( 2147039233, 766324424, 1133356428 ), + new FalconSmallPrime( 2146988033, 1862817362, 73861329 ), + new FalconSmallPrime( 2146963457, 404622040, 653019435 ), + new FalconSmallPrime( 2146959361, 1936581214, 995143093 ), + new FalconSmallPrime( 2146938881, 1559770096, 634921513 ), + new FalconSmallPrime( 2146908161, 422623708, 1985060172 ), + new FalconSmallPrime( 2146885633, 1751189170, 298238186 ), + new FalconSmallPrime( 2146871297, 578919515, 291810829 ), + new FalconSmallPrime( 2146846721, 1114060353, 915902322 ), + new FalconSmallPrime( 2146834433, 2069565474, 47859524 ), + new FalconSmallPrime( 2146818049, 1552824584, 646281055 ), + new FalconSmallPrime( 2146775041, 1906267847, 1597832891 ), + new FalconSmallPrime( 2146756609, 1847414714, 1228090888 ), + new FalconSmallPrime( 2146744321, 1818792070, 1176377637 ), + new FalconSmallPrime( 2146738177, 1118066398, 1054971214 ), + new FalconSmallPrime( 2146736129, 52057278, 933422153 ), + new FalconSmallPrime( 2146713601, 592259376, 1406621510 ), + new FalconSmallPrime( 2146695169, 263161877, 1514178701 ), + new FalconSmallPrime( 2146656257, 685363115, 384505091 ), + new FalconSmallPrime( 2146650113, 927727032, 537575289 ), + new FalconSmallPrime( 2146646017, 52575506, 1799464037 ), + new FalconSmallPrime( 2146643969, 1276803876, 1348954416 ), + new FalconSmallPrime( 2146603009, 814028633, 1521547704 ), + new FalconSmallPrime( 2146572289, 1846678872, 1310832121 ), + new FalconSmallPrime( 2146547713, 919368090, 1019041349 ), + new FalconSmallPrime( 2146508801, 671847612, 38582496 ), + new FalconSmallPrime( 2146492417, 283911680, 532424562 ), + new FalconSmallPrime( 2146490369, 1780044827, 896447978 ), + new FalconSmallPrime( 2146459649, 327980850, 1327906900 ), + new FalconSmallPrime( 2146447361, 1310561493, 958645253 ), + new FalconSmallPrime( 2146441217, 412148926, 287271128 ), + new FalconSmallPrime( 2146437121, 293186449, 2009822534 ), + new FalconSmallPrime( 2146430977, 179034356, 1359155584 ), + new FalconSmallPrime( 2146418689, 1517345488, 1790248672 ), + new FalconSmallPrime( 2146406401, 1615820390, 1584833571 ), + new FalconSmallPrime( 2146404353, 826651445, 607120498 ), + new FalconSmallPrime( 2146379777, 3816988, 1897049071 ), + new FalconSmallPrime( 2146363393, 1221409784, 1986921567 ), + new FalconSmallPrime( 2146355201, 1388081168, 849968120 ), + new FalconSmallPrime( 2146336769, 1803473237, 1655544036 ), + new FalconSmallPrime( 2146312193, 1023484977, 273671831 ), + new FalconSmallPrime( 2146293761, 1074591448, 467406983 ), + new FalconSmallPrime( 2146283521, 831604668, 1523950494 ), + new FalconSmallPrime( 2146203649, 712865423, 1170834574 ), + new FalconSmallPrime( 2146154497, 1764991362, 1064856763 ), + new FalconSmallPrime( 2146142209, 627386213, 1406840151 ), + new FalconSmallPrime( 2146127873, 1638674429, 2088393537 ), + new FalconSmallPrime( 2146099201, 1516001018, 690673370 ), + new FalconSmallPrime( 2146093057, 1294931393, 315136610 ), + new FalconSmallPrime( 2146091009, 1942399533, 973539425 ), + new FalconSmallPrime( 2146078721, 1843461814, 2132275436 ), + new FalconSmallPrime( 2146060289, 1098740778, 360423481 ), + new FalconSmallPrime( 2146048001, 1617213232, 1951981294 ), + new FalconSmallPrime( 2146041857, 1805783169, 2075683489 ), + new FalconSmallPrime( 2146019329, 272027909, 1753219918 ), + new FalconSmallPrime( 2145986561, 1206530344, 2034028118 ), + new FalconSmallPrime( 2145976321, 1243769360, 1173377644 ), + new FalconSmallPrime( 2145964033, 887200839, 1281344586 ), + new FalconSmallPrime( 2145906689, 1651026455, 906178216 ), + new FalconSmallPrime( 2145875969, 1673238256, 1043521212 ), + new FalconSmallPrime( 2145871873, 1226591210, 1399796492 ), + new FalconSmallPrime( 2145841153, 1465353397, 1324527802 ), + new FalconSmallPrime( 2145832961, 1150638905, 554084759 ), + new FalconSmallPrime( 2145816577, 221601706, 427340863 ), + new FalconSmallPrime( 2145785857, 608896761, 316590738 ), + new FalconSmallPrime( 2145755137, 1712054942, 1684294304 ), + new FalconSmallPrime( 2145742849, 1302302867, 724873116 ), + new FalconSmallPrime( 2145728513, 516717693, 431671476 ), + new FalconSmallPrime( 2145699841, 524575579, 1619722537 ), + new FalconSmallPrime( 2145691649, 1925625239, 982974435 ), + new FalconSmallPrime( 2145687553, 463795662, 1293154300 ), + new FalconSmallPrime( 2145673217, 771716636, 881778029 ), + new FalconSmallPrime( 2145630209, 1509556977, 837364988 ), + new FalconSmallPrime( 2145595393, 229091856, 851648427 ), + new FalconSmallPrime( 2145587201, 1796903241, 635342424 ), + new FalconSmallPrime( 2145525761, 715310882, 1677228081 ), + new FalconSmallPrime( 2145495041, 1040930522, 200685896 ), + new FalconSmallPrime( 2145466369, 949804237, 1809146322 ), + new FalconSmallPrime( 2145445889, 1673903706, 95316881 ), + new FalconSmallPrime( 2145390593, 806941852, 1428671135 ), + new FalconSmallPrime( 2145372161, 1402525292, 159350694 ), + new FalconSmallPrime( 2145361921, 2124760298, 1589134749 ), + new FalconSmallPrime( 2145359873, 1217503067, 1561543010 ), + new FalconSmallPrime( 2145355777, 338341402, 83865711 ), + new FalconSmallPrime( 2145343489, 1381532164, 641430002 ), + new FalconSmallPrime( 2145325057, 1883895478, 1528469895 ), + new FalconSmallPrime( 2145318913, 1335370424, 65809740 ), + new FalconSmallPrime( 2145312769, 2000008042, 1919775760 ), + new FalconSmallPrime( 2145300481, 961450962, 1229540578 ), + new FalconSmallPrime( 2145282049, 910466767, 1964062701 ), + new FalconSmallPrime( 2145232897, 816527501, 450152063 ), + new FalconSmallPrime( 2145218561, 1435128058, 1794509700 ), + new FalconSmallPrime( 2145187841, 33505311, 1272467582 ), + new FalconSmallPrime( 2145181697, 269767433, 1380363849 ), + new FalconSmallPrime( 2145175553, 56386299, 1316870546 ), + new FalconSmallPrime( 2145079297, 2106880293, 1391797340 ), + new FalconSmallPrime( 2145021953, 1347906152, 720510798 ), + new FalconSmallPrime( 2145015809, 206769262, 1651459955 ), + new FalconSmallPrime( 2145003521, 1885513236, 1393381284 ), + new FalconSmallPrime( 2144960513, 1810381315, 31937275 ), + new FalconSmallPrime( 2144944129, 1306487838, 2019419520 ), + new FalconSmallPrime( 2144935937, 37304730, 1841489054 ), + new FalconSmallPrime( 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1950165220 ), + new FalconSmallPrime( 2137526273, 1947629754, 1500789441 ), + new FalconSmallPrime( 2137516033, 719902645, 1499525372 ), + new FalconSmallPrime( 2137491457, 230451261, 556382829 ), + new FalconSmallPrime( 2137440257, 979573541, 412760291 ), + new FalconSmallPrime( 2137374721, 927841248, 1954137185 ), + new FalconSmallPrime( 2137362433, 1243778559, 861024672 ), + new FalconSmallPrime( 2137313281, 1341338501, 980638386 ), + new FalconSmallPrime( 2137311233, 937415182, 1793212117 ), + new FalconSmallPrime( 2137255937, 795331324, 1410253405 ), + new FalconSmallPrime( 2137243649, 150756339, 1966999887 ), + new FalconSmallPrime( 2137182209, 163346914, 1939301431 ), + new FalconSmallPrime( 2137171969, 1952552395, 758913141 ), + new FalconSmallPrime( 2137159681, 570788721, 218668666 ), + new FalconSmallPrime( 2137147393, 1896656810, 2045670345 ), + new FalconSmallPrime( 2137141249, 358493842, 518199643 ), + new FalconSmallPrime( 2137139201, 1505023029, 674695848 ), + new FalconSmallPrime( 2137133057, 27911103, 830956306 ), + new FalconSmallPrime( 2137122817, 439771337, 1555268614 ), + new FalconSmallPrime( 2137116673, 790988579, 1871449599 ), + new FalconSmallPrime( 2137110529, 432109234, 811805080 ), + new FalconSmallPrime( 2137102337, 1357900653, 1184997641 ), + new FalconSmallPrime( 2137098241, 515119035, 1715693095 ), + new FalconSmallPrime( 2137090049, 408575203, 2085660657 ), + new FalconSmallPrime( 2137085953, 2097793407, 1349626963 ), + new FalconSmallPrime( 2137055233, 1556739954, 1449960883 ), + new FalconSmallPrime( 2137030657, 1545758650, 1369303716 ), + new FalconSmallPrime( 2136987649, 332602570, 103875114 ), + new FalconSmallPrime( 2136969217, 1499989506, 1662964115 ), + new FalconSmallPrime( 2136924161, 857040753, 4738842 ), + new FalconSmallPrime( 2136895489, 1948872712, 570436091 ), + new FalconSmallPrime( 2136893441, 58969960, 1568349634 ), + new FalconSmallPrime( 2136887297, 2127193379, 273612548 ), + new FalconSmallPrime( 2136850433, 111208983, 1181257116 ), + new FalconSmallPrime( 2136809473, 1627275942, 1680317971 ), + new FalconSmallPrime( 2136764417, 1574888217, 14011331 ), + new FalconSmallPrime( 2136741889, 14011055, 1129154251 ), + new FalconSmallPrime( 2136727553, 35862563, 1838555253 ), + new FalconSmallPrime( 2136721409, 310235666, 1363928244 ), + new FalconSmallPrime( 2136698881, 1612429202, 1560383828 ), + new FalconSmallPrime( 2136649729, 1138540131, 800014364 ), + new FalconSmallPrime( 2136606721, 602323503, 1433096652 ), + new FalconSmallPrime( 2136563713, 182209265, 1919611038 ), + new FalconSmallPrime( 2136555521, 324156477, 165591039 ), + new FalconSmallPrime( 2136549377, 195513113, 217165345 ), + new FalconSmallPrime( 2136526849, 1050768046, 939647887 ), + new FalconSmallPrime( 2136508417, 1886286237, 1619926572 ), + new FalconSmallPrime( 2136477697, 609647664, 35065157 ), + new FalconSmallPrime( 2136471553, 679352216, 1452259468 ), + new FalconSmallPrime( 2136457217, 128630031, 824816521 ), + new FalconSmallPrime( 2136422401, 19787464, 1526049830 ), + new FalconSmallPrime( 2136420353, 698316836, 1530623527 ), + new FalconSmallPrime( 2136371201, 1651862373, 1804812805 ), + new FalconSmallPrime( 2136334337, 326596005, 336977082 ), + new FalconSmallPrime( 2136322049, 63253370, 1904972151 ), + new FalconSmallPrime( 2136297473, 312176076, 172182411 ), + new FalconSmallPrime( 2136248321, 381261841, 369032670 ), + new FalconSmallPrime( 2136242177, 358688773, 1640007994 ), + new FalconSmallPrime( 2136229889, 512677188, 75585225 ), + new FalconSmallPrime( 2136219649, 2095003250, 1970086149 ), + new FalconSmallPrime( 2136207361, 1909650722, 537760675 ), + new FalconSmallPrime( 2136176641, 1334616195, 1533487619 ), + new FalconSmallPrime( 2136158209, 2096285632, 1793285210 ), + new FalconSmallPrime( 2136143873, 1897347517, 293843959 ), + new FalconSmallPrime( 2136133633, 923586222, 1022655978 ), + new FalconSmallPrime( 2136096769, 1464868191, 1515074410 ), + new FalconSmallPrime( 2136094721, 2020679520, 2061636104 ), + new FalconSmallPrime( 2136076289, 290798503, 1814726809 ), + new FalconSmallPrime( 2136041473, 156415894, 1250757633 ), + new FalconSmallPrime( 2135996417, 297459940, 1132158924 ), + new FalconSmallPrime( 2135955457, 538755304, 1688831340 ), + new FalconSmallPrime( 0, 0, 0 ) + }; + } +} diff --git a/crypto/src/pqc/crypto/falcon/FalconVrfy.cs b/crypto/src/pqc/crypto/falcon/FalconVrfy.cs new file mode 100644 index 000000000..4f28a77d9 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/FalconVrfy.cs @@ -0,0 +1,860 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class FalconVrfy + { + FalconCommon common; + internal FalconVrfy() { + this.common = new FalconCommon(); + } + internal FalconVrfy(FalconCommon common) { + this.common = common; + } + + /* + * License from the reference C code (the code was copied then modified + * to function in C#): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + /* ===================================================================== */ + /* + * Constants for NTT. + * + * n = 2^logn (2 <= n <= 1024) + * phi = X^n + 1 + * q = 12289 + * q0i = -1/q mod 2^16 + * R = 2^16 mod q + * R2 = 2^32 mod q + */ + + const int Q = 12289; + const int Q0I = 12287; + const int R = 4091; + const int R2 = 10952; + + /* + * Table for NTT, binary case: + * GMb[x] = R*(g^rev(x)) mod q + * where g = 7 (it is a 2048-th primitive root of 1 modulo q) + * and rev() is the bit-reversal function over 10 bits. + */ + internal ushort[] GMb = { + 4091, 7888, 11060, 11208, 6960, 4342, 6275, 9759, + 1591, 6399, 9477, 5266, 586, 5825, 7538, 9710, + 1134, 6407, 1711, 965, 7099, 7674, 3743, 6442, + 10414, 8100, 1885, 1688, 1364, 10329, 10164, 9180, + 12210, 6240, 997, 117, 4783, 4407, 1549, 7072, + 2829, 6458, 4431, 8877, 7144, 2564, 5664, 4042, + 12189, 432, 10751, 1237, 7610, 1534, 3983, 7863, + 2181, 6308, 8720, 6570, 4843, 1690, 14, 3872, + 5569, 9368, 12163, 2019, 7543, 2315, 4673, 7340, + 1553, 1156, 8401, 11389, 1020, 2967, 10772, 7045, + 3316, 11236, 5285, 11578, 10637, 10086, 9493, 6180, + 9277, 6130, 3323, 883, 10469, 489, 1502, 2851, + 11061, 9729, 2742, 12241, 4970, 10481, 10078, 1195, + 730, 1762, 3854, 2030, 5892, 10922, 9020, 5274, + 9179, 3604, 3782, 10206, 3180, 3467, 4668, 2446, + 7613, 9386, 834, 7703, 6836, 3403, 5351, 12276, + 3580, 1739, 10820, 9787, 10209, 4070, 12250, 8525, + 10401, 2749, 7338, 10574, 6040, 943, 9330, 1477, + 6865, 9668, 3585, 6633, 12145, 4063, 3684, 7680, + 8188, 6902, 3533, 9807, 6090, 727, 10099, 7003, + 6945, 1949, 9731, 10559, 6057, 378, 7871, 8763, + 8901, 9229, 8846, 4551, 9589, 11664, 7630, 8821, + 5680, 4956, 6251, 8388, 10156, 8723, 2341, 3159, + 1467, 5460, 8553, 7783, 2649, 2320, 9036, 6188, + 737, 3698, 4699, 5753, 9046, 3687, 16, 914, + 5186, 10531, 4552, 1964, 3509, 8436, 7516, 5381, + 10733, 3281, 7037, 1060, 2895, 7156, 8887, 5357, + 6409, 8197, 2962, 6375, 5064, 6634, 5625, 278, + 932, 10229, 8927, 7642, 351, 9298, 237, 5858, + 7692, 3146, 12126, 7586, 2053, 11285, 3802, 5204, + 4602, 1748, 11300, 340, 3711, 4614, 300, 10993, + 5070, 10049, 11616, 12247, 7421, 10707, 5746, 5654, + 3835, 5553, 1224, 8476, 9237, 3845, 250, 11209, + 4225, 6326, 9680, 12254, 4136, 2778, 692, 8808, + 6410, 6718, 10105, 10418, 3759, 7356, 11361, 8433, + 6437, 3652, 6342, 8978, 5391, 2272, 6476, 7416, + 8418, 10824, 11986, 5733, 876, 7030, 2167, 2436, + 3442, 9217, 8206, 4858, 5964, 2746, 7178, 1434, + 7389, 8879, 10661, 11457, 4220, 1432, 10832, 4328, + 8557, 1867, 9454, 2416, 3816, 9076, 686, 5393, + 2523, 4339, 6115, 619, 937, 2834, 7775, 3279, + 2363, 7488, 6112, 5056, 824, 10204, 11690, 1113, + 2727, 9848, 896, 2028, 5075, 2654, 10464, 7884, + 12169, 5434, 3070, 6400, 9132, 11672, 12153, 4520, + 1273, 9739, 11468, 9937, 10039, 9720, 2262, 9399, + 11192, 315, 4511, 1158, 6061, 6751, 11865, 357, + 7367, 4550, 983, 8534, 8352, 10126, 7530, 9253, + 4367, 5221, 3999, 8777, 3161, 6990, 4130, 11652, + 3374, 11477, 1753, 292, 8681, 2806, 10378, 12188, + 5800, 11811, 3181, 1988, 1024, 9340, 2477, 10928, + 4582, 6750, 3619, 5503, 5233, 2463, 8470, 7650, + 7964, 6395, 1071, 1272, 3474, 11045, 3291, 11344, + 8502, 9478, 9837, 1253, 1857, 6233, 4720, 11561, + 6034, 9817, 3339, 1797, 2879, 6242, 5200, 2114, + 7962, 9353, 11363, 5475, 6084, 9601, 4108, 7323, + 10438, 9471, 1271, 408, 6911, 3079, 360, 8276, + 11535, 9156, 9049, 11539, 850, 8617, 784, 7919, + 8334, 12170, 1846, 10213, 12184, 7827, 11903, 5600, + 9779, 1012, 721, 2784, 6676, 6552, 5348, 4424, + 6816, 8405, 9959, 5150, 2356, 5552, 5267, 1333, + 8801, 9661, 7308, 5788, 4910, 909, 11613, 4395, + 8238, 6686, 4302, 3044, 2285, 12249, 1963, 9216, + 4296, 11918, 695, 4371, 9793, 4884, 2411, 10230, + 2650, 841, 3890, 10231, 7248, 8505, 11196, 6688, + 4059, 6060, 3686, 4722, 11853, 5816, 7058, 6868, + 11137, 7926, 4894, 12284, 4102, 3908, 3610, 6525, + 7938, 7982, 11977, 6755, 537, 4562, 1623, 8227, + 11453, 7544, 906, 11816, 9548, 10858, 9703, 2815, + 11736, 6813, 6979, 819, 8903, 6271, 10843, 348, + 7514, 8339, 6439, 694, 852, 5659, 2781, 3716, + 11589, 3024, 1523, 8659, 4114, 10738, 3303, 5885, + 2978, 7289, 11884, 9123, 9323, 11830, 98, 2526, + 2116, 4131, 11407, 1844, 3645, 3916, 8133, 2224, + 10871, 8092, 9651, 5989, 7140, 8480, 1670, 159, + 10923, 4918, 128, 7312, 725, 9157, 5006, 6393, + 3494, 6043, 10972, 6181, 11838, 3423, 10514, 7668, + 3693, 6658, 6905, 11953, 10212, 11922, 9101, 8365, + 5110, 45, 2400, 1921, 4377, 2720, 1695, 51, + 2808, 650, 1896, 9997, 9971, 11980, 8098, 4833, + 4135, 4257, 5838, 4765, 10985, 11532, 590, 12198, + 482, 12173, 2006, 7064, 10018, 3912, 12016, 10519, + 11362, 6954, 2210, 284, 5413, 6601, 3865, 10339, + 11188, 6231, 517, 9564, 11281, 3863, 1210, 4604, + 8160, 11447, 153, 7204, 5763, 5089, 9248, 12154, + 11748, 1354, 6672, 179, 5532, 2646, 5941, 12185, + 862, 3158, 477, 7279, 5678, 7914, 4254, 302, + 2893, 10114, 6890, 9560, 9647, 11905, 4098, 9824, + 10269, 1353, 10715, 5325, 6254, 3951, 1807, 6449, + 5159, 1308, 8315, 3404, 1877, 1231, 112, 6398, + 11724, 12272, 7286, 1459, 12274, 9896, 3456, 800, + 1397, 10678, 103, 7420, 7976, 936, 764, 632, + 7996, 8223, 8445, 7758, 10870, 9571, 2508, 1946, + 6524, 10158, 1044, 4338, 2457, 3641, 1659, 4139, + 4688, 9733, 11148, 3946, 2082, 5261, 2036, 11850, + 7636, 12236, 5366, 2380, 1399, 7720, 2100, 3217, + 10912, 8898, 7578, 11995, 2791, 1215, 3355, 2711, + 2267, 2004, 8568, 10176, 3214, 2337, 1750, 4729, + 4997, 7415, 6315, 12044, 4374, 7157, 4844, 211, + 8003, 10159, 9290, 11481, 1735, 2336, 5793, 9875, + 8192, 986, 7527, 1401, 870, 3615, 8465, 2756, + 9770, 2034, 10168, 3264, 6132, 54, 2880, 4763, + 11805, 3074, 8286, 9428, 4881, 6933, 1090, 10038, + 2567, 708, 893, 6465, 4962, 10024, 2090, 5718, + 10743, 780, 4733, 4623, 2134, 2087, 4802, 884, + 5372, 5795, 5938, 4333, 6559, 7549, 5269, 10664, + 4252, 3260, 5917, 10814, 5768, 9983, 8096, 7791, + 6800, 7491, 6272, 1907, 10947, 6289, 11803, 6032, + 11449, 1171, 9201, 7933, 2479, 7970, 11337, 7062, + 8911, 6728, 6542, 8114, 8828, 6595, 3545, 4348, + 4610, 2205, 6999, 8106, 5560, 10390, 9321, 2499, + 2413, 7272, 6881, 10582, 9308, 9437, 3554, 3326, + 5991, 11969, 3415, 12283, 9838, 12063, 4332, 7830, + 11329, 6605, 12271, 2044, 11611, 7353, 11201, 11582, + 3733, 8943, 9978, 1627, 7168, 3935, 5050, 2762, + 7496, 10383, 755, 1654, 12053, 4952, 10134, 4394, + 6592, 7898, 7497, 8904, 12029, 3581, 10748, 5674, + 10358, 4901, 7414, 8771, 710, 6764, 8462, 7193, + 5371, 7274, 11084, 290, 7864, 6827, 11822, 2509, + 6578, 4026, 5807, 1458, 5721, 5762, 4178, 2105, + 11621, 4852, 8897, 2856, 11510, 9264, 2520, 8776, + 7011, 2647, 1898, 7039, 5950, 11163, 5488, 6277, + 9182, 11456, 633, 10046, 11554, 5633, 9587, 2333, + 7008, 7084, 5047, 7199, 9865, 8997, 569, 6390, + 10845, 9679, 8268, 11472, 4203, 1997, 2, 9331, + 162, 6182, 2000, 3649, 9792, 6363, 7557, 6187, + 8510, 9935, 5536, 9019, 3706, 12009, 1452, 3067, + 5494, 9692, 4865, 6019, 7106, 9610, 4588, 10165, + 6261, 5887, 2652, 10172, 1580, 10379, 4638, 9949 + }; + + /* + * Table for inverse NTT, binary case: + * iGMb[x] = R*((1/g)^rev(x)) mod q + * Since g = 7, 1/g = 8778 mod 12289. + */ + internal ushort[] iGMb = { + 4091, 4401, 1081, 1229, 2530, 6014, 7947, 5329, + 2579, 4751, 6464, 11703, 7023, 2812, 5890, 10698, + 3109, 2125, 1960, 10925, 10601, 10404, 4189, 1875, + 5847, 8546, 4615, 5190, 11324, 10578, 5882, 11155, + 8417, 12275, 10599, 7446, 5719, 3569, 5981, 10108, + 4426, 8306, 10755, 4679, 11052, 1538, 11857, 100, + 8247, 6625, 9725, 5145, 3412, 7858, 5831, 9460, + 5217, 10740, 7882, 7506, 12172, 11292, 6049, 79, + 13, 6938, 8886, 5453, 4586, 11455, 2903, 4676, + 9843, 7621, 8822, 9109, 2083, 8507, 8685, 3110, + 7015, 3269, 1367, 6397, 10259, 8435, 10527, 11559, + 11094, 2211, 1808, 7319, 48, 9547, 2560, 1228, + 9438, 10787, 11800, 1820, 11406, 8966, 6159, 3012, + 6109, 2796, 2203, 1652, 711, 7004, 1053, 8973, + 5244, 1517, 9322, 11269, 900, 3888, 11133, 10736, + 4949, 7616, 9974, 4746, 10270, 126, 2921, 6720, + 6635, 6543, 1582, 4868, 42, 673, 2240, 7219, + 1296, 11989, 7675, 8578, 11949, 989, 10541, 7687, + 7085, 8487, 1004, 10236, 4703, 163, 9143, 4597, + 6431, 12052, 2991, 11938, 4647, 3362, 2060, 11357, + 12011, 6664, 5655, 7225, 5914, 9327, 4092, 5880, + 6932, 3402, 5133, 9394, 11229, 5252, 9008, 1556, + 6908, 4773, 3853, 8780, 10325, 7737, 1758, 7103, + 11375, 12273, 8602, 3243, 6536, 7590, 8591, 11552, + 6101, 3253, 9969, 9640, 4506, 3736, 6829, 10822, + 9130, 9948, 3566, 2133, 3901, 6038, 7333, 6609, + 3468, 4659, 625, 2700, 7738, 3443, 3060, 3388, + 3526, 4418, 11911, 6232, 1730, 2558, 10340, 5344, + 5286, 2190, 11562, 6199, 2482, 8756, 5387, 4101, + 4609, 8605, 8226, 144, 5656, 8704, 2621, 5424, + 10812, 2959, 11346, 6249, 1715, 4951, 9540, 1888, + 3764, 39, 8219, 2080, 2502, 1469, 10550, 8709, + 5601, 1093, 3784, 5041, 2058, 8399, 11448, 9639, + 2059, 9878, 7405, 2496, 7918, 11594, 371, 7993, + 3073, 10326, 40, 10004, 9245, 7987, 5603, 4051, + 7894, 676, 11380, 7379, 6501, 4981, 2628, 3488, + 10956, 7022, 6737, 9933, 7139, 2330, 3884, 5473, + 7865, 6941, 5737, 5613, 9505, 11568, 11277, 2510, + 6689, 386, 4462, 105, 2076, 10443, 119, 3955, + 4370, 11505, 3672, 11439, 750, 3240, 3133, 754, + 4013, 11929, 9210, 5378, 11881, 11018, 2818, 1851, + 4966, 8181, 2688, 6205, 6814, 926, 2936, 4327, + 10175, 7089, 6047, 9410, 10492, 8950, 2472, 6255, + 728, 7569, 6056, 10432, 11036, 2452, 2811, 3787, + 945, 8998, 1244, 8815, 11017, 11218, 5894, 4325, + 4639, 3819, 9826, 7056, 6786, 8670, 5539, 7707, + 1361, 9812, 2949, 11265, 10301, 9108, 478, 6489, + 101, 1911, 9483, 3608, 11997, 10536, 812, 8915, + 637, 8159, 5299, 9128, 3512, 8290, 7068, 7922, + 3036, 4759, 2163, 3937, 3755, 11306, 7739, 4922, + 11932, 424, 5538, 6228, 11131, 7778, 11974, 1097, + 2890, 10027, 2569, 2250, 2352, 821, 2550, 11016, + 7769, 136, 617, 3157, 5889, 9219, 6855, 120, + 4405, 1825, 9635, 7214, 10261, 11393, 2441, 9562, + 11176, 599, 2085, 11465, 7233, 6177, 4801, 9926, + 9010, 4514, 9455, 11352, 11670, 6174, 7950, 9766, + 6896, 11603, 3213, 8473, 9873, 2835, 10422, 3732, + 7961, 1457, 10857, 8069, 832, 1628, 3410, 4900, + 10855, 5111, 9543, 6325, 7431, 4083, 3072, 8847, + 9853, 10122, 5259, 11413, 6556, 303, 1465, 3871, + 4873, 5813, 10017, 6898, 3311, 5947, 8637, 5852, + 3856, 928, 4933, 8530, 1871, 2184, 5571, 5879, + 3481, 11597, 9511, 8153, 35, 2609, 5963, 8064, + 1080, 12039, 8444, 3052, 3813, 11065, 6736, 8454, + 2340, 7651, 1910, 10709, 2117, 9637, 6402, 6028, + 2124, 7701, 2679, 5183, 6270, 7424, 2597, 6795, + 9222, 10837, 280, 8583, 3270, 6753, 2354, 3779, + 6102, 4732, 5926, 2497, 8640, 10289, 6107, 12127, + 2958, 12287, 10292, 8086, 817, 4021, 2610, 1444, + 5899, 11720, 3292, 2424, 5090, 7242, 5205, 5281, + 9956, 2702, 6656, 735, 2243, 11656, 833, 3107, + 6012, 6801, 1126, 6339, 5250, 10391, 9642, 5278, + 3513, 9769, 3025, 779, 9433, 3392, 7437, 668, + 10184, 8111, 6527, 6568, 10831, 6482, 8263, 5711, + 9780, 467, 5462, 4425, 11999, 1205, 5015, 6918, + 5096, 3827, 5525, 11579, 3518, 4875, 7388, 1931, + 6615, 1541, 8708, 260, 3385, 4792, 4391, 5697, + 7895, 2155, 7337, 236, 10635, 11534, 1906, 4793, + 9527, 7239, 8354, 5121, 10662, 2311, 3346, 8556, + 707, 1088, 4936, 678, 10245, 18, 5684, 960, + 4459, 7957, 226, 2451, 6, 8874, 320, 6298, + 8963, 8735, 2852, 2981, 1707, 5408, 5017, 9876, + 9790, 2968, 1899, 6729, 4183, 5290, 10084, 7679, + 7941, 8744, 5694, 3461, 4175, 5747, 5561, 3378, + 5227, 952, 4319, 9810, 4356, 3088, 11118, 840, + 6257, 486, 6000, 1342, 10382, 6017, 4798, 5489, + 4498, 4193, 2306, 6521, 1475, 6372, 9029, 8037, + 1625, 7020, 4740, 5730, 7956, 6351, 6494, 6917, + 11405, 7487, 10202, 10155, 7666, 7556, 11509, 1546, + 6571, 10199, 2265, 7327, 5824, 11396, 11581, 9722, + 2251, 11199, 5356, 7408, 2861, 4003, 9215, 484, + 7526, 9409, 12235, 6157, 9025, 2121, 10255, 2519, + 9533, 3824, 8674, 11419, 10888, 4762, 11303, 4097, + 2414, 6496, 9953, 10554, 808, 2999, 2130, 4286, + 12078, 7445, 5132, 7915, 245, 5974, 4874, 7292, + 7560, 10539, 9952, 9075, 2113, 3721, 10285, 10022, + 9578, 8934, 11074, 9498, 294, 4711, 3391, 1377, + 9072, 10189, 4569, 10890, 9909, 6923, 53, 4653, + 439, 10253, 7028, 10207, 8343, 1141, 2556, 7601, + 8150, 10630, 8648, 9832, 7951, 11245, 2131, 5765, + 10343, 9781, 2718, 1419, 4531, 3844, 4066, 4293, + 11657, 11525, 11353, 4313, 4869, 12186, 1611, 10892, + 11489, 8833, 2393, 15, 10830, 5003, 17, 565, + 5891, 12177, 11058, 10412, 8885, 3974, 10981, 7130, + 5840, 10482, 8338, 6035, 6964, 1574, 10936, 2020, + 2465, 8191, 384, 2642, 2729, 5399, 2175, 9396, + 11987, 8035, 4375, 6611, 5010, 11812, 9131, 11427, + 104, 6348, 9643, 6757, 12110, 5617, 10935, 541, + 135, 3041, 7200, 6526, 5085, 12136, 842, 4129, + 7685, 11079, 8426, 1008, 2725, 11772, 6058, 1101, + 1950, 8424, 5688, 6876, 12005, 10079, 5335, 927, + 1770, 273, 8377, 2271, 5225, 10283, 116, 11807, + 91, 11699, 757, 1304, 7524, 6451, 8032, 8154, + 7456, 4191, 309, 2318, 2292, 10393, 11639, 9481, + 12238, 10594, 9569, 7912, 10368, 9889, 12244, 7179, + 3924, 3188, 367, 2077, 336, 5384, 5631, 8596, + 4621, 1775, 8866, 451, 6108, 1317, 6246, 8795, + 5896, 7283, 3132, 11564, 4977, 12161, 7371, 1366, + 12130, 10619, 3809, 5149, 6300, 2638, 4197, 1418, + 10065, 4156, 8373, 8644, 10445, 882, 8158, 10173, + 9763, 12191, 459, 2966, 3166, 405, 5000, 9311, + 6404, 8986, 1551, 8175, 3630, 10766, 9265, 700, + 8573, 9508, 6630, 11437, 11595, 5850, 3950, 4775, + 11941, 1446, 6018, 3386, 11470, 5310, 5476, 553, + 9474, 2586, 1431, 2741, 473, 11383, 4745, 836, + 4062, 10666, 7727, 11752, 5534, 312, 4307, 4351, + 5764, 8679, 8381, 8187, 5, 7395, 4363, 1152, + 5421, 5231, 6473, 436, 7567, 8603, 6229, 8230 + }; + + /* + * Reduce a small signed integer modulo q. The source integer MUST + * be between -q/2 and +q/2. + */ + internal uint mq_conv_small(int x) + { + /* + * If x < 0, the cast to uint will set the high bit to 1. + */ + uint y; + + y = (uint)x; + y += (uint)(Q & -(y >> 31)); + return y; + } + + /* + * Addition modulo q. Operands must be in the 0..q-1 range. + */ + internal uint mq_add(uint x, uint y) + { + /* + * We compute x + y - q. If the result is negative, then the + * high bit will be set, and 'd >> 31' will be equal to 1; + * thus '-(d >> 31)' will be an all-one pattern. Otherwise, + * it will be an all-zero pattern. In other words, this + * implements a conditional addition of q. + */ + uint d; + + d = x + y - Q; + d += (uint)(Q & -(d >> 31)); + return d; + } + + /* + * Subtraction modulo q. Operands must be in the 0..q-1 range. + */ + internal uint mq_sub(uint x, uint y) + { + /* + * As in mq_add(), we use a conditional addition to ensure the + * result is in the 0..q-1 range. + */ + uint d; + + d = x - y; + d += (uint)(Q & -(d >> 31)); + return d; + } + + /* + * Division by 2 modulo q. Operand must be in the 0..q-1 range. + */ + internal uint mq_rshift1(uint x) + { + x += (uint)(Q & -(x & 1)); + return (x >> 1); + } + + /* + * Montgomery multiplication modulo q. If we set R = 2^16 mod q, then + * this function computes: x * y / R mod q + * Operands must be in the 0..q-1 range. + */ + internal uint mq_montymul(uint x, uint y) + { + uint z, w; + + /* + * We compute x*y + k*q with a value of k chosen so that the 16 + * low bits of the result are 0. We can then shift the value. + * After the shift, result may still be larger than q, but it + * will be lower than 2*q, so a conditional subtraction works. + */ + + z = x * y; + w = ((z * Q0I) & 0xFFFF) * Q; + + /* + * When adding z and w, the result will have its low 16 bits + * equal to 0. Since x, y and z are lower than q, the sum will + * be no more than (2^15 - 1) * q + (q - 1)^2, which will + * fit on 29 bits. + */ + z = (z + w) >> 16; + + /* + * After the shift, analysis shows that the value will be less + * than 2q. We do a subtraction then conditional subtraction to + * ensure the result is in the expected range. + */ + z -= Q; + z += (uint)(Q & -(z >> 31)); + return z; + } + + /* + * Montgomery squaring (computes (x^2)/R). + */ + internal uint mq_montysqr(uint x) + { + return mq_montymul(x, x); + } + + /* + * Divide x by y modulo q = 12289. + */ + internal uint mq_div_12289(uint x, uint y) + { + /* + * We invert y by computing y^(q-2) mod q. + * + * We use the following addition chain for exponent e = 12287: + * + * e0 = 1 + * e1 = 2 * e0 = 2 + * e2 = e1 + e0 = 3 + * e3 = e2 + e1 = 5 + * e4 = 2 * e3 = 10 + * e5 = 2 * e4 = 20 + * e6 = 2 * e5 = 40 + * e7 = 2 * e6 = 80 + * e8 = 2 * e7 = 160 + * e9 = e8 + e2 = 163 + * e10 = e9 + e8 = 323 + * e11 = 2 * e10 = 646 + * e12 = 2 * e11 = 1292 + * e13 = e12 + e9 = 1455 + * e14 = 2 * e13 = 2910 + * e15 = 2 * e14 = 5820 + * e16 = e15 + e10 = 6143 + * e17 = 2 * e16 = 12286 + * e18 = e17 + e0 = 12287 + * + * Additions on exponents are converted to Montgomery + * multiplications. We define all intermediate results as so + * many local variables, and let the C compiler work out which + * must be kept around. + */ + uint y0, y1, y2, y3, y4, y5, y6, y7, y8, y9; + uint y10, y11, y12, y13, y14, y15, y16, y17, y18; + + y0 = mq_montymul(y, R2); + y1 = mq_montysqr(y0); + y2 = mq_montymul(y1, y0); + y3 = mq_montymul(y2, y1); + y4 = mq_montysqr(y3); + y5 = mq_montysqr(y4); + y6 = mq_montysqr(y5); + y7 = mq_montysqr(y6); + y8 = mq_montysqr(y7); + y9 = mq_montymul(y8, y2); + y10 = mq_montymul(y9, y8); + y11 = mq_montysqr(y10); + y12 = mq_montysqr(y11); + y13 = mq_montymul(y12, y9); + y14 = mq_montysqr(y13); + y15 = mq_montysqr(y14); + y16 = mq_montymul(y15, y10); + y17 = mq_montysqr(y16); + y18 = mq_montymul(y17, y0); + + /* + * Final multiplication with x, which is not in Montgomery + * representation, computes the correct division result. + */ + return mq_montymul(y18, x); + } + + /* + * Compute NTT on a ring element. + */ + internal void mq_NTT(ushort[] asrc, int a, uint logn) + { + int n, t, m; + + n = (int)1 << (int)logn; + t = n; + for (m = 1; m < n; m <<= 1) { + int ht, i, j1; + + ht = t >> 1; + for (i = 0, j1 = 0; i < m; i ++, j1 += t) { + int j, j2; + uint s; + + s = GMb[m + i]; + j2 = j1 + ht; + for (j = j1; j < j2; j ++) { + uint u, v; + + u = asrc[a + j]; + v = mq_montymul(asrc[a + j + ht], s); + asrc[a + j] = (ushort)mq_add(u, v); + asrc[a + j + ht] = (ushort)mq_sub(u, v); + } + } + t = ht; + } + } + + /* + * Compute the inverse NTT on a ring element, binary case. + */ + internal void mq_iNTT(ushort[] asrc, int a, uint logn) + { + int n, t, m; + uint ni; + + n = (int)1 << (int)logn; + t = 1; + m = n; + while (m > 1) { + int hm, dt, i, j1; + + hm = m >> 1; + dt = t << 1; + for (i = 0, j1 = 0; i < hm; i ++, j1 += dt) { + int j, j2; + uint s; + + j2 = j1 + t; + s = iGMb[hm + i]; + for (j = j1; j < j2; j ++) { + uint u, v, w; + + u = asrc[a + j]; + v = asrc[a + j + t]; + asrc[a + j] = (ushort)mq_add(u, v); + w = mq_sub(u, v); + asrc[a + j + t] = (ushort) + mq_montymul(w, s); + } + } + t = dt; + m = hm; + } + + /* + * To complete the inverse NTT, we must now divide all values by + * n (the vector size). We thus need the inverse of n, i.e. we + * need to divide 1 by 2 logn times. But we also want it in + * Montgomery representation, i.e. we also want to multiply it + * by R = 2^16. In the common case, this should be a simple right + * shift. The loop below is generic and works also in corner cases; + * its computation time is negligible. + */ + ni = R; + for (m = n; m > 1; m >>= 1) { + ni = mq_rshift1(ni); + } + for (m = 0; m < n; m ++) { + asrc[a + m] = (ushort)mq_montymul(asrc[a + m], ni); + } + } + + /* + * Convert a polynomial (mod q) to Montgomery representation. + */ + internal void mq_poly_tomonty(ushort[] fsrc, int f, uint logn) + { + int u, n; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + fsrc[f + u] = (ushort)mq_montymul(fsrc[f + u], R2); + } + } + + /* + * Multiply two polynomials together (NTT representation, and using + * a Montgomery multiplication). Result f*g is written over f. + */ + internal void mq_poly_montymul_ntt(ushort[] fsrc, int f, ushort[] gsrc, int g, uint logn) + { + int u, n; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + fsrc[f + u] = (ushort)mq_montymul(fsrc[f + u], gsrc[g + u]); + } + } + + /* + * Subtract polynomial g from polynomial f. + */ + internal void mq_poly_sub(ushort[] fsrc, int f, ushort[] gsrc, int g, uint logn) + { + int u, n; + + n = (int)1 << (int)logn; + for (u = 0; u < n; u ++) { + fsrc[f + u] = (ushort)mq_sub(fsrc[f + u], gsrc[g + u]); + } + } + + /* ===================================================================== */ + + internal void to_ntt_monty(ushort[] hsrc, int h, uint logn) + { + mq_NTT(hsrc, h, logn); + mq_poly_tomonty(hsrc, h, logn); + } + + internal bool verify_raw(ushort[] c0src, int c0, short[] s2src, int s2, + ushort[] hsrc, int h, uint logn, ushort[] tmpsrc, int tmp) + { + int u, n; + int tt; + + n = (int)1 << (int)logn; + tt = tmp; + + /* + * Reduce s2 elements modulo q ([0..q-1] range). + */ + for (u = 0; u < n; u ++) { + uint w; + + w = (uint)s2src[s2 + u]; + w += (uint)(Q & -(w >> 31)); + tmpsrc[tt+u] = (ushort)w; + } + + /* + * Compute -s1 = s2*h - c0 mod phi mod q (in tt[]). + */ + mq_NTT(tmpsrc, tt, logn); + mq_poly_montymul_ntt(tmpsrc, tt, hsrc, h, logn); + mq_iNTT(tmpsrc, tt, logn); + mq_poly_sub(tmpsrc, tt, c0src, c0, logn); + + /* + * Normalize -s1 elements into the [-q/2..q/2] range. + */ + short[] shorttmp = new short[n]; + for (u = 0; u < n; u ++) { + int w; + + w = (int)tmpsrc[tt+u]; + w -= (int)(Q & -(((Q >> 1) - (uint)w) >> 31)); + tmpsrc[tt + u] = (ushort)w; + shorttmp[u] = (short)tmpsrc[tt + u]; + } + + + /* + * Signature is valid if and only if the aggregate (-s1,s2) vector + * is short enough. + */ + return this.common.is_short(shorttmp, 0, s2src, s2, logn); + } + + internal int compute_public(ushort[] hsrc, int h, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, uint logn, ushort[] tmpsrc, int tmp) + { + int u, n; + int tt; + + n = (int)1 << (int)logn; + tt = tmp; + for (u = 0; u < n; u ++) { + tmpsrc[tt+u] = (ushort)mq_conv_small(fsrc[f+u]); + hsrc[h+u] = (ushort)mq_conv_small(gsrc[g+u]); + } + mq_NTT(hsrc, h, logn); + mq_NTT(tmpsrc, tt, logn); + for (u = 0; u < n; u ++) { + if (tmpsrc[tt+u] == 0) { + return 0; + } + hsrc[h+u] = (ushort)mq_div_12289(hsrc[h+u], tmpsrc[tt+u]); + } + mq_iNTT(hsrc, h, logn); + return 1; + } + + internal int complete_private(sbyte[] Gsrc, int G, + sbyte[] fsrc, int f, sbyte[] gsrc, int g, sbyte[] Fsrc, int F, + uint logn, ushort[] tmpsrc, int tmp) + { + int u, n; + int t1, t2; + + n = (int)1 << (int)logn; + t1 = tmp; + t2 = t1 + n; + for (u = 0; u < n; u ++) { + tmpsrc[t1+u] = (ushort)mq_conv_small(gsrc[g+u]); + tmpsrc[t2+u] = (ushort)mq_conv_small(Fsrc[F+u]); + } + mq_NTT(tmpsrc, t1, logn); + mq_NTT(tmpsrc, t2, logn); + mq_poly_tomonty(tmpsrc, t1, logn); + mq_poly_montymul_ntt(tmpsrc, t1, tmpsrc, t2, logn); + for (u = 0; u < n; u ++) { + tmpsrc[t2+u] = (ushort)mq_conv_small(fsrc[f+u]); + } + mq_NTT(tmpsrc, t2, logn); + for (u = 0; u < n; u ++) { + if (tmpsrc[t2+u] == 0) { + return 0; + } + tmpsrc[t1+u] = (ushort)mq_div_12289(tmpsrc[t1+u], tmpsrc[t2+u]); + } + mq_iNTT(tmpsrc, t1, logn); + for (u = 0; u < n; u ++) { + uint w; + int gi; + + w = tmpsrc[t1+u]; + w -= (uint)(Q & ~-((w - (Q >> 1)) >> 31)); + //gi = *(int *)&w; + gi = (int)w; + if (gi < -127 || gi > +127) { + return 0; + } + Gsrc[G+u] = (sbyte)gi; + } + return 1; + } + + internal int is_invertible( + short[] s2src, int s2, uint logn, ushort[] tmpsrc, int tmp) + { + int u, n; + int tt; + uint r; + + n = (int)1 << (int)logn; + tt = tmp; + for (u = 0; u < n; u ++) { + uint w; + + w = (uint)s2src[s2 + u]; + w += (uint)(Q & -(w >> 31)); + tmpsrc[tt+u] = (ushort)w; + } + mq_NTT(tmpsrc, tt, logn); + r = 0; + for (u = 0; u < n; u ++) { + r |= (uint)(tmpsrc[tt+u] - 1); + } + return (int)(1u - (r >> 31)); + } + + internal int verify_recover(ushort[] hsrc, int h, + ushort[] c0src, int c0, short[] s1src, int s1, short[] s2src, int s2, + uint logn, ushort[] tmpsrc, int tmp) + { + int u, n; + int tt; + uint r; + + n = (int)1 << (int)logn; + + /* + * Reduce elements of s1 and s2 modulo q; then write s2 into tt[] + * and c0 - s1 into h[]. + */ + tt = tmp; + for (u = 0; u < n; u ++) { + uint w; + + w = (uint)s2src[s2 + u]; + w += (uint)(Q & -(w >> 31)); + tmpsrc[tt+u] = (ushort)w; + + w = (uint)s1src[s1+u]; + w += (uint)(Q & -(w >> 31)); + w = mq_sub(c0src[c0 + u], w); + hsrc[h+u] = (ushort)w; + } + + /* + * Compute h = (c0 - s1) / s2. If one of the coefficients of s2 + * is zero (in NTT representation) then the operation fails. We + * keep that information into a flag so that we do not deviate + * from strict constant-time processing; if all coefficients of + * s2 are non-zero, then the high bit of r will be zero. + */ + mq_NTT(tmpsrc, tt, logn); + mq_NTT(hsrc, h, logn); + r = 0; + for (u = 0; u < n; u ++) { + r |= (uint)(tmpsrc[tt+u] - 1); + hsrc[h+u] = (ushort)mq_div_12289(hsrc[h+u], tmpsrc[tt+u]); + } + mq_iNTT(hsrc, h, logn); + + /* + * Signature is acceptable if and only if it is short enough, + * and s2 was invertible mod phi mod q. The caller must still + * check that the rebuilt public key matches the expected + * value (e.g. through a hash). + */ + r = ~r & (uint)-(this.common.is_short(s1src, s1, s2src, s2, logn) ? 1 : 0); + return (int)(r >> 31); + } + + internal int count_nttzero(short[] sigsrc, int sig, uint logn, ushort[] tmpsrc, int tmp) + { + int s2; + int u, n; + uint r; + + n = (int)1 << (int)logn; + s2 = tmp; + for (u = 0; u < n; u ++) { + uint w; + + w = (uint)sigsrc[sig + u]; + w += (uint)(Q & -(w >> 31)); + tmpsrc[s2 + u] = (ushort)w; + } + mq_NTT(tmpsrc, s2, logn); + r = 0; + for (u = 0; u < n; u ++) { + uint w; + + w = (uint)tmpsrc[s2 + u] - 1u; + r += (w >> 31); + } + return (int)r; + } + } +} diff --git a/crypto/src/pqc/crypto/falcon/SHAKE256.cs b/crypto/src/pqc/crypto/falcon/SHAKE256.cs new file mode 100644 index 000000000..eb7c77e09 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/SHAKE256.cs @@ -0,0 +1,569 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class SHAKE256 + { + + /* + * License from the reference C code (the code was copied then modified + * to function in C#): + * ==========================(LICENSE BEGIN)============================ + * + * Copyright (c) 2017-2019 Falcon Project + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. + * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY + * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, + * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE + * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + * + * ===========================(LICENSE END)============================= + */ + + ulong[] A; + byte[] dubf; + ulong dptr; + + ulong[] RC = { + 0x0000000000000001, 0x0000000000008082, + 0x800000000000808A, 0x8000000080008000, + 0x000000000000808B, 0x0000000080000001, + 0x8000000080008081, 0x8000000000008009, + 0x000000000000008A, 0x0000000000000088, + 0x0000000080008009, 0x000000008000000A, + 0x000000008000808B, 0x800000000000008B, + 0x8000000000008089, 0x8000000000008003, + 0x8000000000008002, 0x8000000000000080, + 0x000000000000800A, 0x800000008000000A, + 0x8000000080008081, 0x8000000000008080, + 0x0000000080000001, 0x8000000080008008 + }; + + void process_block(ulong[] A) { + ulong t0, t1, t2, t3, t4; + ulong tt0, tt1, tt2, tt3; + ulong t, kt; + ulong c0, c1, c2, c3, c4, bnn; + int j; + + /* + * Invert some words (alternate internal representation, which + * saves some operations). + */ + A[ 1] = ~A[ 1]; + A[ 2] = ~A[ 2]; + A[ 8] = ~A[ 8]; + A[12] = ~A[12]; + A[17] = ~A[17]; + A[20] = ~A[20]; + + /* + * Compute the 24 rounds. This loop is partially unrolled (each + * iteration computes two rounds). + */ + for (j = 0; j < 24; j += 2) { + + tt0 = A[ 1] ^ A[ 6]; + tt1 = A[11] ^ A[16]; + tt0 ^= A[21] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[ 4] ^ A[ 9]; + tt3 = A[14] ^ A[19]; + tt0 ^= A[24]; + tt2 ^= tt3; + t0 = tt0 ^ tt2; + + tt0 = A[ 2] ^ A[ 7]; + tt1 = A[12] ^ A[17]; + tt0 ^= A[22] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[ 0] ^ A[ 5]; + tt3 = A[10] ^ A[15]; + tt0 ^= A[20]; + tt2 ^= tt3; + t1 = tt0 ^ tt2; + + tt0 = A[ 3] ^ A[ 8]; + tt1 = A[13] ^ A[18]; + tt0 ^= A[23] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[ 1] ^ A[ 6]; + tt3 = A[11] ^ A[16]; + tt0 ^= A[21]; + tt2 ^= tt3; + t2 = tt0 ^ tt2; + + tt0 = A[ 4] ^ A[ 9]; + tt1 = A[14] ^ A[19]; + tt0 ^= A[24] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[ 2] ^ A[ 7]; + tt3 = A[12] ^ A[17]; + tt0 ^= A[22]; + tt2 ^= tt3; + t3 = tt0 ^ tt2; + + tt0 = A[ 0] ^ A[ 5]; + tt1 = A[10] ^ A[15]; + tt0 ^= A[20] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[ 3] ^ A[ 8]; + tt3 = A[13] ^ A[18]; + tt0 ^= A[23]; + tt2 ^= tt3; + t4 = tt0 ^ tt2; + + A[ 0] = A[ 0] ^ t0; + A[ 5] = A[ 5] ^ t0; + A[10] = A[10] ^ t0; + A[15] = A[15] ^ t0; + A[20] = A[20] ^ t0; + A[ 1] = A[ 1] ^ t1; + A[ 6] = A[ 6] ^ t1; + A[11] = A[11] ^ t1; + A[16] = A[16] ^ t1; + A[21] = A[21] ^ t1; + A[ 2] = A[ 2] ^ t2; + A[ 7] = A[ 7] ^ t2; + A[12] = A[12] ^ t2; + A[17] = A[17] ^ t2; + A[22] = A[22] ^ t2; + A[ 3] = A[ 3] ^ t3; + A[ 8] = A[ 8] ^ t3; + A[13] = A[13] ^ t3; + A[18] = A[18] ^ t3; + A[23] = A[23] ^ t3; + A[ 4] = A[ 4] ^ t4; + A[ 9] = A[ 9] ^ t4; + A[14] = A[14] ^ t4; + A[19] = A[19] ^ t4; + A[24] = A[24] ^ t4; + A[ 5] = (A[ 5] << 36) | (A[ 5] >> (64 - 36)); + A[10] = (A[10] << 3) | (A[10] >> (64 - 3)); + A[15] = (A[15] << 41) | (A[15] >> (64 - 41)); + A[20] = (A[20] << 18) | (A[20] >> (64 - 18)); + A[ 1] = (A[ 1] << 1) | (A[ 1] >> (64 - 1)); + A[ 6] = (A[ 6] << 44) | (A[ 6] >> (64 - 44)); + A[11] = (A[11] << 10) | (A[11] >> (64 - 10)); + A[16] = (A[16] << 45) | (A[16] >> (64 - 45)); + A[21] = (A[21] << 2) | (A[21] >> (64 - 2)); + A[ 2] = (A[ 2] << 62) | (A[ 2] >> (64 - 62)); + A[ 7] = (A[ 7] << 6) | (A[ 7] >> (64 - 6)); + A[12] = (A[12] << 43) | (A[12] >> (64 - 43)); + A[17] = (A[17] << 15) | (A[17] >> (64 - 15)); + A[22] = (A[22] << 61) | (A[22] >> (64 - 61)); + A[ 3] = (A[ 3] << 28) | (A[ 3] >> (64 - 28)); + A[ 8] = (A[ 8] << 55) | (A[ 8] >> (64 - 55)); + A[13] = (A[13] << 25) | (A[13] >> (64 - 25)); + A[18] = (A[18] << 21) | (A[18] >> (64 - 21)); + A[23] = (A[23] << 56) | (A[23] >> (64 - 56)); + A[ 4] = (A[ 4] << 27) | (A[ 4] >> (64 - 27)); + A[ 9] = (A[ 9] << 20) | (A[ 9] >> (64 - 20)); + A[14] = (A[14] << 39) | (A[14] >> (64 - 39)); + A[19] = (A[19] << 8) | (A[19] >> (64 - 8)); + A[24] = (A[24] << 14) | (A[24] >> (64 - 14)); + + bnn = ~A[12]; + kt = A[ 6] | A[12]; + c0 = A[ 0] ^ kt; + kt = bnn | A[18]; + c1 = A[ 6] ^ kt; + kt = A[18] & A[24]; + c2 = A[12] ^ kt; + kt = A[24] | A[ 0]; + c3 = A[18] ^ kt; + kt = A[ 0] & A[ 6]; + c4 = A[24] ^ kt; + A[ 0] = c0; + A[ 6] = c1; + A[12] = c2; + A[18] = c3; + A[24] = c4; + bnn = ~A[22]; + kt = A[ 9] | A[10]; + c0 = A[ 3] ^ kt; + kt = A[10] & A[16]; + c1 = A[ 9] ^ kt; + kt = A[16] | bnn; + c2 = A[10] ^ kt; + kt = A[22] | A[ 3]; + c3 = A[16] ^ kt; + kt = A[ 3] & A[ 9]; + c4 = A[22] ^ kt; + A[ 3] = c0; + A[ 9] = c1; + A[10] = c2; + A[16] = c3; + A[22] = c4; + bnn = ~A[19]; + kt = A[ 7] | A[13]; + c0 = A[ 1] ^ kt; + kt = A[13] & A[19]; + c1 = A[ 7] ^ kt; + kt = bnn & A[20]; + c2 = A[13] ^ kt; + kt = A[20] | A[ 1]; + c3 = bnn ^ kt; + kt = A[ 1] & A[ 7]; + c4 = A[20] ^ kt; + A[ 1] = c0; + A[ 7] = c1; + A[13] = c2; + A[19] = c3; + A[20] = c4; + bnn = ~A[17]; + kt = A[ 5] & A[11]; + c0 = A[ 4] ^ kt; + kt = A[11] | A[17]; + c1 = A[ 5] ^ kt; + kt = bnn | A[23]; + c2 = A[11] ^ kt; + kt = A[23] & A[ 4]; + c3 = bnn ^ kt; + kt = A[ 4] | A[ 5]; + c4 = A[23] ^ kt; + A[ 4] = c0; + A[ 5] = c1; + A[11] = c2; + A[17] = c3; + A[23] = c4; + bnn = ~A[ 8]; + kt = bnn & A[14]; + c0 = A[ 2] ^ kt; + kt = A[14] | A[15]; + c1 = bnn ^ kt; + kt = A[15] & A[21]; + c2 = A[14] ^ kt; + kt = A[21] | A[ 2]; + c3 = A[15] ^ kt; + kt = A[ 2] & A[ 8]; + c4 = A[21] ^ kt; + A[ 2] = c0; + A[ 8] = c1; + A[14] = c2; + A[15] = c3; + A[21] = c4; + A[ 0] = A[ 0] ^ RC[j + 0]; + + tt0 = A[ 6] ^ A[ 9]; + tt1 = A[ 7] ^ A[ 5]; + tt0 ^= A[ 8] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[24] ^ A[22]; + tt3 = A[20] ^ A[23]; + tt0 ^= A[21]; + tt2 ^= tt3; + t0 = tt0 ^ tt2; + + tt0 = A[12] ^ A[10]; + tt1 = A[13] ^ A[11]; + tt0 ^= A[14] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[ 0] ^ A[ 3]; + tt3 = A[ 1] ^ A[ 4]; + tt0 ^= A[ 2]; + tt2 ^= tt3; + t1 = tt0 ^ tt2; + + tt0 = A[18] ^ A[16]; + tt1 = A[19] ^ A[17]; + tt0 ^= A[15] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[ 6] ^ A[ 9]; + tt3 = A[ 7] ^ A[ 5]; + tt0 ^= A[ 8]; + tt2 ^= tt3; + t2 = tt0 ^ tt2; + + tt0 = A[24] ^ A[22]; + tt1 = A[20] ^ A[23]; + tt0 ^= A[21] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[12] ^ A[10]; + tt3 = A[13] ^ A[11]; + tt0 ^= A[14]; + tt2 ^= tt3; + t3 = tt0 ^ tt2; + + tt0 = A[ 0] ^ A[ 3]; + tt1 = A[ 1] ^ A[ 4]; + tt0 ^= A[ 2] ^ tt1; + tt0 = (tt0 << 1) | (tt0 >> 63); + tt2 = A[18] ^ A[16]; + tt3 = A[19] ^ A[17]; + tt0 ^= A[15]; + tt2 ^= tt3; + t4 = tt0 ^ tt2; + + A[ 0] = A[ 0] ^ t0; + A[ 3] = A[ 3] ^ t0; + A[ 1] = A[ 1] ^ t0; + A[ 4] = A[ 4] ^ t0; + A[ 2] = A[ 2] ^ t0; + A[ 6] = A[ 6] ^ t1; + A[ 9] = A[ 9] ^ t1; + A[ 7] = A[ 7] ^ t1; + A[ 5] = A[ 5] ^ t1; + A[ 8] = A[ 8] ^ t1; + A[12] = A[12] ^ t2; + A[10] = A[10] ^ t2; + A[13] = A[13] ^ t2; + A[11] = A[11] ^ t2; + A[14] = A[14] ^ t2; + A[18] = A[18] ^ t3; + A[16] = A[16] ^ t3; + A[19] = A[19] ^ t3; + A[17] = A[17] ^ t3; + A[15] = A[15] ^ t3; + A[24] = A[24] ^ t4; + A[22] = A[22] ^ t4; + A[20] = A[20] ^ t4; + A[23] = A[23] ^ t4; + A[21] = A[21] ^ t4; + A[ 3] = (A[ 3] << 36) | (A[ 3] >> (64 - 36)); + A[ 1] = (A[ 1] << 3) | (A[ 1] >> (64 - 3)); + A[ 4] = (A[ 4] << 41) | (A[ 4] >> (64 - 41)); + A[ 2] = (A[ 2] << 18) | (A[ 2] >> (64 - 18)); + A[ 6] = (A[ 6] << 1) | (A[ 6] >> (64 - 1)); + A[ 9] = (A[ 9] << 44) | (A[ 9] >> (64 - 44)); + A[ 7] = (A[ 7] << 10) | (A[ 7] >> (64 - 10)); + A[ 5] = (A[ 5] << 45) | (A[ 5] >> (64 - 45)); + A[ 8] = (A[ 8] << 2) | (A[ 8] >> (64 - 2)); + A[12] = (A[12] << 62) | (A[12] >> (64 - 62)); + A[10] = (A[10] << 6) | (A[10] >> (64 - 6)); + A[13] = (A[13] << 43) | (A[13] >> (64 - 43)); + A[11] = (A[11] << 15) | (A[11] >> (64 - 15)); + A[14] = (A[14] << 61) | (A[14] >> (64 - 61)); + A[18] = (A[18] << 28) | (A[18] >> (64 - 28)); + A[16] = (A[16] << 55) | (A[16] >> (64 - 55)); + A[19] = (A[19] << 25) | (A[19] >> (64 - 25)); + A[17] = (A[17] << 21) | (A[17] >> (64 - 21)); + A[15] = (A[15] << 56) | (A[15] >> (64 - 56)); + A[24] = (A[24] << 27) | (A[24] >> (64 - 27)); + A[22] = (A[22] << 20) | (A[22] >> (64 - 20)); + A[20] = (A[20] << 39) | (A[20] >> (64 - 39)); + A[23] = (A[23] << 8) | (A[23] >> (64 - 8)); + A[21] = (A[21] << 14) | (A[21] >> (64 - 14)); + + bnn = ~A[13]; + kt = A[ 9] | A[13]; + c0 = A[ 0] ^ kt; + kt = bnn | A[17]; + c1 = A[ 9] ^ kt; + kt = A[17] & A[21]; + c2 = A[13] ^ kt; + kt = A[21] | A[ 0]; + c3 = A[17] ^ kt; + kt = A[ 0] & A[ 9]; + c4 = A[21] ^ kt; + A[ 0] = c0; + A[ 9] = c1; + A[13] = c2; + A[17] = c3; + A[21] = c4; + bnn = ~A[14]; + kt = A[22] | A[ 1]; + c0 = A[18] ^ kt; + kt = A[ 1] & A[ 5]; + c1 = A[22] ^ kt; + kt = A[ 5] | bnn; + c2 = A[ 1] ^ kt; + kt = A[14] | A[18]; + c3 = A[ 5] ^ kt; + kt = A[18] & A[22]; + c4 = A[14] ^ kt; + A[18] = c0; + A[22] = c1; + A[ 1] = c2; + A[ 5] = c3; + A[14] = c4; + bnn = ~A[23]; + kt = A[10] | A[19]; + c0 = A[ 6] ^ kt; + kt = A[19] & A[23]; + c1 = A[10] ^ kt; + kt = bnn & A[ 2]; + c2 = A[19] ^ kt; + kt = A[ 2] | A[ 6]; + c3 = bnn ^ kt; + kt = A[ 6] & A[10]; + c4 = A[ 2] ^ kt; + A[ 6] = c0; + A[10] = c1; + A[19] = c2; + A[23] = c3; + A[ 2] = c4; + bnn = ~A[11]; + kt = A[ 3] & A[ 7]; + c0 = A[24] ^ kt; + kt = A[ 7] | A[11]; + c1 = A[ 3] ^ kt; + kt = bnn | A[15]; + c2 = A[ 7] ^ kt; + kt = A[15] & A[24]; + c3 = bnn ^ kt; + kt = A[24] | A[ 3]; + c4 = A[15] ^ kt; + A[24] = c0; + A[ 3] = c1; + A[ 7] = c2; + A[11] = c3; + A[15] = c4; + bnn = ~A[16]; + kt = bnn & A[20]; + c0 = A[12] ^ kt; + kt = A[20] | A[ 4]; + c1 = bnn ^ kt; + kt = A[ 4] & A[ 8]; + c2 = A[20] ^ kt; + kt = A[ 8] | A[12]; + c3 = A[ 4] ^ kt; + kt = A[12] & A[16]; + c4 = A[ 8] ^ kt; + A[12] = c0; + A[16] = c1; + A[20] = c2; + A[ 4] = c3; + A[ 8] = c4; + A[ 0] = A[ 0] ^ RC[j + 1]; + t = A[ 5]; + A[ 5] = A[18]; + A[18] = A[11]; + A[11] = A[10]; + A[10] = A[ 6]; + A[ 6] = A[22]; + A[22] = A[20]; + A[20] = A[12]; + A[12] = A[19]; + A[19] = A[15]; + A[15] = A[24]; + A[24] = A[ 8]; + A[ 8] = t; + t = A[ 1]; + A[ 1] = A[ 9]; + A[ 9] = A[14]; + A[14] = A[ 2]; + A[ 2] = A[13]; + A[13] = A[23]; + A[23] = A[ 4]; + A[ 4] = A[21]; + A[21] = A[16]; + A[16] = A[ 3]; + A[ 3] = A[17]; + A[17] = A[ 7]; + A[ 7] = t; + } + + /* + * Invert some words back to normal representation. + */ + A[ 1] = ~A[ 1]; + A[ 2] = ~A[ 2]; + A[ 8] = ~A[ 8]; + A[12] = ~A[12]; + A[17] = ~A[17]; + A[20] = ~A[20]; + } + + internal void i_shake256_init() + { + this.dptr = 0; + + /* + * Representation of an all-ones uint64_t is the same regardless + * of local endianness. + */ + // memset(this.A, 0, sizeof this.A); + this.A = new ulong[25]; + this.dubf = new byte[200]; + + for (int i = 0; i < this.A.Length; i++) { + this.A[i] = 0; + } + } + + internal void i_shake256_inject(byte[] insrc, int inarray, int len) + { + ulong dptr; + + dptr = this.dptr; + while (len > 0) { + int clen, u; + + clen = 136 - (int)dptr; + if (clen > len) { + clen = len; + } + for (u = 0; u < clen; u ++) { + int v; + + v = u + (int)dptr; + this.A[v >> 3] ^= (ulong)insrc[inarray + u] << ((v & 7) << 3); + } + dptr += (ulong)clen; + inarray += clen; + len -= clen; + if (dptr == 136) { + process_block(this.A); + dptr = 0; + } + } + this.dptr = dptr; + } + + internal void i_shake256_flip() + { + /* + * We apply padding and pre-XOR the value into the state. We + * set dptr to the end of the buffer, so that first call to + * shake_extract() will process the block. + */ + uint v; + + v = (uint)this.dptr; + this.A[v >> 3] ^= (ulong)0x1F << (int)((v & 7) << 3); + this.A[16] ^= (ulong)0x80 << 56; + this.dptr = 136; + } + + internal void i_shake256_extract(byte[] outsrc, int outarray, int len) + { + ulong dptr; + + dptr = this.dptr; + while (len > 0) { + int clen; + + if (dptr == 136) { + process_block(this.A); + dptr = 0; + } + clen = 136 - (int)dptr; + if (clen > len) { + clen = len; + } + len -= clen; + while (clen -- > 0) { + outsrc[outarray ++] = (byte)(this.A[dptr >> 3] >> (int)((dptr & 7) << 3)); + dptr ++; + } + } + this.dptr = dptr; + } + + } +} diff --git a/crypto/src/pqc/crypto/falcon/SamplerZ.cs b/crypto/src/pqc/crypto/falcon/SamplerZ.cs new file mode 100644 index 000000000..b43cd2c38 --- /dev/null +++ b/crypto/src/pqc/crypto/falcon/SamplerZ.cs @@ -0,0 +1,229 @@ +using System; + +namespace Org.BouncyCastle.Pqc.Crypto.Falcon +{ + class SamplerZ + { + FalconRNG p; + FalconFPR sigma_min; + FPREngine fpre; + + internal SamplerZ(FalconRNG p, FalconFPR sigma_min, FPREngine fpre) { + this.p = p; + this.sigma_min = sigma_min; + this.fpre = fpre; + } + + internal int Sample(FalconFPR mu, FalconFPR isigma) { + return this.sampler(mu, isigma); + } + + /* + * Sample an integer value along a half-gaussian distribution centered + * on zero and standard deviation 1.8205, with a precision of 72 bits. + */ + int gaussian0_sampler(FalconRNG p) + { + + uint[] dist = { + 10745844u, 3068844u, 3741698u, + 5559083u, 1580863u, 8248194u, + 2260429u, 13669192u, 2736639u, + 708981u, 4421575u, 10046180u, + 169348u, 7122675u, 4136815u, + 30538u, 13063405u, 7650655u, + 4132u, 14505003u, 7826148u, + 417u, 16768101u, 11363290u, + 31u, 8444042u, 8086568u, + 1u, 12844466u, 265321u, + 0u, 1232676u, 13644283u, + 0u, 38047u, 9111839u, + 0u, 870u, 6138264u, + 0u, 14u, 12545723u, + 0u, 0u, 3104126u, + 0u, 0u, 28824u, + 0u, 0u, 198u, + 0u, 0u, 1u + }; + + uint v0, v1, v2, hi; + ulong lo; + int u; + int z; + + /* + * Get a random 72-bit value, into three 24-bit limbs v0..v2. + */ + lo = p.prng_get_u64(); + hi = p.prng_get_u8(); + v0 = (uint)lo & 0xFFFFFF; + v1 = (uint)(lo >> 24) & 0xFFFFFF; + v2 = (uint)(lo >> 48) | (hi << 16); + + /* + * Sampled value is z, such that v0..v2 is lower than the first + * z elements of the table. + */ + z = 0; + for (u = 0; u < dist.Length; u += 3) { + uint w0, w1, w2, cc; + + w0 = dist[u + 2]; + w1 = dist[u + 1]; + w2 = dist[u + 0]; + cc = (v0 - w0) >> 31; + cc = (v1 - w1 - cc) >> 31; + cc = (v2 - w2 - cc) >> 31; + z += (int)cc; + } + return z; + + } + + /* + * Sample a bit with probability exp(-x) for some x >= 0. + */ + int BerExp(FalconRNG p, FalconFPR x, FalconFPR ccs) + { + int s, i; + FalconFPR r; + uint sw, w; + ulong z; + + /* + * Reduce x modulo log(2): x = s*log(2) + r, with s an integer, + * and 0 <= r < log(2). Since x >= 0, we can use this.fpre.fpr_trunc(). + */ + s = (int)this.fpre.fpr_trunc(this.fpre.fpr_mul(x, this.fpre.fpr_inv_log2)); + r = this.fpre.fpr_sub(x, this.fpre.fpr_mul(this.fpre.fpr_of(s), this.fpre.fpr_log2)); + + /* + * It may happen (quite rarely) that s >= 64; if sigma = 1.2 + * (the minimum value for sigma), r = 0 and b = 1, then we get + * s >= 64 if the half-Gaussian produced a z >= 13, which happens + * with probability about 0.000000000230383991, which is + * approximatively equal to 2^(-32). In any case, if s >= 64, + * then BerExp will be non-zero with probability less than + * 2^(-64), so we can simply saturate s at 63. + */ + sw = (uint)s; + sw ^= (uint)((sw ^ 63) & -((63 - sw) >> 31)); + s = (int)sw; + + /* + * Compute exp(-r); we know that 0 <= r < log(2) at this point, so + * we can use this.fpre.fpr_expm_p63(), which yields a result scaled to 2^63. + * We scale it up to 2^64, then right-shift it by s bits because + * we really want exp(-x) = 2^(-s)*exp(-r). + * + * The "-1" operation makes sure that the value fits on 64 bits + * (i.e. if r = 0, we may get 2^64, and we prefer 2^64-1 in that + * case). The bias is negligible since this.fpre.fpr_expm_p63() only computes + * with 51 bits of precision or so. + */ + z = ((this.fpre.fpr_expm_p63(r, ccs) << 1) - 1) >> s; + + /* + * Sample a bit with probability exp(-x). Since x = s*log(2) + r, + * exp(-x) = 2^-s * exp(-r), we compare lazily exp(-x) with the + * PRNG output to limit its consumption, the sign of the difference + * yields the expected result. + */ + i = 64; + do { + i -= 8; + w = p.prng_get_u8() - ((uint)(z >> i) & 0xFF); + } while (w == 0 && i > 0); + return (int)(w >> 31); + } + + /* + * The sampler produces a random integer that follows a discrete Gaussian + * distribution, centered on mu, and with standard deviation sigma. The + * provided parameter isigma is equal to 1/sigma. + * + * The value of sigma MUST lie between 1 and 2 (i.e. isigma lies between + * 0.5 and 1); in Falcon, sigma should always be between 1.2 and 1.9. + */ + int sampler(FalconFPR mu, FalconFPR isigma) + { + int s; + FalconFPR r, dss, ccs; + + /* + * Center is mu. We compute mu = s + r where s is an integer + * and 0 <= r < 1. + */ + s = (int)this.fpre.fpr_floor(mu); + r = this.fpre.fpr_sub(mu, this.fpre.fpr_of(s)); + + /* + * dss = 1/(2*sigma^2) = 0.5*(isigma^2). + */ + dss = this.fpre.fpr_half(this.fpre.fpr_sqr(isigma)); + + /* + * ccs = sigma_min / sigma = sigma_min * isigma. + */ + ccs = this.fpre.fpr_mul(isigma, this.sigma_min); + + /* + * We now need to sample on center r. + */ + for (;;) { + int z0, z, b; + FalconFPR x; + + /* + * Sample z for a Gaussian distribution. Then get a + * random bit b to turn the sampling into a bimodal + * distribution: if b = 1, we use z+1, otherwise we + * use -z. We thus have two situations: + * + * - b = 1: z >= 1 and sampled against a Gaussian + * centered on 1. + * - b = 0: z <= 0 and sampled against a Gaussian + * centered on 0. + */ + z0 = gaussian0_sampler(this.p); + b = (int)this.p.prng_get_u8() & 1; + z = b + ((b << 1) - 1) * z0; + + /* + * Rejection sampling. We want a Gaussian centered on r; + * but we sampled against a Gaussian centered on b (0 or + * 1). But we know that z is always in the range where + * our sampling distribution is greater than the Gaussian + * distribution, so rejection works. + * + * We got z with distribution: + * G(z) = exp(-((z-b)^2)/(2*sigma0^2)) + * We target distribution: + * S(z) = exp(-((z-r)^2)/(2*sigma^2)) + * Rejection sampling works by keeping the value z with + * probability S(z)/G(z), and starting again otherwise. + * This requires S(z) <= G(z), which is the case here. + * Thus, we simply need to keep our z with probability: + * P = exp(-x) + * where: + * x = ((z-r)^2)/(2*sigma^2) - ((z-b)^2)/(2*sigma0^2) + * + * Here, we scale up the Bernouilli distribution, which + * makes rejection more probable, but makes rejection + * rate sufficiently decorrelated from the Gaussian + * center and standard deviation that the whole sampler + * can be said to be constant-time. + */ + x = this.fpre.fpr_mul(this.fpre.fpr_sqr(this.fpre.fpr_sub(this.fpre.fpr_of(z), r)), dss); + x = this.fpre.fpr_sub(x, this.fpre.fpr_mul(this.fpre.fpr_of(z0 * z0), this.fpre.fpr_inv_2sqrsigma0)); + if (BerExp(this.p, x, ccs) != 0) { + /* + * Rejection sampling was centered on r, but the + * actual center is mu = s + r. + */ + return s + z; + } + } + } + } +} diff --git a/crypto/test/data/pqc/falcon/falcon1024-KAT.rsp b/crypto/test/data/pqc/falcon/falcon1024-KAT.rsp new file mode 100644 index 000000000..48b12f47d --- /dev/null +++ b/crypto/test/data/pqc/falcon/falcon1024-KAT.rsp @@ -0,0 +1,902 @@ +# Falcon-1024 + +count = 0 +seed = 061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1 +mlen = 33 +msg = D81C4D8D734FCBFBEADE3D3F8A039FAA2A2C9957E835AD55B22E75BF57BB556AC8 +pk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sk = 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 +smlen = 1305 +sm = 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+ +count = 1 +seed = 64335BF29E5DE62842C941766BA129B0643B5E7121CA26CFC190EC7DC3543830557FDD5C03CF123A456D48EFEA43C868 +mlen = 66 +msg = 225D5CE2CEAC61930A07503FB59F7C2F936A3E075481DA3CA299A80F8C5DF9223A073E7B90E02EBF98CA2227EBA38C1AB2568209E46DBA961869C6F83983B17DCD49 +pk = 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+sk = 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 +smlen = 1340 +sm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count = 2 +seed = BFF58FDA9DB4C2D8BD02E4647868D4A2FA12500A65CA4C9F918B505707FA775951018D9149C97D443EA16B07DD68435B +mlen = 99 +msg = 2B8C4B0F29363EAEE469A7E33524538AA066AE98980EAA19D1F10593203DA2143B9E9E1973F7FF0E6C6AAA3C0B900E50D003412EFE96DEECE3046D8C46BC7709228789775ABDF56AED6416C90033780CB7A4984815DA1B14660DCF34AA34BF82CEBBCF +pk = 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+smlen = 1373 +sm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count = 3 +seed = 58C094D217BC13EDFDBEA57EDBF3A536F8F69FED1D54648CE3D0CCB4847A5C9917C2E2BC4D5F620E937F0D329FCF8A16 +mlen = 132 +msg = 2F7AF5B52A046471EFCD720C9384919BE05A61CDE8E8B01251C5AB885E820FD36ED9FF6FDF45783EC81A86728CBB74B426ADFF96123C08FAC2BC6C58A9C0DD71761292262C65F20DF47751F0831770A6BB7B3760BB7F5EFFFB6E11AC35F353A6F24400B80B287834E92C9CF0D3C949D6DCA31B0B94E0E3312E8BD02174B170C2CA9355FE +pk = 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+sk = 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+smlen = 1433 +sm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count = 5 +seed = 75224ECC026C18159FF92256844D0ADF953F0A4DD8D74D4EBF1DC5EE8F5630B011A447FD4DC34A2404D620CA0E1F273E +mlen = 198 +msg = DBE5B6C299B44F8D60FA972A336DF789EF4534EC9BA90DF92AD401D1907951EB6285EDA8F134277AB0A1145001C34E392187122506AA2DBB8617D7943A129EB5C07DF133D7CCDE94A7CB7F1795C62493ED375353D1F044257DA799F7D112C174FBC35687E2F87FEFBE2D83D29D7314B30A749FE41B1B81095638F112BC4563420AF235280E466FFBE7050C4937C60FC18D1A6025BCBD489F0C538E088E906ABE8597E2C8EBB64F01D225C847AAE4B77BAE6EBA9269962C4B94A9732CEAA2CB4093D442FFBCDD +pk = 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+sk = 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+ +count = 6 +seed = 447F03C8CD27EDAA1FA0436DA492812F57AC946479A9F1F90EC4F5E913A05F8AB0DD7645026A96510F6D40AF05D85B07 +mlen = 231 +msg = 0073BEE97FC97C0FBC750D474AEB93189F061E1A5CF6600C04FB0464338EC7E85252F94FCBC7B2BD00E438480D9AF3ADD92A92E3E2E8ACB55077C3278FC7503988A76E9B6062996B20889AA55B343D5A003C8A8852D738F955799FA3426BE5CCD3AA6B6EDA04D4884941FFC0B69C5ACF12B347A74D0580CC3335BA816200F87674A4C1D98097C70F2F27C74E94A661850610ECF4847AB5B58344F958C5719E06BA396225BBE21ACB0FDC512B885D391E11B0C0ED5CE6B5DD8FAFF91F50025C69D43072F7706D80D9FD786E1104125D79A5F4B5FD838815D44FC8B1AB678078CC174DDE970D448B +pk = 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+smlen = 1569 +sm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+smlen = 1636 +sm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count = 11 +seed = D34A0AAD27ECAD31A5E08E9A2D7901A9B85F864D9B1B46F40CDCA0B3615B2CBA04EF82AD7BD8CF627C3E861477030BE2 +mlen = 396 +msg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pk = 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+sk = 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 +smlen = 1665 +sm = 04CB8934EED6BF931B3192B123259D3B9C3046D22E9A9F58FAADCAFF020FDB52F1948B12BA0D622DDAB15C4B2E1A344DA1418B0F4BE3FD99505FC30F2A1E5B696E943BEE2451D7B268F722E04F8E00FDD9E1A470F8C977A6D45A5F621B8815E352FA14F64977D1FA08082A48AF495719EA6AC1C0B3D898603B4CF7EC88E68DD7190884382896D953D612CC21ABECFB01A04A1BB1BBE8986D34625756396CCD84BD1A6B5454DDA98824CD4844D98F356AB485EEB19F9196ABB1C3088C0C3C5846C88760B696D91A232D6F4CFFC85BFF33DE1A3433A27A209A461FCF37F2289F98BEA7CCF183DB1FC42A7EDF958E7913F8711DC375E43F09BE7C7A2C2B1318AE2A9CF5988FBC2CE0735A2CD9FB6C8496C34406C538C01BD494193240BFF947FED47B7CCE99A1747973F1FAA5223AC564BBA0CA8973D1310B5BFA1452CACE9110BC22A8D4080A8BAAA8ADFA3CFB6685679B648484E3A43F9B1B2531949BBB8FAE1846F6D45D9272FC2CAA2913B5D9F8D322E9B18A685122D74634C60730C101578BEF2480711FEFFE02123E76D6C846559E2EA99A98923EF095630102A5573EF027E0AB6E52555A9EDE0D15A73C8B2FEF87CA6FD9F903F02A54F2DB39AF0C519B5494662646CFD8CA1F2C638EE2B767F3D5360F49A26D084B8719AFEB5B0C64AF92EB27A60F6070A944F6770F5013196A050B2666FD27E288DB027C7B5E9C79FED73ACB3C9545FFEB4DE497673F760803008C2E9DBC9D299E979AAC4E6FDDE6C33A9EBDFB088E08795ACCA059DB37F18D56AD4B0CB2BE89B06FAB395595671EDF9514DECE65B147C18B7FF1BAB37B4ABFC134FE7C910CB2286C8967374311866192DA21AFD9227CEA6A41E47F25F027A7A71B21EE622DC28BECD8D8AE6BE1E490A4DC7AEA4F096AEA44557180413B5FAEC79E6A90B0944312AFE6918BE717C5F9DC551C36B14971A1890E997DA3AB191AB65D088DA6F774BF6ADB1B076B6E78369B530F934255FEE482D898999D095D8CAAF20B6A0BE4C7D729565BB6B126ED494A5B6327D5A4EEC48200C35F95ECDF5E5846F2C45F3CAFC439E88EBE085E28381105C6F8A7DEBEDB2118C8282FBF21E8C3E3578FCD8A2A92E521C703FD9FD13471362BEE3A1666B8A71368227067101D85474E61B35036D60653E4E80BBD32D2219EAE65868B3DF17AD26E7C5D45971AEBA5734E8C20DFEA66D5675A3888BA349BBCF66D6612428ACFD88A461BE4E9C0BEA9DAC5B4CD7CB4EEEAA4B75C52BD72490A6B9CB7FD753D2EEBFEE9E2F424B342C9351E12AAC966A77416A50B55BC4B1E9B4C96DE20B1FF15762AAAB7CCDF7735624DD87FB432A37094F3FBF198065D9F6B4EEC038685B7F8F665D9E5ED687F49E948F2902360F335E5A1AD45B8B9E6294796335E04661B7F7C3FD45EDD61047A0C1765D64B98F79F574DDE3B56DBD4F673C03B2FACA06D6D35D81ECCCA9A6A4388EDCE68ED2D13497DB2DFD413C42937741D70C2683B3199033155F6E75EDD1220D20D6677D3B1BE0C979525929B392B654EBD1E78FF66CB8033FA11FBC0272CB271935A31FA98B66984C14BE599E682729DD9B07AEF7C5CC3C9744E9A7B0C500AE6F8E234AE7C9A11022BA80FC928482CCDAB074A2BB9351BC35C371E888742D65BE4DE6C39B036AAEEC9FD87AC1D6CF225F76E4511ADBF989D5EC5339462FD1D6186F03A500AE445458CD1D60F6267E2AF19C40C8747E2FF6EE364F0D194781669A7B5685A066E0AC1EAF25595392565151B5C1839F6DB6BDA2AED22EA8B6EFF994AE22047518E04422524FCF59A84E25CADC3F586B2AAC2791DE624F063500664759B72F9145F080E8EA97DC17C72F24BEA8ECB2D57D49A7944733691FBF9066FD2CD2789CD46C808F5CE72289BA68F54E557E575C1833729ADAACB18D847A7B284B5F975B67EBFAD1B619CEEEB9A099A3D9394E3D56812955D9912D984E25CF2CD754C4BADE884104B7A78E4A445D59C939F270F18F53D5CAEA7E6134B42FB3E96C6B5A665982FB4FECB06523BB16DD96AEF64A60A14E2C7F88D39E281DDEF43D48E2464E118E241D895C037F453148258154A9522AB55873C4D5594B66FEE93BF9E5B9D30874D30876E18E6EE9D969AA3B25E762404820D36D3B182EA38A50A21E7A090059956508FBA313E92CB0F9686630F75DB17EB318C6B15E9444ABCE169A091FCD7BB2DDCE5C1E0D62892C9B8BCFCB6711D21216AE41344159096296C9236CBC189054877E847CB2277E595AD8123FCFBD3641ED925CD906617713A296FBAB7E41FED5792356153518687A3A62013181379373FA994F5233E7E0B4987C628FCAD2F13BDED927EB4847B2480 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= 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+smlen = 1800 +sm = 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+ +count = 16 +seed = 5B485527C3B9A5E5B7579950049CD357975D4BCFEF83FE33C087ACBFCC10A0BE4225E7F8A5F77203B5FC7C0B5FC0E78B +mlen = 561 +msg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+sk = 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+ +count = 17 +seed = 327CE565CFF6CD9A25EDD84F482FA0758B78CBC246567DAE98B818314AE28CD438E339043EB3FF16E1C2B4B104A717B8 +mlen = 594 +msg = 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+pk = 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+ +count = 22 +seed = 3222E4B55D6767E300FDE03DB3D8227E19FB8B08EA9B923FEDE18D699DC3694EFFA7C4DAE2AF57E4A0162B7C564199BD +mlen = 759 +msg = 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+pk = 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+pk = 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+sk = 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+smlen = 2065 +sm = 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+ +count = 24 +seed = A08AD391E0FC57A83B74CA8CF44DB67F8178262ED9B20AA0163CDD8274AC2BE05F558B112B094244370C1AAAB75077E6 +mlen = 825 +msg = 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+pk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sk = 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+pk = 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+pk = 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+sk = 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+pk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sk = 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+pk = 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+ +count = 31 +seed = 9E6E12F025B2A57B0F5A3A9FA70396FC332E1802608E5CA07CC4FBA922F1FE5DEA6721B96F1BA2BFB97825A19F08FF2F +mlen = 1056 +msg = 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+pk = 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+pk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sk = 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+pk = 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+sk = 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+smlen = 2394 +sm = 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+ +count = 34 +seed = B0C7530A52AC9F561C2C14548D3A5F5053396B738EA1C7A5190F5AB01C9C38719C4DBE856E42D37A114FA24FD5DF5081 +mlen = 1155 +msg = 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+pk = 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+sk = 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+pk = 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+pk = 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+sk = 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+pk = 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+pk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sk = 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+smlen = 2623 +sm = 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AFAC14EF697ADB2447E7C7DCC7EE9305DCCA0945C543E653AD5BDD95629D026D5A98DEF52DD9BA72BC135BCC3FD5F63F65AA8FDFB7F0E208C3B66440A1360E0BB2BCA24846658068B6D8B33C70D30D2E56C348202674EB5FB684C589A41D7EE91F62A74A2C8BEF2E3B2EE73165CFD3FC1975909742586A8CEF7880 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+pk = 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+sk = 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+pk = 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+sk = 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+pk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sk = 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+smlen = 2722 +sm = 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+pk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sk = 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+sk = 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+pk = 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+pk = 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+sk = 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+sk = 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+pk = 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+sk = 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+pk = 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+sk = 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+sk = 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sk = 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+sk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+pk = 0A9012F69A6294CB76C5B0B4BF64AE4CB155D884DB15A9749D92AA45B64F3CD39BE316BE9369008BA969D5973EF3A0B8D7B65281042BEF0FBE26187E60F643E43036F3B53C93E192093B8935197726F6D5869141893D4208EA9B2B7250368128F64C6C2C726DE2DA8F809118FD76960C2332B81915B4011CAEED1306B405D077B9754163E58C6F8A6108D58F1963394B3944E6FF5DB1B72B5C47572450FAD2BC821F0F75008ACE8A9A75BC4F506F9ADC6354A2A1420E401F621B543FD11B06882B27392DFAB4008201A6105D8C8ABA19682614215E83862F992CAB4EAD220595DE86B960E77D6EA70D2C9D33281D8D4C096CFB5D88CF1C154B78D3907F7D2CCCC2D20C01B4B022A80C264155D869F954A3A2A149F2C0632B7B3CC4170132C76DAEA8A2A53A66568B5814A422C55C847CC750AFA0CA923CB4E853AFF080F1B244355FC356446BE6775F2D188DD8FBCA86FE9015DBFB2B11A39AD803717DD7383850B5B83D82C810B5F386FD9553B542C7C0AE591103703D042A8568862A40A1DCD30325E94ED84F919B09E645C3B395328FB04036446BE0980D7BF4A1886F4EBE445830227CA5584462326CE60A987DDA59A122A096E360D76D8447FE3FBBA224597A384B64AFD26C2B50F685694C0F191E61E4AE000309AE45A9B1CDAE24558AD4C6ED26665AA8B2705DF58110DF95F6E3C386656102956C7396996B0B2362582BCE984218AAE2A9E60122D1268A33F1A5259B5FB1A0B51B54DF29996C3CAE17115FEE754A94FAA492750D268D792E2BD200C2F413F465A357EC349096A58C0DDCB89B9A2E4A21E973D9EF26111189BC196C42795DD8A19A761BD516A1BBF50625B3AB8ECBC04C57A6A6F2C1F124DF0395F8DEE6490B0D9DCDC1E712E3554FB9C083AFE9D132B5FA15D5AF9A6635D38B1F63B2B534F75710CCA6515E914A870FA498C6FE5B208A88636144C686CC028B4DE4853F48A24862A162E8435B864D61A6E38BE21C39D787DBA7A8ABB6CB0315685994C8FCC2092D3898563BAA6E6585242EDE154747FC65946842061D1221DD5A4A955A8546EE8930C04ECD4F41CF6BF35B6941B6D522EF82E5787DB7E09E61BE883EAD24EA963E5771A2F599529F2E3155001E95D593CA9AB09B1C933409DC44A95F468D6D977233EFEF5C8216DB2903878228DEBA005AC41566D6B305A6EB705145E63D5D595051A475680E70485571F9788747B95413C1ABE9508F0982FB3826B304F1B9C4672D3891AA1D1345890109F0B7477598744A6015F564845AA54999E112169D9BE057522211A675E8F67B9EC92CAC8156D6A805B65AA6DC6727DFEA8322F2436C603F4558BEF771AFF1BA7C195B2C008CA15DFDDACC43D835BA1CA7419E4D5795BC7B5B01D8568C7A6255A90C0844B0A253AB8B5B982C69C70F5105B5FA661D8704014622C947E4361910ADE57CDC469AE1E18B8C0E5C394A6D3191C7F29AA8EFF169C2E214A499780A8A041B4C2BAAEA67D6A24E9B8B206BBC9B3980360CE0C537955193E069878FBE03856FE24A1091374B819E0EBB847AB17F56491AF955841ECEE9857C21AB02893AB564A4C94F162F593180F6D554DD23F52A51AADA2A299297A5DA8B509FE485796EA5E1846E929A4F9958665952875F2DEA792C3AD7A79BD88DFD4DABB714DB421C8F872288A925D1B154D140B92DA8D419F1DA66909DD36B4BE2C293793D720B80125324A5274E912350A4C43B6067A2339A28394F5AC03B164938B205630391904760428B42A681B15082F943406EB4B5EE419CFAFA47C841DBBF59CB81EC62BC6285E822989C7B0BD18CC473D76C09F8181685829B7E857EDA7CE2C753028FDAACDFB2451149825489DD73F5E80466AB072D31B2A7878A39239EAD01A0A4CFA558CDB6306D6769E6B0A18E66A4723ECF410A24CBBF2D9D9A709B94235277DB23A3B17F1A81723DA2C8A2CE58603AD8CDB8F0EFB3B86D74532068E9BB96C89E343F55C2278FA841C07887C22EA63DC6F3454484BBD593319D450A24F850E286267F2B5D6F89B5D1316A26D63243D10920A0673837EC425590C20430E5CA65E6EC2299D04F5E55A96334E900461DD7F2DAEF4697FC8ED3251F37054846940E01B733F9CFE87824C8921AC522C3061603BD5F331F230A62544ABA584D28ADFA2507EC5F5F9C981FE157CD8D7AE0DD3B4451115114C5581ACC6E97BC699AE74AF700A839AA855CB168080D4617EAAA1D8CCA32664DE23E24F280271B0264B61F2B82A1C300B1AD27809E0A279AC456728E3E0486216020CE908F7AFDE7B1CC486F06B2ABB9CC7FB95E2B04E4C7665CC138925EDB8A8E62212AEFAE628DA54845D48C8A77716202B26F1CAA0E20B8E55E07791A4CC626AEF676580E17CFCE7B8AC67378B2D24E7AD0B2B5E7D5A62F586CA1A79A2B6EDCDD72ACE87C581E36395E2B324AC09255366F0784ED9CB14325501CC598C2E3E3CE2B25BB4041E4F2BCF2E64994540A6C627999A6D4AB9586EFFAB81A58A0ACD24AE7479E6F90AE714C0DA3 +sk = 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+pk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sk = 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+sk = 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5610FDE22856B229A3121D8B81EE83DEE4A6A9FA3FE8C75351574CB000BF7F3746CA1CC5414AEB23A2 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+sk = 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+pk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sk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sk = 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+pk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sk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+sk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sk = 5AF03C2377C0F03BEE7BE3088C0F03A2110BE108613F7410F85D0003F00C44E0FA217FDF0FFC50FC80FFC98EF87E178BF204DDFFC4021BC10002418B5EEEBFE0743BEF41D0781E103FEF8465008C10FB3D07463E8082F03BEE8802DFFBDFF7C1F7BBB084C00076318C3EF87DED804107BC017FC21783FE783DEFC02F740110402303E2087E307C3EF08BFFFC5B27FBDEFC02173210FC1FF884621B85F8F9FE0821FFB9EF9C1F37BC5FF4803FC3CEF42307840D8F9D0EC000687F1139FC93C007843EDBDEE83C727780117C400FDDF8FA0FF49C2041A18BBCF7C20E77A2E93E4F0CE217C1EF007FDFB5E127BD10440E8BE3190BFEFFFE0838100BDEFF4A31F821017A11FC5B1E42037C3E104E0D7C842782200C03F87E007C7FF77FD003A00EC3FFF43F06FFE17BC200BBD100FC00805FFC7C0109B10C4317424FE05FD805F2045A07BE2F8C24107FE17CA307FBFFF021F04C6F006100BBCCF84038BDE0083A08780C83A1284BF17C7E17C1FF8803277C10FC41003BFD03C2EFC43C849F107E20901FC744017405F70A0F87A0E7C5F08FA316FE1F07C4E83BE1045BFF43E287C126BBDEEFFFD8BA1E07BDF7FFEEFC65FF41A0883FE705F287E0288FFE00A1F0422F8782DFBFCF7BFB17C42FFC3F17B82F87FFF87E20042220BDE003FC0101C08480D7023F7BC1FFC020085E18002F88990039F1885DF03E0F839E0FBC708024D083F0FC5FEE840068021EBDBF845C10BE1E006307444FFFFD1FB8006BA2207FDF785EF87E0F882009BC2D0BE20003FF7C3FD837CD785AE87BDD14033FC00FF89EF8860F0C06D83DC11043F807E284212804207C7DE8440084050FFC207BA4003BEE90BE083FFF753C003E1E783DEE3BD088BFF83FAFFFE0F6C01113DDD843E1803E000C5F0FBB083DFD085E08B85003FBF1B81F08400883F18BFE05FDCF0BFD27C3F2147E0F3E4FEC3CF7801F8B82D730217C01F743EFF4BFD8864007DFD9420F64401804610FFEF0F9C0880107C241805FF841F1901B2E3A4F83C5088A208CDDFF7BA087A027C44E847CFFC1CF07A10185F2EC000F43B0F35D1E85BF743E007FFFFFDDFFBE1F905FF7C3FD74270E8050044309040F8F5EEFC4421C1F30BFE17FFB373C308BDEF7FFC07862EF042183A100022107F908F5E1FC40F60C019C7DC047EC048108B86E83C1F87E4084002001F08FC0F83E03704210024278220743DF641B087841801FD703F27B80F7FE407F43207BF26F40FFFE2E8421E082208FFD1885D00FFCFEBE30841E20BA6F0843E8862F7BA007B5F0F4610880020FBD287C4F145EF884007FA2190A1FFC3CE9C3DE7C3FF847DEE860FF43CEFC36E9BBCF7BE02002216B7E003C0407E0178400FC3DE881EE746419042FF385D8FFE283E10042510884E0863F8380F876101023087E2FFC00100590F000DFFE109060F7C231847C00841F803FDF81D08421D90231F0B8EF40317804103FE083A00843FF83A50ECC01FFA1107E31FB7DE87FF373FD173C1F0400E8460F0C28D8466F848216F21FF461D0823FE820077C32880007BDFEFFA3007FE09FA3173BF16C02EE89F083C3104621FC42F6B83F93FB1841DFF462E74222FFE4F7BFEF7FE32FC44F03BE0041EF83831FC82F8724F03E11FF60D9BDC09024E801FF082120C61313A2E0883013A41EC002FC82E840217FBDF839E210210FC20FF8BBFFFC3F00A3003E31782600BDAF0C1A087A0FFC9EF104210C1D1F8212FFDF007DDF7BFCE647E10C1F27F8027FFD1084327C2010C3F1885DE80221F7FF0804037B61D7F602FC3DFF803EEC3EFEF6EC130E23E8180DF8ECD8E00109C4F202051F44100BF7270D161207F2FDFFE8090D0D0CEEE0D70FF8FF18F9213FFDF6D52CEE03000CFDFEDFFB00F503C0EBFDFB102AEB1109DB021F020ADA0AFEF7F8B2C4D10F09FC07CEDCF3F603EDF211102223FD20E0F5C625F20FE80F0A150FFB1013FFFA0FF1D2FFFA17EAF5E90C34112C070027E4EFF3F53BE735E82FE8E202F412E723E7FCE0FDFA03DB00F711DBE404FE020514FC2AF6EED1001205100AF6FB1FD203DCD91D021409180208371D14D1E8D1F0150402FE23FE101CDF0210ED0DB5EF08E32810FC08F3151014DFF0FD20E9010DED01EE152326FFFCE9080812F7E0EE141808080916FC20FF0400EED32F2705E1DC2B13262316D2EC02080CDD07FCFB0823190B0340F814FCD8103724F00C05DAED0E22FA090CED23FFDCD607F614F425E5F0F413EE1124E603FD180B42DBFF0C1DFAE4DFFE100F031500F0F0FE14E60609FAEBEA1D24040B01D420EB2601F0191C1AD7DF040321DDDE1C3108F10B0F16E81A20EF4514ECFF12150F0ACAEE080AECE3FE140815120BD3F0140902FDD5E9F5E450C5EF07172231E4F8E712FB180DF6C00F1734ECFB23C80FEA06E2091F382D2F03F6181DFEF8EBEEF42E15E2091BFE09FCF6290604F7EE2814211D260612EC321810262BF0E5BAEFFC1403EFF3EC36FE22FE36D813F00DFA050604F7DFE9E3082001F712FBE6C6D6FB33F7FEFD04FDF2FBF8EFD0EA1FEE04FEEE22BC02141EF6EA07F9FCC5D8F228F0E1E910E1DF0AE7D20ADFE005301F26135044EFC7F7260500F022E029FD18F83DF8080916EA0D09B90FD10511FF084CF602D6050B11E507EEEAD7E00913E4FA012FC9080AD70505F40EEF0926E7162705F2F9F21000EF0AFF31ED0D041A19D703FC38D90EE3E643F0060AF808FF0FF6F50C1510B6D0CFFAF6FCFE2F07130416F0030F06FE16DD3BD628F72D230314DC1FECF7EEFCE100EF0AD026EB05D0FEEAEBD9F4F018161FFE051FF03613D4EDD2D620FFBFEDEE282B0FE5DFE3F61DEDE804F0080F2D0324D3150BDC03DA20FB12D809E0E11C23E513DC0421E8F105F2F8181338F8F7D7170720C80AD208CCFCFF1C0E2734040EE515F935F6FBD501FC3BF0340306DFE206EE330C06001FEC001C001A1CF1C5D1E514011C0DFBF40EEB0C153000F5171BF523E9F1F108DC2008F7141011DA02FFEAD512F4F7FD17050D0A1510F30D1B0A2C00CD19D50BF6C318EDF31B17F9F3D20023F71EF5EE20271DE1FF02102600FF25F70E1915F7F2FAF3BFFEF2FAF0E7E6161727EFE1F4E3EBFE00021E09DEFE0E09DD3BBCECCE14E415F22AFC121AE2232202EA12F6EBC1EEF113F00AC41EF1F60F07FEEBF1D1F035FCC7110A0427EAE715E616E613F0F01D22F300FF15690142E8181306D31207031F3705253A0A38F7F8DA27EAE7D93BE3EF2013 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sk = 5A07F6000039F87E10003DF0C5E0F0601F4002779E21BDDF907CF005F10FBCE17E1E0C600109F097DE0EBE3E0421FFFE5E7FC000FFFF0C83F9021E783B1103F2182517C430F024EF804104621FBC208B9AF83C1F1402088A30FC7F1785E208C42805A0843BF7C9FF7C63F8464F9061FEFDD2FF80F845F100250785F00001F87A006CFE07C822803F09781EFFC20F83E187A21002318C23E03A4277DC006C1F7C1DFF11E2FC03107C01844227725E9365DE8221FC030049E17CFE2EC81FFBBE0849F078DDC84200F881004C3C001D078BEF783F07B80E2420D845F0FF83F03DCF8C5E07822203DFEFC1C083DE06C01EF041103E00FC7DD00DFF801DF879D10421F005C0111F083E0EF81DEF8DF17BE5E744307F8107B9EFE8611EFE10845DDF88427825307FF0FC9CDFFA10FFFC08F9F103A218780170C3E88211905C187800901EF84DF0F01D00BE12F03FF78431FFC41707EE87BAE789F1037AF53DEF03E000083203C1F90020701E07C01188BF073E11001C00F7EEF49B2ECA1E041E1F802087BD00FFD06FA3187C4103C028883F7C3EF081E0F81CEF7DE20C6217C5D017A3113A0F7865F03FFEEBE5FFCDE217BF20761D802100481F07FFF83BDF0C41EF7DD1083EEFC650FFC5EF700DE441FF042E7BC31841EFEBC1F07E2F0422F90223047FE1421DF0640FB820FF7DE07E22009FF0FC230BFFE7C3FF87FE080A2283A4EF7C0FFF7C2085E1845EE8460F941FE7FFFFFFDF10C040785FE0BE6D185C1189F170850701F0077EFE85CEFBA308B8220783003E22803F10C21F044320C1A087A3EFC1FF84A40F7E118C7FF93A2FFF7F07FDEE00A3D001E083BDF0745E7CBFF83E3EF81E187A318FFF08001F049E1701FE809F01C61FFBFFF0BA220FE307842E785CD0F801879F083BFF80C0E8BA009062103E11041E007A1F7405FFC9FFF3BCF8002017FF38B69F8821068420801EF880108BFE1FFBC27C5CE0C63D943A36BFE273BDF8C2226C1FF6C7DC77C30F7DEF7FE0F743E18000F849C0FBDE2F41F0FFBE20C40E8041FF8630FFFD087A101400084230001AEFC21E93A408C1AE783A0085F18C3CFEFFFE803AE93BC3740100F9F28C7D083C0F0C430FC3D0847C00819C07DFDF863177C10841F01BC4F7021F00800FC231F81F0845E1083B1EC9D003FA008C2087BE080A4F904217C9A37026E7C7BF6801DEC5E078400085DFF7C2F8C20EFC6117BFFE08BFFEFE2F0FE20046200C62E0880DF41FF7FE3FF3A00704128EE6F7B64177BF0FC1FF0FFFFFC6317C4200003278A1F77E7E93E0F73FCC877E07BC327FFDF7C1FE04BF28BFBF1323F0382E036400880F80A318083100040F025F0BE007FE2E8C4101BBB0F47D0080301421FFB60F77C30F3A116CA6E8864077BED7BC11841F1EC9FD80A3F04021841E013DC08BDEF9320EF382E13C3EF85C18781F87DFF6BE3F883E307FFF0B5B087A0F17C2F07FF0785E08B9CE17C1C14410806718C60E83BF20BE2060A6E87C2F789F0F804F8461187E3F789D18782E787E0FC42E075BFFB9BF0C421907C00866107E209B5FEFC3EF8762204BF180041FC9ED709D1087AE0BE4FFBFC08420E8400F78C4EFBFF0F81E007E4003E4F7FA3F8421EA3E2D93C0180BEE909A16FE000C5DE6FFD06FE2DF8A10783FFEBBEF784000BA0FF85E1FC9FF881E2F83C17C81088830883EE93810F385E8043F0C1F27FC0074810845DE041D17020F809F0981E203FC083FFF77E207C802883E27860F0466087E12F09E01402F7FA4203A220842FFC3DF7840F7B7FF08C30F382F6C4718F9CE082316D3E32816ECF6FFF00607E5D5E93120E83DF8130A1B070DDE0335F4DAEADF0AE603F208121DF9FF2F04E5F8E7E4FBDB0B22FBFEE3F21E03042D35E3E715F0E90AEF0AE611F8F5DEEF16DE1DEBEAED0FDC05EA0F0B1FFA0DF81A10F110FAF3E8F40A1D192AFB292834E3EF0E1D11F4FA0E0B05FDE0FCF8EEFA0AE20707E41E011206F7F1FBE0050CFB36FB250E1113DD1CCF18F4F6082F1204E7C614F901E3DFCFFA24F7E706F20DEEDB31F3111424E7CBDB1310F5E22EE7F207082BCD3DF7F9FFE909C90EDBD0F01405E9171D031FFEDF24261EFD1AF4D41BD522F924FA0406F92CF8E7F1E70FF8FE0D22D6EA270EE90B0EE6F43DFCF9FEFE011CE8EDFAE5F506DF10C5D62D2CCB2600360BFAF5261403FD2DFCE8092A08D6FA2DF8F60102DE16F9F8FE1EC7E81026EDFF0FEEFBF700EEF3FBCD03E1FC0115F3FF0204FCF31C0BE50522FE1BF9E1282A46E248F9FAEC1916FDEB24F3DFED0D09020F09F2F2D90C23FBEBD9FE14FF01F3E4ED2C110AE50937E90A24F2F70205E8E2E100DBFE00F313241CE6131E2812DFF4EC22F8E6FBF42412030EF3EEF4EFE30F0E1CE2F01134DBFCFBF81C19EFD102FDEE13E82024F2F0E3F40ACC21EC17BBFB0B32FAF60BF805280E32FDFBF6FDFAFC1AD6EE08EDFE0A09E6FFFA0CFFE5FDF6EA200C2DF0F1F3DFFE010AF7C817F71614D4FBEEFB20FAE5DCEF2331E5F82AF710EBF5FC2B201405EB1CFA05F6DBFCF0CCEA0AF312DAFE0A23F3E700DA1010F1270017D8FF00D4040DF324F415F01004D5D204FDF70EDF202826F411EE01EBF30FE20A2DEADFF0FFEAE719DAD60709EFE8F22DCB2611FBFB1200E805E2FDEC23EEF5E103DE0802ECD72520F00EE217EE411CEF1BC6F9F20F13D203F91038EAF3080FFB1304E301E931FC07E524EDEAF5F6E51013FE2307FF062EF7D5F71325EC08F3FA11F2E204DEEDC52C2321FA1F31EA2423060A0AFAF5EFC71EFB16C524E1F7040D1BFBD90B37F8F7042DF7F63A1AFCE1381113F4F406F0FBE9F204F4E81B27F5F304EBE905FF281C12E10A160002051E0DF20AF20AD30A49EBCD0037FEEAFBFB3F1829F2B9EB0ADEF70FE9F2130DEF2C18D408EF06FFD912EA1426FBF80AFE27DFDEFCFC23150901130011020D020D171834F6DD16F530FF0DFDFDF3000FFCF8F3EE1224DCFA1028FF04EDE1192115DFFE0B49F90EF41B0D2AFE0E0A01F10FFDD6D504070E1025D6E8F8E407B80CEBF93BEADDC1F70F32F6095E0725F9F70F0ED4DF0711FFE7E30112E90F07F50C0BF0E6EE11111AECF401E7392AD0C61711DBF2F5EA14130AFEDB06FEE608032212E9C4FD1D0BCED7FDFBEB28DA1FFA2AE2F601EF0B02DFECF3D7110E12E9060717FCE80AF5FF1407D017DB320B0DFCE700CA140DE0E1FC1818F6CFEA0417F7E5EA32FF050CECF30B1606EDD8F915FFF9FDE719DA15 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+pk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sk = 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+pk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sk = 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0A4ABDC01825879ABCF02C566F12123575EE5015E1C853C6DD3534E515009DFD6233ED38B364FFC84A0847A4F175AB684897B975DA3284E1F36032EFE9B16E8F3981F8F7529F750541820A04C801508528966A2AB261D5C94371831D69865A16D8D356664C21910C2F2C8BE2C5C9AEE1366DC6AE18F6D354A1064FFA19629C32E444348E9D522766546A3C9F8865EEBB5257DB2EA46CD7402C502A083D2995BECF4C0A6464A17D2BC7552D9E2A96CA9C747545F57C203C8C761BF04D467D00449DE9E8921A21E889D2EA0F2E90D823D9FE16EDB38E068BA1AE8F54760231DEDB7C794A6F0174AAED26A8B7E352C1F3436EB7EB4BE6329B907116FF956360025EC5BAAB60792113BB96C1B63DD9DB47625B9937940D4BA9CA7DAB5C6287FB679DAD5072C15F51CC9F9EEE53049249969DC5237A22D7B7FDDBB295A78460915D269C16E4279AB9C18610E150490F986C9833174E3F4461D83E8F16FC1A5864B20269B7C6300CA186A10C336EA9D88B917091459EED81025ED115419D08AA15E749AE02757223F34D0E0A18E8CAD6518253A2C53993B58A26203618C1E8DEA570605E219B817041ED24F5DAA71E9E2E3EE87AE3AC8C361CEAC5D66D04B5C97BADE9A94AFAA8D1E7EC793C6624FA0F25EA31E44F1B9EDA4224CC3FD93517AB891014189944A0BAADB848B4E86484B15E66D9656FB5C4C6552E6206111C19A7A662C1293C1D67A7C87318B8333283AED2A7EE2733322995571193D71287F52BE6C9435AE1355A685B6588001EA48CD0F4221F5EB3A97BCA5A0FD2432E1922E38FF0010DFE59FD1C517FCE59B7221253568931003EC0F123C845BAC81DA38E80861A1A11F4892EF4159A4DD35D4E64B34EE27B3310BAA2DFC3AF3F756B159FC5FD2E1CB534C7C740376929B6099095AF1D147A67A69BB9183F7A1D082DB63EFED88C91804B7DC4B7AF9BDD9B6D8603574FEE3132C644E85C7A96A2DFD6F3E54FB62D5C74624C376E616EF91C9F2E34C94F77691D6E38343846658576A79D3BA637D3908F4AD55660082D06FE703A77D6E36D1A14A502198DAEED67C94EEABE4F84F3222867B0430AC681AEC40972A8D0481E18F110B182299D10DF0981B0F32BC23F70819B6881C30B4905760AE8D8E8A966C93725CC49AB047E701F97810990CC41034C72B7A6DF95F767541B3E95601A23522761D3A43288458FD94AE11DC6B7AF22EB80D7C926ADC5CDD85F8DED347962232464D4605EA80063DE8B96621BEBA26F11723A16176A279F90355603A9659B6AA18986189636881227009C83C0A629F71A3E968788C63EB478D4006FC43FD23C663651B4B2E75886C1003A02AB236C9E6E264543255C1EBA94F86B54AA3A985EE8FAE511D422C86CBA0DAF6021EEEAB50D172B768C3A88DAD09025BDA48539572E3D1C4C86B99CE53BD093C755C64B79ECCAA482D8471A4CE0F477404ABC340778572BB11F0DF1BBC2EAD70B1D99C12240AA1192E4A0B061F960BD5EB110E1AA33A95488CF938DB3557F12E150FE111235F7B8286C29DEF497FA5C6971956A90D0807898C01BE9CA802D607A75B24F58C14CD8DAB11A43CE4E7244F6020D2C080082E3071D1B3011D0C11F8C0F409973B3BAE57D59664C95562CEE350E38D11F043F8A5CF0D9BB4FE894066D203F0C6C331DBBA0BF50209D2D30338255470039C641CC6C2443FCAD9AE9CF1324E19446B92DAD041EBE0B8D80897A319E09CE516C7CED7AE492EBACBA5CABF546137F3678C329EE09F572D8702821C21E2E9D8C06C4C18E413075568D513DB454CD90D18A31858405E060986B4DBCB52605D9DF2BED0323E0193F24A817E40419820F5693B980024E03EC6DB1344134494A7B70222D35866676AAC34C280D795A23865FCD68BEC771668B5F48F9C40538DDC112AAA8649222AFB559827229EB0BABAE71D8CC8D4B16AE9119E205108530FDA76A26484D16F3386E926F9CFEC331518E6188B44E493E5BBCBAA27EABA4278C7E71E99264AD9D5D5DDE7797C1184D79B8796094F8A4BCABFBE30DDD93229E2B84D1656F89C200E306AB99B2907B4D2431379D28E7736C1010D25270E92269ABE05972D44D6F27022E897A8C800E52E807D713958EAE52FA81D4921780CD49C963C2BAC91333CAE2E59159D76739CF9A230A8F600588B6AAD684176FE46C79550E714411CE9B841964AD2E3095C28A2A3449D072ADBBF48890665F190C84CA0FDC6F940932945A3431E8E1A71FC5B349E2B50A3B5E1F6A1149D9F142F462504EB86C8BB80125EA77A08379A5B1DE01F78AC502D4BF8A024AC64D64F64659D1F01F0D86DB14038EB3258543501B7651487A124E57330610BEC724E9262460DAD91C0F895FC5A6E4F2546E5FC6F74366629950325039C70B855316C8C1A49824ACE0642353E2DF01419D607EE8934752ED12D34323486E8F09F9A79F3A984F9BDB64287F1CC847008945689C82B0C05C7E14F9D024F25F7207A0A77B48A0025DE63ED321C86F988D764B32023D14959C323C878E +sk = 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+smlen = 4571 +sm = 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+ diff --git a/crypto/test/data/pqc/falcon/falcon512-KAT.rsp b/crypto/test/data/pqc/falcon/falcon512-KAT.rsp new file mode 100644 index 000000000..930c93fde --- /dev/null +++ b/crypto/test/data/pqc/falcon/falcon512-KAT.rsp @@ -0,0 +1,902 @@ +# Falcon-512 + +count = 0 +seed = 061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1 +mlen = 33 +msg = D81C4D8D734FCBFBEADE3D3F8A039FAA2A2C9957E835AD55B22E75BF57BB556AC8 +pk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sk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+sk = 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+ +count = 2 +seed = BFF58FDA9DB4C2D8BD02E4647868D4A2FA12500A65CA4C9F918B505707FA775951018D9149C97D443EA16B07DD68435B +mlen = 99 +msg = 2B8C4B0F29363EAEE469A7E33524538AA066AE98980EAA19D1F10593203DA2143B9E9E1973F7FF0E6C6AAA3C0B900E50D003412EFE96DEECE3046D8C46BC7709228789775ABDF56AED6416C90033780CB7A4984815DA1B14660DCF34AA34BF82CEBBCF +pk = 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+sk = 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count = 3 +seed = 58C094D217BC13EDFDBEA57EDBF3A536F8F69FED1D54648CE3D0CCB4847A5C9917C2E2BC4D5F620E937F0D329FCF8A16 +mlen = 132 +msg = 2F7AF5B52A046471EFCD720C9384919BE05A61CDE8E8B01251C5AB885E820FD36ED9FF6FDF45783EC81A86728CBB74B426ADFF96123C08FAC2BC6C58A9C0DD71761292262C65F20DF47751F0831770A6BB7B3760BB7F5EFFFB6E11AC35F353A6F24400B80B287834E92C9CF0D3C949D6DCA31B0B94E0E3312E8BD02174B170C2CA9355FE +pk = 095A4CD8DBB5E94C93FE67A111582D99659B90E15B8A8CDD282AF74E7F9576063A01D00E8C0A1F96CC8D944450F2E13E6978854CF645BAED424C060040214BF90892EF584110E282D572164E51DC7E7E29B0DE8DAA7BE034521F2CD46890FDA0A8C5970A69BF96666FEA57E9982AC20B93A78DFECBDD9E8A54BCFCF040AE7679E533A13D527816917762D2A2779225AE0345EBF0245A98A4C493B610DD8126E30EF4265EA112016C325D5D1C08F9E8610B1AF0441CD0BD729209A4D900906A11852327E9AC6E504BA0EB1E343B9828094F4648248A03E00C0E944AD9496568D8D03CFEC9149645D359066960B8E7A2092C5EB4BC9AB24ABD196442872B612EEBA910ABE9945A24E14451C58DE91660152CC72596347993EF8F39C953F2E26057AA0C5404C1A28445B0B0E8681F5CA714B3C4B48EAA4920FE47D1A7B304B4E2C4F29C10968C454A2448A24ECCAFBB6494E1A400CB909B8D6A205CD085A5C444BCE049C098603B9FA8C9B7BF4763338A9461A32885220CF6B85BD4597D0A63E6D92E677151E329D3EB75A200DD78CC419044DA6B72799ED847F2C8650215DB04A8FC7BD3A48B7108703483E4556C78E8078B2EED0E5ABB3A44052E9CE07E96CD095DAB3979F8E886BCB9EA69B5D4D8A8A3726AA0B849F315217C877CA56B42DA44A1B884C5BE6D3D46C16BD01DF24478CEDD8DBD61FC36651ADC42AA41E51C8A8B5A5514C08BECEB6F820BA023D9867DDD2D1131C03C55DDD70A4BC60B16AAA380089DA07BAA1CE9D7C218B3B298E868EC5A492645CB7F5E6229EDCF394493725699994044C63AC000C6B18802880D5083D1CF928203646DA23F8FAA6F5EEC49D181AD166983E5C147B172CA8D48D210AE9BCAA5C5845A0D44C0AFE6C31C956FB0E0D77387D56150A37982DA6B7F8EC279189F1F09086040935B2EB756C47789537EBBFCB1F197D57F6F49A6893328279EF9BE2B76C8EA4AE2B06233E057BCFD34D5C22CDC61700A7A1D926381D035FA468CF396ECBB29614B0B7E2C4BBB6624AC6A40EB24320EF3548A2115DBCD2B571CF795C7DA111F80434802CB1D6A5A8764C9DF861A026EA34B698D25321907452046B3AA6D5154D902065A7D618E5AD102613551EF6EE684100B45564110A2CE86563FE4EFB1753B44C8AE0999524A51BA4DF49AEE8E3780E0E027F4D6376206187B8E3C17868B1E810C38455983AA4335C4E243D5201125AD99CB1408A7AE9EF51DEB6816FD418BDDEB988F78BD091EEC23 +sk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smlen = 788 +sm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count = 4 +seed = F1902A7815F37BC7F5802D8CBCE5B48D82EB85691718062BFB84D8C06AA41D6E9039B0A107245DAFA4EC109A57332914 +mlen = 165 +msg = 1CDF0AE1124780A8FF00318F779A3B86B3504D059CA7AB3FE4D6EAE9FD46428D1DABB704C0735A8FE8708F409741017B723D9A304E54FDC5789A7B0748C2464B7308AC9665115644C569AE253D5205751342574C03346DDDC1950A6273546616B96D0C5ECE0A044AF0EDEFBE445F9AE37DA5AFB8D22A56D9FD1801425A0A276F48431D7AF039521E549551481391FE5F4EBFB7644D9F9782D83A95137E84EA3AEB3C2F8099 +pk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sk = 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 +smlen = 818 +sm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count = 5 +seed = 75224ECC026C18159FF92256844D0ADF953F0A4DD8D74D4EBF1DC5EE8F5630B011A447FD4DC34A2404D620CA0E1F273E +mlen = 198 +msg = DBE5B6C299B44F8D60FA972A336DF789EF4534EC9BA90DF92AD401D1907951EB6285EDA8F134277AB0A1145001C34E392187122506AA2DBB8617D7943A129EB5C07DF133D7CCDE94A7CB7F1795C62493ED375353D1F044257DA799F7D112C174FBC35687E2F87FEFBE2D83D29D7314B30A749FE41B1B81095638F112BC4563420AF235280E466FFBE7050C4937C60FC18D1A6025BCBD489F0C538E088E906ABE8597E2C8EBB64F01D225C847AAE4B77BAE6EBA9269962C4B94A9732CEAA2CB4093D442FFBCDD +pk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sk = 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 +smlen = 853 +sm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count = 6 +seed = 447F03C8CD27EDAA1FA0436DA492812F57AC946479A9F1F90EC4F5E913A05F8AB0DD7645026A96510F6D40AF05D85B07 +mlen = 231 +msg = 0073BEE97FC97C0FBC750D474AEB93189F061E1A5CF6600C04FB0464338EC7E85252F94FCBC7B2BD00E438480D9AF3ADD92A92E3E2E8ACB55077C3278FC7503988A76E9B6062996B20889AA55B343D5A003C8A8852D738F955799FA3426BE5CCD3AA6B6EDA04D4884941FFC0B69C5ACF12B347A74D0580CC3335BA816200F87674A4C1D98097C70F2F27C74E94A661850610ECF4847AB5B58344F958C5719E06BA396225BBE21ACB0FDC512B885D391E11B0C0ED5CE6B5DD8FAFF91F50025C69D43072F7706D80D9FD786E1104125D79A5F4B5FD838815D44FC8B1AB678078CC174DDE970D448B +pk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sk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0264047BC8FEAE6A114B23BBC1CB16E0D84A736ABA26D079DD6523288A3DF2D54D26DE658BB00675A3010073BEE97FC97C0FBC750D474AEB93189F061E1A5CF6600C04FB0464338EC7E85252F94FCBC7B2BD00E438480D9AF3ADD92A92E3E2E8ACB55077C3278FC7503988A76E9B6062996B20889AA55B343D5A003C8A8852D738F955799FA3426BE5CCD3AA6B6EDA04D4884941FFC0B69C5ACF12B347A74D0580CC3335BA816200F87674A4C1D98097C70F2F27C74E94A661850610ECF4847AB5B58344F958C5719E06BA396225BBE21ACB0FDC512B885D391E11B0C0ED5CE6B5DD8FAFF91F50025C69D43072F7706D80D9FD786E1104125D79A5F4B5FD838815D44FC8B1AB678078CC174DDE970D448B29C5C5E95118EAE78FA4F66B7C775DA8A0C8B9668527A5D56A094E6D97B85AD286B4C5C46CC9BA10CC57156B7F6254F1D33549DD759750F28F8D37256DB6F6EA5DA9E2D110D87FCF63E5DBEE2B9CEA4A7CA050BC8CF63CD8E7156E06A26B3AE4A0AD9F4287794BE0B60188AB8C8BF7DD471E98022CA4B81A4D4DCE211CCAD07733CC6E648DE7519AFFA2C2A431EA17F6051441E3755CE0987433778FA76A0483A5DD87420098B3CCCFF706E0A8B00B027EE654E34BE27FF9F154CA56155AED2B19DAE696382CCC410431EBDD926FB53DCB4238D8EF3ABE7996E998922EB9566E97B03EBAFE7D2601BE75139C9641219075584E16DCEF326E69EC579102C382669016C9ACBE501BA5F3A2B2D35DFEB218ECF9951DCE39EEAEA6D04BF9FA803CCDEC574F9D974B0DF2E792363ABCD616849E4823F5554E02F9285E117369D48F0FDA6690F44D775662DA3D4C1E731D4640EEFDBBAE8590572F76382B42AF3B1476BD0BACF75A34571793499B88EC11994E5F868A88D9EEA615FC13592F473639B93AE5957B4C473F5DA390137318AEB27736A58446EB52685612570E5212AF2C54E449D9E3F9A58C5B5276CF0EF4E953DF367A04D373F22B2144E46250A0DD3715746B0F3557E1E70B827D152E2997A4940E2082CC95F9F66E3135E061305BEA4A813F7E2EDF1F5C68EE5F10EC9A2679CF445525C13DD7BB4E0635E28FC039F47AE9AD6D2EF912238A1A1742F0C4A617BEEC11227C70EB3400AD3B7967309CA419A72296F5C665920CE4E0A6E502044190C4269B1D225AB423EB9EA3D0D3241FED1340C90A6F89C7228F08B332DE29AE3AB29065517ADD313A8D3F1C7AE39E9C40A2AD4CDE + +count = 7 +seed = 8C151C556DA912A82DEB32144C8A8C9090CFAF5C12AB822AC3C72618837A41C2453B715EEFF3724CAFE69B1ADCAE9DDA +mlen = 264 +msg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pk = 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+sk = 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+ +count = 9 +seed = 11134936880F5A11ED3504CF7B273E55A351FCCB10943BBBD186623EE6C7A13A6565C3080D1F536BFDB018F99C4E46CD +mlen = 330 +msg = 0998114C84F84080E7EEBB47D248980FAC9D28F1ABB6DBAB3DD59A5CFD2C7CFF7F308372874DD5447C7B02E30165501C0C673128E4C543A414222BDF47E7F4E8DCA757B0F4A3281C0D10C4F02AB52AAF5B9A715E012607BA310947A60A5F62D6B8CFA96386D27CFA709189202421C078934AA2D955468E550AD4D0D4ACDD98B168A9568E232192E92789830317FBC959087FFFE353B6C168F3EFBE7164444F1D6CBA5246E31658C65440A841DBA78257E78502843EC1A6E9710229C8EEB85D6CDDC7D543285624AA1F756A5DD4F1A5D4FA52DB8C5C34880ED448FBB6D254509FBEEA0FA022F276B6A66BEF7ABFEA6049FF74291BABE781F718683397077B29FA9E2B46BC6B09251E587CC5B182195DD4060CC4A319BFBE251A5B660A739DFE5D0E5B93F3CB7E440194F1C8BDA922CB1A3EE3D27EDFD61C1D31A7F4534E84889EC83B51F1641892766434 +pk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sk = 590C20FD03E039EC6FC3E84000F00D7E002EFE2BCFBD0FD17B03AF081000FF208E8113DF7607B103F39FBB042F84D7F0C103F0BD1FEE40F7C1CD181180F86FC3143089001FC204117F0FBFFE03A1010C60BB1010400891021010C303CEBEFFFF83E430C3F84187F7F0BDF84E83EF9E3B1FF03DFF9F7E0C40810BBF43F41041FC30BD13E043144FC6FC20FA03ADF71FEFC6081F7FFFBEB9EC5F7F109F82FBB101FFE0BFF7B0BAE412C2EFEFC1F80E02F7EFFCFC0101FFA07D0C317F13C0C30B9000082F8007AFC1E0317A240EFE0BFFC1FBC17B0BFE84FC0000DC51851BF106DBEFFDFBE03F1C2F42202FC4140DF7FC1F7FFFDF0AFFB0801030040C1FBE0BB280174FFAFBF2391BE07E17FF451031411FFF83F07F81E7FDBCFC0F7B2861830460FCF3EFF6FC3F460411020410C3FC507D102100F77F7C0BD0840C0FFE138F7F08003E0C0FB913AF04F4018423D004E3EE41146FBF086100F3D03903AF41FBC0FD0000BA0810BFFFC03CF79039E3E000EBD0BBFC1EFD044EC1F7E044080FFFF42FFEEFE008FC3F00E8018123AF02005F82FBEF7DF44F84EBDF7E0C00FCF7BDC50C1F39FFE040FF903D07CF82001002EC60BBDFE04003D13ED40FFE1481FFE7E0C30BF081F020BFE7C143E84F04F7BFC6F400FD0BB041F82EBEF4507C046E410C0E7E041005FFDF7DF7E0FFFFF18313E10003B180F43F83040EBD0BB046101188104042144F7A002002E85F04E3F0830BED7E1BC07F141F8404007E106140EBF13D17CE8AF7A0BE0C5F7CFFF0FEEC2101F800C50BE07C0BB345FCCF06180F83DFDFC507E03D08004023E10413D004FBC00307E080001E3CF85FBDF8207FEC2DFA03BFC0084140EC507CFC0077201102002FBEF43F8404313E145E3F17DF41180F3E13EFF7E81F070F9D441C0F37F3FFBAF7CFC0F3FF7D07E03F087F7C08217AF800FD07F0000C0F4503F0C00010BE07F13AF84FBC0780FF043EBDEC60BEF40181F00FC00C6F7F0FEF81180EBFEFAF3E1830330050050000FFF7D23E1BC0BE0F8E821BDFFF07DF3A03DF7EF7CFFC04600BE85DC5043040FC118103F143107EBF0B9F7CFBEDF3E30F1BEB101F1B0AD0E1E10FE0251AF302EF14D6DFEF12DA42E70503ED03E200F8E8E332CC3EE9FC17FBF50DF631F3310ECF0CFB2AFC00C1E7F3D1ED37E4021A10D8F6E1D8F4DFE21A03EF44051FFD3CF8111C19F611F5FF10000716EB00DAE21E0418140CE0FEBA1917FCF118E806FC0006F81FF00708FE1C03210807301E1024EBF8EA320AD712F5FE2B2CF6DF090005DDFFD7222AFD1B24181C08FA211E0B0813E9312907F8EC03181BDEF43003DDF10AE0FDC709E81021041F17F2FBE7EA34E211FFF6EBFA21F70305E836FAE217FEF2FE09F61702F221162112E00ADCCCF8ECB5F2F81023EC0BB922DDCDD321110FF7E9E1E8F8DBDED3FF0A18F92215D73117CA27FB0212F7FE241202E7FCEBCE24F8040115D3F30AFBCEDBCDF20FEF0A242DDE2A0C1A1BE61B08192DC2FFDDDCF00F06FFE8F4F1D903F6F308CFE51D0117E7D82215B336FB040EF6F720120FD408D3FB19EB1000E6F5F6F3FBF3E7D8DC160F3A090AC210E00C25DBD40E220E2E13F1EFF7D80E07D3FCF90AE71BF443C90C0818F203E8EFF8E905E4F814F50225E4060216130AF1DF01FD02F7DDE3E4081CD3F8250DFE17EDECE92C03082A222C1814E11DFA12ECD9E4051A20E50B08EAEEE01F12EC1814F304EF01F706EE18FFFC261A15EAEAF31BF842263346130DE9F5F704FBEDEA32091F421A121D27F7ECE6070E04EA01F8DDFE06FB1717 +smlen = 988 +sm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count = 10 +seed = 98DDA6B97E89A479D5EE214E660DD6B5D8F6CC638A1CD4F462A0EC545F5B0B0A1A403AADF566F7B1C0C5FFCA29B36FCB +mlen = 363 +msg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pk = 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+sk = 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count = 11 +seed = D34A0AAD27ECAD31A5E08E9A2D7901A9B85F864D9B1B46F40CDCA0B3615B2CBA04EF82AD7BD8CF627C3E861477030BE2 +mlen = 396 +msg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pk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+ +count = 12 +seed = 4FDA9FB6929E3F391901D69FA0AA2F25A9657D249A620F1B9E305A5965676BA76794CAD3355EB632579C3958CA7D443D +mlen = 429 +msg = 49755A7B1A7CDC5C9BDF5149968061D3C95EE67BFBAF02750C45094303A9D9CD23A08F19B9C768ADC63FFD1527186D09CA4E0356BB882E263BF015CBE3716C05B31A69DDDB790BA82C341AC9B6BE68A81B8BEF8D882304BAF0020D761A0DB04412033DC369961A5213B04E81736A580F1162780599CC029E262D67F31B2773AFB457A1ADAAA292163144F17DE384234F3303111FCD89BCB30333C6C6486F775ED099043C34E6C86450B650F1A02D03781B1D20691B767D166DADF1DCC4D8604D976EFDC9168373A7316DDA9B9FB02A4A321218D9F54E287B7167A08BC0153843BD6355AEA1310824DD5D5EC458BE694AF176119D9E588A29C650FF5500293659EA478B39A62149F819CDB7E7CB32E1D7B1284F159E2AB1B1EA41AF4D0AC94FF3111FC1CCD818F9B2CC7A259701405FDF6A51D2D3EF62789297BD16A659F14968EF902C4A23DA409BF13A4913467B5C991854B2CA6CC006D3F4197A6AA58BD5DD95C36928DA9583332C3FB134FA3890FE7E299F1C17205366C4F4230724C43E4803912E72B816658BBB1B63780865A1F66A2A49B96E93711B1BE97B827D12173402828B1A065B94310D5BD6098D +pk 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+sk = 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+sk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smlen = 1120 +sm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count = 14 +seed = 0A98A2BD2B9FF42CFC18D3396BAD052E1D0F3372854DA69A318B142F7A1AAC609C3861263BD8FB0549DA7266784DB8B4 +mlen = 495 +msg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pk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sk = 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+smlen = 1151 +sm = 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+pk = 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+sk = 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+ +count = 18 +seed = 790FC03F956D1301A735504075B67A05944A762E0A4BDA77BB8C036C5CF911E2B561EC1CA6AA355D5CEC919AED42A1D2 +mlen = 627 +msg = 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+pk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+pk = 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pk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pk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sk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smlen = 1380 +sm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count = 22 +seed = 3222E4B55D6767E300FDE03DB3D8227E19FB8B08EA9B923FEDE18D699DC3694EFFA7C4DAE2AF57E4A0162B7C564199BD +mlen = 759 +msg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pk = 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+sk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count = 23 +seed = F41B3C6225245C06455272A6A073F363E5F19F09A0B146AFCDFC2B3B0EA64BAA3F90359F32B2D1017608B03064E90AB2 +mlen = 792 +msg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pk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 +smlen = 1450 +sm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count = 24 +seed = A08AD391E0FC57A83B74CA8CF44DB67F8178262ED9B20AA0163CDD8274AC2BE05F558B112B094244370C1AAAB75077E6 +mlen = 825 +msg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pk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sk = 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 +smlen = 1484 +sm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count = 25 +seed = 6E0A8EF5156D693FD0140BC4A31084E79773A83F42C8D133AC8A9D62DE3CD74511F893DCB26041E6B35E2B175408FCE7 +mlen = 858 +msg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pk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+smlen = 1547 +sm = 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+ +count = 27 +seed = C33EE43A9CBB4347BFAF71147B7FBDD88D212462CB06FBE695A35402C503CD15732B7D0E8BF829A555B9167BCFA2F2BF +mlen = 924 +msg = 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+pk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sk = 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+smlen = 1583 +sm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count = 28 +seed = 19CB4BE2332F7FF0C078BC001FAB3C5FD8569A76EBCE373D1ED4FC8EB5D744C6464E2B5EECB9EE836CD5D87BEDA78BA7 +mlen = 957 +msg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pk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sk = 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+smlen = 1618 +sm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count = 29 +seed = 6BD93FD13C0299B3EC7403638673F3DBC449F3A617B691DDF73C072B62BF028913375D7460BED2CF9FDCA517690CBAC3 +mlen = 990 +msg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pk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sk = 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 +smlen = 1649 +sm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count = 30 +seed = 1787C82DA9F2E6CA9ACF7D6CCA70116A1724902C81EDC1439F332C74807AF2BCCCCDC7AC1788BA798520B2999F39DC3B +mlen = 1023 +msg = 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+pk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sk = 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 +smlen = 1678 +sm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count = 31 +seed = 9E6E12F025B2A57B0F5A3A9FA70396FC332E1802608E5CA07CC4FBA922F1FE5DEA6721B96F1BA2BFB97825A19F08FF2F +mlen = 1056 +msg = 9C311FF20F574CD9B7BCE1DF705AE7DCE6E7A621C935A6E57A59EB31FC443AB1E014AD332FA784583260AA6153C464565C4568108D60CC126F6E8EC3BC9120E5659C86CDA8A31A7131936DE7B3DB39A4692808DC3D2BEE8A99880FF9D1D5EFF1E825A0F043D908D62A99779E013845AC0C21ABE8E4DF0EE901E4C6BEB8BB36B30228B7756D617A8F30C16351D8FF91786F7406F75D9FB648830F88EA4537F42EAD62E8790E9CF11F72C31D718221049C9AA35376AD8FB065F4809F4383A23C2B29425836C2DBCE4680450896EEADEE6B83539ADFDF59AA4FCE709D601640EB9A22DC3B41108A8EE1FCCDE9945EBB1D3F676EC8395255E125E62A32149C73451F597E1C32AD979E5BE914FFC7C548D6AE92ED08501831E9007770A0233E5778F22ADF7F1AAADF9C9A7C82D2F42989BF21627D3EF8BD0377A5BE5C9F5A585A246A73DE4340E6B43B36DB775B34033962646C16F26A2B7179C40A721FEA54805B9EC42177B42160B1A67341235B5AF9F30B2703BFF8CDEEE5BD7CE506B0707A69F84225B6E5A92E80EDFA235803DBE2CEC47CFEF0D9FAC95C3379816A39F4550BDBFB45609C76D0351DDF8D61724BD5E8BE94673B3013EEBE172CACE247D79925B12B5DBA2F6FB72E797B2DA849B79DEE3DB76775F5F1DD4595678671C7B18BB3749FBB0C6A7135D639F16B3864B5A251114DE7E9F8CB02B4CC69902EC8D7D544D98E24A05F8ACCB182E2EB44BDE868B077B1FAC4726E8B01CDD0D024405665F7ADB60A23FDBACF421246354E824CB74DFB35E57902794E459493905400D0A0BAD51D8EB94EFAD55C67CD0C7CEFE7A1B055F06371AEC7F490FA685C611D553D8430992EE7B1855A9CB305B5CE53154345D7DEF6110DDBDB5CB59559EB664C6439E057DC022F8686F2AA0CA81552428437B0CEB5FBB5DF254036BD2BAE7290D947C963046771A39D2656312236569E775E7D2A041B7EECCEC99C1B9D2757C7370E474012AE707AE00AC37B73ED9C8E1A2774E54BACEB42E8B31BEA734463CC15576BD4F7A33430B1987D62E47473391938312F2481838F286C4DFAF701ECBC6EAB1A9F074C1F8D8963457DFAAC9A9A8EEA70C50CE70D1BA1006760AD3887605EC38861DC1A777D21E46EA169537057CDFE256CC08699D73B1AC4FBC62F863353581CAD358B9C573D77585DF6544E5D55048D66A352828CD1ADF5F42310FFAC022A25824430F741371027B2DC14717DC87342A74F0038674187E478D8ECEFFC16474A4AA8BDA0C8D41962EF2A4B64A036C888CCF4EA628E1CB9EE0F9A918FB1B22B9367FEEEE0218C83CC7E27C5CB2AC64DC7E111E3C85CA0E6BD4F685E5DDD428E028D192142CCEE3F0C8337BDF43CE4B62704AA53C703EC334FB56FFDFB81D7D4419535D17E5FCC0E6F558AD82149C591FE0357DA15660F61544B4041128218B6DE2B75D3801510669A3977E2983BCAF957EE2942E504C29890A81542EA208E1CEC +pk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sk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smlen = 1713 +sm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count = 32 +seed = 569B8B9BDB707B19CD6F9BEB29F304D603C1509B9CF25987C280C342E870B1E13EFC7DD7E41DC85BF4F42D0493B84B0F +mlen = 1089 +msg = 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+pk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sk = 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 +smlen = 1748 +sm = 026986734218879D5A676E906D60725DD48BECB9FB270DFFE982B44C0E20BB46CDC8032A9C81C0E39CF47FF38725F35312D75E58845FBC33E112DD95D5C1CF78119CB413AC839377C7051BF5F17ADD1484F5EE12F42B0587AB41DF487BA5E4D8836777B614A9931A5FEFDC4AC451662B342D675C940061C4FF01F747B69CFF585FC5317636E2A830140C0007F73C76FCAB96195C86DB98E5E65C733825DB0325407E5BB059490F2E9133F9B4AA328976256EAAED2FBC59D00288D4830D99731A3AEF36E5BF5239F2899C500F942B80B00C3B33307450FF0C105BEDB7DF84231C5D24C3C3475AE2F46336582DE93AADBFD385C824F21362C19B1C6A75F56B69297FB3084B6164204E2348CB1D7CD3AB494BFA7EC8FE346251C874085F803BD7F4DDE1995F0D3D17033C461D06B49ECCEEE0D5312C3A435AF5BEC9808ACC524599668AACD95ECEA7EF07C4CA3FAB1CF964FDBA987C345046E6507AC3D372BF07D72CAB816BA627C2BD452AB8DC3044A7F0A01D8C0EA47904A5DD66C6B7EF9130D628A4F2CEA5A0D05AEAB7DAF2729C1041FBDB3C2D17BD66AE293C03E77A0837419471C29691EDFB20CF69BC6260975089AA437628F140A44FA2E2967357AC1BF1345E4208C33CFFEDE6CD634B371E7745143FF848F77E5130D1E0F51868585509F9CD3B906EE0A5072CA2E908D6765C74D9B5C35B6BA784A3EA59D808ACBB1C24D6C088CA6C9E17BCEB18337A4DA0C1DAEB5D51EFB35712A475D6C5A2EA51E93FD79F7DEB127F3418F354DF06489E10B42BC1F20651660CAEA17F67F306F48E15DB7E67A1B56578BA7BE6C229FED9567E128D48551E6EEFA17AF5B95A716555571F44FBC41AB29208DB7C1846E130866D5C9BE6F73E601C55610DFD0F67D98933D252059DAA1DEC20AE0E5BED6568A6322322D8A40E6835FA66E317733E1B465434532EEA8FA76886B600E06EFC1DA41F8DCEC0A5E8BA8419F0B7879CC0A93BD14D99608B5BEA931D8971DA8D2D89053E1DE40209E257E741BEF48C17FA15467F1312A368D4A061BFC76C2B7BBD900B4A34DA51B7CB5BD6E2FB08806A53C0D60273167D822FB6982785F2C3B0EC7D893B615724D0193928D0EA8EA2A1DEC5ABDCAA904C754CB7747449E87221B3D86BD5DF26E11DA753E768A8B481C306E485EC91074377DFC68BE74A444906E420C2D8BCCD84BE13AA5CCD11115B669C89E9C0CE374BC4059C696E5F8344FEE467AC8C8ADE37DAF614992914C763D971327B60946943847FB6B82672CC376B780953B6F4433DF69AC61E110FBF1A35F6272561193D8652EBCE3291333FDD4D84B9CFBC60A57E1F8B817E84EA15D440D4A4B4F7E19C08DDFC5949FE8CBDDCD0296A62F12F53D48B1288B80E24C756FC38E2FAE9C7A3315D1C6DA42AE838AFBBF5569F633A68289EB7073BABCB210F4E08856FA65057BFABC70AD3B58C2C870DFB5E1B0D11B6FA6D5BBB68285D8F9C21BD89669781C9F4DC32EB1EF58B80B1D371334D36FA66A2B3DD4B3E4DEDBA7AA9FB7E0245F5FDBB66CDA653C5232A131EC1F0C21DB1C47B990A64A24DC8C4DA951F419F57C03FF506E0147C22E9946129468A933824738F9185FABABE4814112E3B3CA47BC1CDEBDFB6B37C353D91701B4C921DE7F598AE476EF50CB15DCC2C3BB7B7DF9C9A4A70882C7FF30D528679FEF4D85163C6A9712E5A179217FA516CA81841A687B2F1AE0ED8D591571309AE641DEE6A026B70CD90F2CB14351F72C3559D1673BBA036E8B64CCC790CE36AA2313226F0BFE11757F3DBDAF2EDB4347E84BE6CD3A09F11334DBD1AC6EFAFF0C9619265339EA04F7FB3ED0D031BC941060DF534C8B31E79F74FCB3AA5B58588F8E4302DB65690C14992A43E87EA44A6AEE23AD63391E6FE6DE8C2CBE9F6F8CAAC85D0AAE47AACC1CDB2C305C66210530ECB16E5E78F48ED3CD2FA8F69BDDCE67D163BAE5CCED89A3283C18527983D5255896ADFBE6D622C94B3B32A1C51538283A19CC9739B8419F663D0064D01D0DCD1C7651A29E5212AC672D9D77EA1C243501723AFABADD1C8867FC91396C851C91A5AD0C04D7087E619624257FD3788DDD2A3E05EB80C27B3CBA925BD3620C9BBA9DC31DC39917F3B3C9CA23036A1B9D02ECE4379548819A749037A27D37F1A706D23B9B69FB32757CEEDFE854DF2C218422A4DE7BE8B2E365AA8E8A1B799D5D95D40DC5CE1D3B10D8ACD824A39E789E0F4F539A461045150E732DBA2A44DD1AC83B04A2FBAAF23EC812ECD25B61D2B6B2EF8282F0C6DF831FE0AF19B77D4DBA42D4886275B0BE42F73CC8D9BA99C3BD76689EA372DFE6A5E30F3911F818CF5C2DAAE4E58073E5D8E83C559B9132EA74C64FCDE4C70BADC1C14D1EECFB75F06191DCF4ABBA5DA00E3286ABEEA1ACA746E0AC4B4F3E790C2ECD8694D24DCD5B48B8300A89DB5C26C4F9082B4A9F374DC4A8C30C84D599668BDE708 + +count = 33 +seed = F32C3715B0BA8C1D0BD59F0645E9697DFCF9AEAF761A71ECDF9672215B9F138C0502D7214F6B1BB4D6612432F9FBED5E +mlen = 1122 +msg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pk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sk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smlen = 1776 +sm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count = 34 +seed = B0C7530A52AC9F561C2C14548D3A5F5053396B738EA1C7A5190F5AB01C9C38719C4DBE856E42D37A114FA24FD5DF5081 +mlen = 1155 +msg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pk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sk = 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 +smlen = 1814 +sm = 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+ +count = 35 +seed = B2FD7BFAAFB667C9DABE5915C3BC271EF41F18588666A6F4990C09D098E62DB590110DF6A56F08C5E0DE65B00F91D60F +mlen = 1188 +msg = 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+pk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+smlen = 1844 +sm = 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+ +count = 36 +seed = C08E846A8E039C8655651919A8433D475F494899FB617DC3B4715DEF0C992C195CE38158B7FF40E0684B30FD7E623265 +mlen = 1221 +msg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pk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sk = 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+smlen = 1876 +sm = 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+ +count = 37 +seed = 1D9C060EA0408A068BD982D9694D39D02BA5A473378F6F9F09349F686566F331E767263FAFF5DC0E823BB6F648843876 +mlen = 1254 +msg = 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+pk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+smlen = 1908 +sm = 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+ +count = 38 +seed = A4563D09AD21D3916BF4636301F2E64183A8F003DA186753D7F2DC3BE0089BA09C62B8A52B72C2C8451213606801FB29 +mlen = 1287 +msg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pk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+pk = 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+smlen = 2008 +sm = 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+pk = 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+sk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+ +count = 44 +seed = ACC98B16DCC9A50EF57F332D66255CA56C2BB679CAE705B4297F1418DA845861448DA6CC5CC458DE6C6E96128EEB2898 +mlen = 1485 +msg = 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+pk = 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+pk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sk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+ +count = 50 +seed = C10427EF0B26328163F85D45E22EC5215415326F013FF31EDD58BD3E97B1A72FF07D275D4C1B517F4661B0638F75640C +mlen = 1683 +msg = 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+sk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smlen = 2370 +sm = 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+ +count = 52 +seed = 3D4607399F6FCBE074FD2BEAB1A7571239D6BE6308617866B65B892EE65399E14DC7FA612CDBC5F7E23116FA86C3133D +mlen = 1749 +msg = 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+pk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4A1EEE2EF68F354A572D11713CA85979E8B1B29238B954B8B0C368BD7A55BA9336AD31ED82454FACCA8AC39F4EA59C467962C01244C24B97971474C7757F69235B4F4E04675BD4 + +count = 58 +seed = D9281003AC5F7673E0E9A7BC29C4ED75E6B0F228DF49D11A2599BFF2DA9E887163BB26DBA4F071FBCE02891540EC6F1C +mlen = 1947 +msg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pk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sk = 59001FFCF4403EE44F3FF8507AF4003FF3C13D24CFC01FA004F81F80FFA185FBEFFE0040BC0840C207AFBF07CFC01C7FFE138FC507C13C0411820BE001F471B80FE17D03C07FEBFEC00001C2FFE0BF083144000289FBE04F140FFC1450020FE03BFFB1FEF441FF0C2E80F3FF01E820C117DF7DF7E1FC178176101103003F39007F82200E41D811C3F81EF81FD03B0FF2000BDFC0182E85F7A0BCF7F07A03E0FE0FD07907C03F0FD003FC1EC80050FD181084E010FD1431C2E80FBFF3BFC0182F4103D03CFC4108E85F0403F04523DF411F903CF0608407E07C100F02FFB042F84F02245F7F044F7918013D03FF4103CF00005F7EF40081F492020C1039187F77FFF03D202F840FB03A17EFBF04118507EFC0FFC202E3D07F00107AF8007DF44EC0EFFF810C1000185FC0E84F7C082109FBFF7C0C713CF41042F3CF4107BDC11411450F8EFE1BF08107B0BC0FCE3B2B71070BEF84FBFF02DBCF421040060821BBF78106206FFCE44F44FFD0FE13F0442C2040F7C0C0EBEF7DEBEEC0F7FFC503FEBDFC6F3AEFD0031BC17E1FB13CEBB0401FF1021FEF3EEC507D27F23E0BC001E7B14207FF8303C0B9DC40FC00007ED3AF81EC4F09084F7F0BE0C01BD000E46175040DC1F82EC3FFCE80F8207A13EF440480BBF3EEC70BDF4407D0FAE82EBE13A08008223C204E85E7D040F4603CEB9E4007903FF40FFFDC5141EC4FBBF44FFE0BFFC50FDFC100003F0C104218013B03F080F00FFF13F0460FDFC6F840C607A000046002FBA04013F17EF7FF421030C2FFEF4103FFBF101FC0FBDEC1184001F04001F40181240F7B0B90C2FFD077038DBCF01E3D040042102204E45EBB13C13E0880BB005FC413DF06E44F7F186EC2F81FFD0FE23DEFF1FDE83080F020040BE080FBAFFE07F27FF89000F79F3C0B9F44038F7C042083F4C03FFC103AFC50BD1BFF7FF470BCEFBF06F3CF00E750010C3F42FFC0C4F03FC1FBDFC2039EC1EBFF0207DFC7FFEEFC1BFF0107D03E1400010BF1430BE042FBC27E041F47FC2142F7BF41080E42186F03143101F80EFDEFEEBDF7D1030BCE38DC2045044D040FDF03FFC1C5280CC5F3040E1EEEE4060B16F0FBF73F1CFEEDFDE709FFE8EB280841FCDDCFF9ED2115DEECF204132021132DEE14E7F8CC18E63AEB23080A0EE700EF081A1822170A36EFC91FF8F1220BF5022414F3F4E4F0EC28F5DFFD080D14E2F6F9FEF6FA1A1B2B08E7F7302822ECD21AEADA24F90C1A1BF99FC7F3200601E4F7E0FFFDEECE020A173FE8E9FD0107211846E80309ED292417FBC9F517F8191702070FF1DAC9F4D0F31D16D0FE1AEFEDFB08EEEC08E91EE0E62CFDDC2F09EB310EE8F4FD0C06DC0A05EAF2DB13021902DBCD03FC04FE1DCEE30D2305F82BC9F7FBF3F1E6E6CB1D3710321314C1F30001F8E91706E6FFCBDC031F09D5070904E0CAFBE50CF7E23F1D1E340DF70511FEEBF600EA3C0A101BEF1EF8E0D3D3F0192200D6CA311417E3FADD1DE518E0F018E5D7F900111A2036F2F6EAFA1703F4E91CFA120C120E5333EDF2FF0B00E7D62E120CEF1F0820242BE3F5DFF4F01801FE1BE7F3EAF40114F9E8F4E3FDFF10C7E0DF15D91CF8E9EA02F8D8E6E629E8120A15291CE3FCCE0EFF0B0EF4F22017F7F7FC1F2DEFFADF230113EDE1F4FEF903E7E80405E8D9FFC716E10FF6C902FC02F810021EEC14FA2FFEFFD6ECDF2B180B2AF1F012F1EE03DE04160CE7F21BFBF11E07D60E0C092AEE0106E121F3E0192E031BE409F6D5D3FFFA1EDCF9EDE41C13F8F4EBE014CDF6D7E4F71A16F8FBF5180247EB08091F38 +smlen = 2604 +sm = 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AFD3CACD32C3119D51D7D4D627A9475B2E76BA6796EB5AE2F01BB539F8E248F0645D9845D1AD7DBCE5BDCCB3F487C008D23381FD489190B66A75085EDE27586C714C39290E949AD99342FF6B4FF1ABF7A26C3E460CCBE96A448F1D60A3C6BBEC4402C74F35F9D99C + +count = 59 +seed = 750A74866BE8DF4E60BC14BF36E6D83ABF6DCBB86792D125CF0980007C5435F40F87BA96498A88252D9C5C6710807652 +mlen = 1980 +msg = 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+pk = 0966D4F49B45697AA47CB2FA6005127ACD5F0339522243E10CA96A1E0C1786CD6AB36EBAB9D535E2BE9290999160C95FE9E99681D751E71CFF4E8ADAB0AB023609FD20C2A4084579508FA7F380C980F95C077E075821FEF171A59BC305853A27465E166EE943CB0E2F5F341E7BE9CB2C9881818DE0762C460401DE85D24758103024DA1BEA9318B4D58B5C6FC6082E13820EE86489914D9BBB038D57FC45C3A803E69D5CCEDB64CD35460DA556E1104B2998F79A0180BFA87010A4C74E39453801968F29E022740D7943AF5BB1C63DDABFC97AB2B655F70906CA2681FA909A4F5F682D16F48512473E4CD3832566E9037540B15FC6E6B1E9C605DD611E067487600AEDA22A1A05C736EF5C1D75701B5A2AB343DC65224A18A01A10771A9A0DB7B432830ACD442015E8CB180BECFD6DC0D7E29D04028692BC19FAC1F15C16F18161C35F756A81F780565579A1B8D06A8DE1BE5A4431C0E5F36995008701AA996B8815D887E73F89CA4EB4D2E3275D64358B19520158D171A3969DCD44918DA6C5C57B30BAF0725095CBBEDC1A25EFA58712B6800A92821F11563EC7A0E836710E7B65889A4FB55C52FB23992F1DCC756BB61E078691F7E6C3A011AA20133A03208B6F254B5967DB704200AC30D7A5F880B2F15B2FECEE94C662E8C11E68B2BCE2327C4D859BD24718FD41214865B72056812A09964C539E89F6B2D0E0E303285A07D8BB616DDB5D9A2894F6B2AC7F687DA7E7E06DD288C5D8C5D188CF4F700CB8B288EE4BF07ABB34CAF05C268D17E9C2429099E824766054B4D44AE4DB23202F64ECE96218565CE0A2C00359CEA8A50FC023673B3BB486D756849807C948E81851EB77B0F481A10382B759B4167C0A3D69C40C39CCCC7D7C205017E64D7C366EFC33BE587D570E55B99382535C46DBF625A92AA9E0B8C73AD97E7B5153207122BFA460D058C580CEA2516A9AEB47A703B9A470BA8DFF7BAAEFD331234072541B48F627064048CE8B97CCA42D0981040BAF0A8EF09E45D9C1343A9E1044859E5B01FDFC7269A40697FEB8401580A59BC51715841E9C5F345D29E28348BB5550E881C7A026B95F220252D3921D10C690EC8C515445117FDA9122B0CC238DCF2B80626AD3EA290FA591E7D078A74E69C575C58E57D29ED0600012438D49F20402192D53A106FFF0026E2F1F44CA884E15FF5898DEFAB6114D5A9A894573EF6F0304E8815A547A524EB1A6B257102A2C45290C625B5B9DCF80D58F241A31B40A5058CA +sk = 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BB2C3328C6FAD7434893E8823C657ED27C912C73F87677A3FB7A275C4E7750E1137634A1254FFC413EDF9944ABF53165EB0E6470CFAF6CBB7BD5DCB21AFA0A93FB9D6DECDC64BE1B9D87ADC46B2F958A3A3CA53D8976A8E4D9904EB239FF2E3713EAC872E0EE322246E4F4D75904665E26726FA7B267A6ECBC4DAFDD24398C54753EAA4EA6F9073C80 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+pk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sk = 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59F3A002FC9FFF07AFBCFF50FB0000C00841060BEF04082EFDFFB0410B9EB9EFB08007B23E1BA0C407FF45F86042043F42F800C21C203E182F7D188FBE0BEF3F000F7D1041FE0C2FFFFC3F80FBFFFCFBEFC1F3DF4503C03DF7D0830FF13EF8304117F17D07CDC00840C0EBEEFE1010C307BFB5F03E0417DF3E040F3E0C107EE41F39FC0EC20C50BEEBEF42EBFFC404217BFC2F3A103EFA145EFFD881C40C403BFBD101F850831030BA07F102E7D07907F0BE079082FC50420FFFBDFBDE3AF4023CF4013E181F3BF3C180080F3FFFA08407EFC6184E87186FFDFB903F081F420800C3EC10BE0841C607C0FB13FD82F3BFB91FF2430C0F7B03B0C70B908204517DFC5FFC0C1E74F03FFE0FC0BEDBAF4617AEC0F3E0BD000F03E80080FC1F3EF82188239F7C07DE840FC0B70371C1F7F0FFFFAF43F01FBF102147F81080F3DF41001FBEEBFFBD03D27F087E010FD00113F000F86D7A102DC6F86E3EFFFF03FBD07F006F78E84FB600007B102F40F7FF80F7C1FDF3D048242180E881FBE8617FF83F39000FBD0C0FF803CF02E84E0204113B0FC0BEEFD100002F84EFF000044FC0FC60BB040E41FC1E851431040000F40070810C4FFFFC2F79EFAF7EFBC141FC0E49EC11C20440C808107C0820800F8F3C001FC41FEEBB17CFFFF3EEBDFFFF43EBF17D03CEC5F7FE811040430BBF3F201FC300300503D0FE0BE048005FFE1B9E390BAFC2F0203FE78FFF10707FEC1080E810830C3F7A17F0C3F8104714117CF8707A17FF81FBB181EBFE82F49EFA001F7D13BEBC07DFFF141F44EFF0FD1040C1EBF003006F85F8207EF450C21000C2F05F3D0FF0C6042088FFD1C007EF81FC2EC21BCEC4E83041F48F7BF820FEEBD0FD07AF44F0303F0BDF3FE7E00107F13E07D004F7FFFB07D0FFEC20C31BCFFF1400C1242FC818917A07CF081811FCF79F80082D81105E44FC22031810FB0BE0C20C103A082181E7CD770C2E84F03279FFE04103FE86E010FDF40FC310613DFBD0C1F4413F145FBFEFDFFA105EBF1BB07CD40180047FFAE7DFC31BFF44FB9EF71831440470BA10103AF8213E2050FDEFBF7EFC41060A14090B060AF9F70DBCE6FA0927170F1F12EDE7F2FB16ED0DE2F70610FD03222D09E015F205D91A100F22FD031FFAF1EF19F7D4120300F0D6F230FA1E0C09E30B011C3D2A041C10F3451B0A0522F9D5C6D604EF1017ECDD06D1F7161F282229EADBF42925ED19F9F4F41901FBEE3E20C41DE518ECE32FF00010E224F322001A000B1BE7ECDBFDF700E629DFE5D907FDDE060D00F92701025505200810F90AEF1EF8E62134EA04F8E80B03010CF105D31817FCF312E100E1F9D9FB05EF1219F6030204DF1C1DE6FCDFE8EBE5D63F0E1AFD07F9D9F1FA0005F10EE9EFCC2DFC13FC2C211104F52CAA1BED0CFAFAF00DCF2F201BF9052A1E00030904FE06FED9FFD412FB0D060A07F1D0FAEC081A13F0092BFB230DF2142A271BFA0D4B14F814FE0BE0D922F1FE20FFE3EDEB11F6FCC91613F409FD02ECE7180D0A08F4EFE1CFE82B3301100F0C15D2D810FBD8FFF7E8DAFB201A0E1EEDDCEA2007EF1E0106DDE0FD14301723DBDAEFE2043C09164400F9DA09DEE71EE61D2EFD2FE7031AD821FDD7E015FEF82C042BDBDBE6F8D5F2F4E9E8E10701190807252A07E914E1F238F9F1F1151CF312EEF0DC05F907C9ED07040C2C3B020B01F00019FFF4310AF7C6E0F7BDE00C27FC0FFC25FEF2002A0BEDE6F3F2D0EEF7FDCD37F0CDFDD3F415F22031F118120A2219C7FD0A17E0F0FE32F6ED2DFCFFC8F3FDD5FEF1F5E3D01CE4CD 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+ +count = 62 +seed = D2629CEEAE5C95D3C34C1FFCC2338B4A97782BDFCD39111E18540B69DB035B352D012857111F816F03550BFE5F56ABEE +mlen = 2079 +msg = 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+pk = 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+sk = 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 +smlen = 2737 +sm = 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F74A890C11BFF32AAD3A3DB71A460D446C0E4BC68CEB35391645295E11EDDA8538618C829CD8AA5843530B4195173A7FEA46166C3AE29C2EB025A5926E79898369084E1926B24F1C458DE3B4DB48A6FEBD1BDFB7C3E0752ED37297FF123525A568B4C6ACE8F0EDE8D6B19ED7A5B70AE264947DB9B5DC376B87D8FEFBB65D7253C6F453622394411A9C0CE331F54D92EC1C38B4B0DC16AD45F1E92C137ED5A18ED9D45606227A8B3E8E07ADF0AB95FED43F2C88A7B85EA578856DD688D5CA2990E03824B0E84FFC2701C892624DA9357578EA323584807613B41208D4127A1CAC9635784E135CC520E79DA3BEC0 + +count = 63 +seed = EAA4FB8EF0290A499A1D92EE398A8D7E71CD3CBF01A36750DA4B7EFF175DA26D17AC4ECE49A84C88D1D2C2493563C26D +mlen = 2112 +msg = 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+pk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sk = 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+pk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sk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smlen = 2866 +sm = 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+pk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sk = 59F81F7A07DEFD13E08013DFC0FC2E801FE0BDF38F330C20FFFC207FF83E83042F7F10223EFB90B813C042F4707C07F0031FFF3FFFD0860C4245F83FBFFFC103F02047F4504007FF4318500008117F180042049F45F460080C817F145FFC17FEBE10224103ED42182DB9085EC1188FFF08204627800113BFBF105EB9F3E001F8107CF00DFBF81F00FC50BFF7BE82185FC4F3DEC70060C20FF0450FBFBA07D07D03EFBB0BEFBCE7E03F03D23A00120617A004EFF1400FDF3BDC6EC3041EC80BAE09F440C0280143003FFB182E82FBBF43F0203D1BF045004FFFFC517F0872C3F7F0BA1021000BFEC0F80F0303E13CF42FC304DFC2F79F0123FF40EBCD7CE3F03EEC1184081142FFE0401C3FBFEF7000FFEF7FEBA102EFFFFC07F0FAF820BD00413D13F1BE0C2E851C9F420C503FF41F3BFBCFFC03FF84E7BFFF0FE27DEFE0470BC27A004FBFF820BE0FF07D1F9EFEEC0002E3F140083F8507FFC3002048043E830B8E82EC10BFF04100FFFF7E084FBEFF7FBF083F7CE0307EF8207E0400FFFBF002EBB041FFC07FFC200003FEC5043042F7E0BA18004A07BF410C2045E82F40FC3003F010C910303DFC7F490860F91000BFF81F7CF7C0471FE27DFFE17703DF7F10103C002F7CF01143080E000C80BEF800BEFC4D84F05038E3AE3D28803F17C1C708000813F03AEFF17B0C6106E400C1FFF18314703EEC5F8007C08103C03E0C117FF08086004E83FC1FBE140FFF04003E03FF430BA006079EBD0BD0430FBF870BDEFF03CF02001F821C1002FFA1FDF7BFF803900403FEFE03F0BAF81F87D44FBF0FD17808123EEBC07D03FF85FBF0800C0240003F02FFF03C0C003C23E03FE41EFF148FC01BF1FEF890BBFC30BC0FBFF8F7D2F9004F81F0117CE4007C204F8400AF7EEC108118014408203EFC1FFDF3CFC124407A042084FFC042DBA03D1BA1030FB0FFE8007D08007EFC1286FC713D275E7E07F080FFDF01148281080F880430052051C21000BE07D04517F0FD2F9FC6FBC187F7BEC1FFF082041004E001FF0F9FC20C2F3CFC20490C1E880C6F3FFC2F7E17D18217D0040030BFFBF005140F7FE7EFFC03061FF5EAEEF40AFC2100F3E0FB0AFCF70E210A0B1233012D182DF5F90B08E8F9F00331211F0E0BEDFBF4EB050BF5FBECFE2AF42AE1F8D6DC04E20CF3FAF7184C0CF5FAD80B261129FBE9C2E2F900F2D311152DD4D7D115F10106100318F1FA03F717E314ED042BEF08E62BF52B0FE2D7CFC9064422F0D4F905132E03FE06D4F00EF710FDF8061D021ACC04E008F400DD1EF4EEDB06EC221FF1E7FA20FBDC1D1D0413F6F6F000E625DFD7EDC2F924EF05EC1919FEF60335E3F70EFA080CF703E63715122125F2ED1FF3104019F0FFC317FD1DF8F50EC6FDF800E60313F91C2501102DDA35DE35FF4A15EE1F19011ACFEE0B1111C808F200FDEC1AE0F3D907050A0901EF07EB08060722E5F4E52933E0F3E6FE3BFCF3121105E31A0B09E7E405F309320A19FDF80CB4E8D5051211E5D302BEF0F21BFAF4CBF6020213E80504ED1017030315F3DEEFEFFEDBDB14FEFFDBF005C4FD0EEA1A26E0E7F1DFE0170AEB1413F4041422DB38FCF91F1004DF09FA010B00212AFC05DCF609CADDECF6F8DDF9002EE4E8F10011E90505F82AF80A0020051514FF1C0614310E1E0604FFF92BFFECD42E1BD5C823EFF90DF80F3323F81E232D2112FF1D1A2EEE0AFA10F31AFC12C4F0D82C232000DBF1F7D202DAFEF0F91DCA15C5FDEAE5E9110BF71311EAE80AC60DFFFFF3FE0CCC03E0FA0A1300C8DCFE0D0E13050EF1CA043519DD 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+pk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sk = 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+pk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sk = 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+pk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sk = 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+pk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+pk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+pk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433211B93078735F909F985F557D0DE52CB9203DDC67BF9DC8632ACD8D4F90196AF6BD2E79834371C5E9FDF5992ADB04AEA186AF36F56271F763ACFFBF94DF4B0512CA6B7CA8FF486504E565BDA367E044FCD0F25FBC2A6C720867F95BFD92109780D2E6DD60CE90A4CA8EEB8C4CAB289DCF99E687B017B37695C3B99B4FE97D7E5D52BB9813C04D03C9AD71770FE0986C7F3A3FFD3A261AC771DE88C7ACDEF253E5CE2B50BC5C576D132B68CCC694BA883770B80F5ED7D527CEE816527F69CA2C101747A0088879C3663037DB5B +pk = 0922AA6C4A882CDF3244F1B78BEE7408D03CE840D6463CC5B37B4D0B92A199CAF9EFE7D3833980B4E2605F3ACAB79B8B1DBB6CF09479ED4A4BBB7C4B480EAFFF2B35B2C6F1518C3E46A2C1F1CB73822D5657916C300A1E67ABE44D205E4023F089AFF032B65EE0ED913385D2E94A500FD26D0A2A612320F732115D329D598D651007B9FC162857EA60303718B2B3E86D3744417CA1C8574123AAB34AD629092E8F894B0692DBE59596B069416506A4CC2B6A0498B1D5DE698C2AC4B683C89B902857D68D378110C3C41AC795965823884159507C669D21C0A7143A2A83E87A2280AE7C3248A1C908716CF6845C0A66AD562AA9E1E9AE84C5EA081E945157563CC4516C0CB988AA653AE5EFAB4E21188498903296A6D8212FFD27D82001EAE8577AB022C49EEF6FA64DC5D43F677AA1781892C650CD7E4813F82F6A5144C094DBA4818072A8D36205CBEB9FDECC30C7001F8EFE93B1B004E424766EC775D1F66A08DB66340E2E6CA105283FEE6039CE9A394B9C826F59DD162DD15A3144C986F460FC0DB8C736BF2C03B67AB61115C4FA422057576511FB88FDCED24B99D0371496300A918E57F4E298DC2FAC7E2A320ADC5BA37132073B531BDC44E0FD58682D4784C6C6B3DBACF9849D5BCA1E210D949D7942949D71997156E1221A5B4926FD024B0F27247122616F9A405F903E654E4B69B3A480207B16130BE1F1A1932E5B8332D49101D811B11DEF809AC05C5ECAD9C4681411BCEE94097AA399985A92C3409E5D4DEAB90376C8A509715F9308C6D55A34DEDA61EF6B14BCFFF6B9DF73156D3DF1A6000A8021A7E3668DA017BDAFCB16229F20B93F472DC32E32288E8B86E6CBA8C28041A0AE136221D947835BD7A9344D728A2817AE4AB0977D5D96B90249D088D9629000C774626AE124A13E3B7EED820084DAF31CADDD725E43317B03284B55A35A94562D3C7400691CEEC018ACC327A454D750A53DA0162C423A55038BAC96832C1974355F60118596FC86E91A542BA8A227FA1E644014BA05AC21DB9AD9C53882C31357719B5A5CDA5B08F280CB1A8C0A4B5C970956870202F87D109BD4788B013AC5F75AB780B25A633396F5AAA12003AC1E090A2C8B753642D5AF55697BD9C1AF7160C01009915E9EE926EA6BDA4A68BA5930D82FE79F013AB33395F40F641274A5015283962C359F2673A922E8B3FA8B9303E5806258627D793CE06B15991B384E2707BB5E1D52E5394BA1C27867E4B280F526F65912C4B1B12BA3 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+pk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sk = 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+pk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sk = 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+pk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sk = 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+pk = 0912A19C5AFCD12328C576D6A38D0366C455B7DB2C6350E99577AD9BC8A729DDBB688ADE4FB257EB7F6827B8EDA7E6AEC2898C995A844125C865E0C8996EE8362030D720772BF892CAA7C2345E76967EC8C5118BB5A5115F0B345AB96F71288BBC46A70BA01FF274DED137BA74D02D69DA72D5D46316E74991B5FCF85206002FA299540C66362A9DD434BC9851555D66C72295515B51C1598B836E9D66EA8AF08C8F3774F01768D453764CB815C4573F8D894621461E5228097DD9AED269B015E235035E95963D33C7B323EF63F903D327060E0E682767CF05159A4C9CD05B286F64EEA64AB5E16587817456AC01D81382614722C2D563DEAF228081FB41DE3C667F20D6772A8CD829E988A5C86071271E2879C1AC5B022CF8332D2AB608034EBCC2DE8735019F28F1A1992CD22D33DA30757342C28FDAFB686EA882A1B24760D3D2395B30E603400D8C038D57C6D6A9AC0F294694780CE006A62737F71F968C463BC1EB17D7A2B230264086A261F5A4644BDE1F9F90F1912BE8DC514962F11381F42DC6254883042248C63129F8CC68B6AE11EB381A702E7E1018C206F215C25C14841A3BA1AA0283242DB22B7E149A8B19357165B82788866228AE8E3083C92416406DC3DD9EAC11A23D97FA2F94A7200D687D4BB202205CF5FD00EC17C432640EE2E76BB84EC512AFEB643D59A3C7C63F02F93CD11483634F9C28A871C79539CD54409FEFF711C14B689D8A206F515637B89FE4194218933BD6FA02ADE32203EA15A2B9029812650DADB583668DEF8FAB09E4745C8D87084E5BF18C9DA11160BD1567966048A50E495BC7197FD57E0440E7652D78414A74AA8F1D010D1237CE488861F455BCEAA42971C49AC008DEBCE2D0677A8BFE70D54F672F03F346E8B8F59C2C0D49C144762BE90164D57F76EBA31E436143958D0061A9B29E85C744698F2A5E200CACE7A881E727D6D764BEA6E16BA043566F3419F37D5817981D88316717CD62B092092ADD7A4E41DCB7D5C3B3229CEB3389C08A41459647C8C737AC58DDE821EDA81C1E80C955D4DF7CDE5CC714E85142F2DD6AC56AF2BF08B60791EB4818445FA7CA5DE4523C84E7C4E5CDA5604D3254127D4F864D953EDC388549C4A2E7EA9E0080EAF3B7934E321EC24087C37EA729AAF8B6205E733C8D09262F2B4041EA882B1DA173C6E599F0CFD32FACBB1AF32851288D3337C9022C94968FA5926AC5999441B3A160311486FA743721FC64D915E556A5F609C56543408D7C +sk = 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+pk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sk = 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sk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smlen = 3956 +sm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diff --git a/crypto/test/src/pqc/crypto/test/FalconTest.cs b/crypto/test/src/pqc/crypto/test/FalconTest.cs new file mode 100644 index 000000000..f923f699f --- /dev/null +++ b/crypto/test/src/pqc/crypto/test/FalconTest.cs @@ -0,0 +1,153 @@ +using System; +using System.Collections.Generic; +using System.IO; +using NUnit.Framework; +using Org.BouncyCastle.Crypto; +using Org.BouncyCastle.Crypto.Parameters; +using Org.BouncyCastle.Pqc.Crypto.Falcon; +using Org.BouncyCastle.Utilities; +using Org.BouncyCastle.Utilities.Encoders; +using Org.BouncyCastle.Utilities.Test; + +namespace Org.BouncyCastle.Pqc.Crypto.Tests +{ + public class FalconTest + { + [Test] + public void TestVectors() { + string[] files = { + "falcon512-KAT.rsp", + "falcon1024-KAT.rsp" + }; + FalconParameters[] parameters = new FalconParameters[]{ + FalconParameters.falcon_512, + FalconParameters.falcon_1024 + }; + + for (int fileIndex = 0; fileIndex < files.Length; fileIndex++) { + string name = files[fileIndex]; + Console.Write("testing: " + name); + StreamReader src = new StreamReader(SimpleTest.GetTestDataAsStream("pqc.falcon." + name)); + string line = null; + Dictionary<string, string> buf = new Dictionary<string, string>(); + while ((line = src.ReadLine()) != null) + { + line = line.Trim(); + + if (line.StartsWith("#")) + { + continue; + } + if (line.Length == 0) + { + if (buf.Count > 0) + { + string count = buf["count"]; + Console.Write("test case: " + count); + byte[] seed = Hex.Decode(buf["seed"]); // seed for nist secure random + byte[] pk = Hex.Decode(buf["pk"]); // public key + byte[] sk = Hex.Decode(buf["sk"]); // private key + byte[] sm = Hex.Decode(buf["sm"]); // sm + byte[] msg = Hex.Decode(buf["msg"]); // message + uint m_len = uint.Parse(buf["mlen"]); // message length + uint sm_len = uint.Parse(buf["smlen"]); // sm length + + NistSecureRandom random = new NistSecureRandom(seed, null); + + // keygen + FalconKeyGenerationParameters kparam = new FalconKeyGenerationParameters(random, parameters[fileIndex]); + FalconKeyPairGenerator kpg = new FalconKeyPairGenerator(); + kpg.Init(kparam); + AsymmetricCipherKeyPair ackp = kpg.GenerateKeyPair(); + byte[] respk = ((FalconPublicKeyParameters) ackp.Public).GetEncoded(); + byte[] ressk = ((FalconPrivateKeyParameters) ackp.Private).GetEncoded(); + + // sign + FalconSigner signer = new FalconSigner(); + FalconPrivateKeyParameters skparam = new FalconPrivateKeyParameters(parameters[fileIndex], sk); + ParametersWithRandom skwrand = new ParametersWithRandom(skparam, random); + signer.Init(true, skwrand); + byte[] sig = signer.GenerateSignature(msg); + byte[] ressm = new byte[2 + msg.Length + sig.Length - 1]; + ressm[0] = (byte)((sig.Length - 40 - 1) >> 8); + ressm[1] = (byte)(sig.Length - 40 - 1); + Array.Copy(sig, 1, ressm, 2, 40); + Array.Copy(msg, 0, ressm, 2 + 40, msg.Length); + Array.Copy(sig, 40 + 1, ressm, 2 + 40 + msg.Length, sig.Length - 40 - 1); + + // verify + FalconSigner verifier = new FalconSigner(); + FalconPublicKeyParameters pkparam = new FalconPublicKeyParameters(parameters[fileIndex], pk); + verifier.Init(false, pkparam); + byte[] noncesig = new byte[sm_len - m_len - 2 + 1]; + noncesig[0] = (byte)(0x30 + parameters[fileIndex].GetLogN()); + Array.Copy(sm, 2, noncesig, 1, 40); + Array.Copy(sm, 2 + 40 + m_len, noncesig, 40 + 1, sm_len - 2 - 40 - m_len); + bool vrfyrespass = verifier.VerifySignature(msg, noncesig); + noncesig[42]++; // changing the signature by 1 byte should cause it to fail + bool vrfyresfail = verifier.VerifySignature(msg, noncesig); + + // print results + /* + System.out.println("--Keygen"); + bool kgenpass = true; + if (!Arrays.areEqual(respk, pk)) { + System.out.println(" == Keygen: pk do not match"); + kgenpass = false; + } + if (!Arrays.areEqual(ressk, sk)) { + System.out.println(" == Keygen: sk do not match"); + kgenpass = false; + } + if (kgenpass) { + System.out.println(" ++ Keygen pass"); + } else { + System.out.println(" == Keygen failed"); + return; + } + + System.out.println("--Sign"); + bool spass = true; + if (!Arrays.areEqual(ressm, sm)) { + System.out.println(" == Sign: signature do not match"); + spass = false; + } + if (spass) { + System.out.println(" ++ Sign pass"); + } else { + System.out.println(" == Sign failed"); + return; + } + + System.out.println("--Verify"); + if (vrfyrespass && !vrfyresfail) { + System.out.println(" ++ Verify pass"); + } else { + System.out.println(" == Verify failed"); + return; + } + */ + // Assert.True + //keygen + Assert.True(Arrays.AreEqual(respk, pk), name + " " + count + " public key"); + Assert.True(Arrays.AreEqual(ressk, sk), name + " " + count + " private key"); + //sign + Assert.True(Arrays.AreEqual(ressm, sm), name + " " + count + " signature"); + //verify + Assert.True(vrfyrespass, name + " " + count + " verify failed when should pass"); + Assert.False(vrfyresfail, name + " " + count + " verify passed when should fail"); + } + buf.Clear(); + + continue; + } + int a = line.IndexOf("="); + if (a > -1) { + buf[line.Substring(0, a).Trim()] = line.Substring(a + 1).Trim(); + } + } + Console.Write("testing successful!"); + } + } + } +} |