diff options
| author | Peter Dettman <peter.dettman@bouncycastle.org> | 2014-01-22 09:45:19 +0700 |
|---|---|---|
| committer | Peter Dettman <peter.dettman@bouncycastle.org> | 2014-01-22 09:45:19 +0700 |
| commit | cbc0848b90917fa606be8049f056de2acc1712a8 (patch) | |
| tree | 36632d05242cc14daa08e8acf759f5a72246caf6 /crypto/src/math/ec | |
| parent | BMA-119 (diff) | |
| download | BouncyCastle.NET-ed25519-cbc0848b90917fa606be8049f056de2acc1712a8.tar.xz | |
Port LongArray from Java and use in F2mFieldElement
Diffstat (limited to 'crypto/src/math/ec')
| -rw-r--r-- | crypto/src/math/ec/ECFieldElement.cs | 211 | ||||
| -rw-r--r-- | crypto/src/math/ec/LongArray.cs | 2023 |
2 files changed, 2079 insertions, 155 deletions
diff --git a/crypto/src/math/ec/ECFieldElement.cs b/crypto/src/math/ec/ECFieldElement.cs index fb0e8535b..9ebf6f41e 100644 --- a/crypto/src/math/ec/ECFieldElement.cs +++ b/crypto/src/math/ec/ECFieldElement.cs @@ -873,41 +873,38 @@ namespace Org.BouncyCastle.Math.EC */ private int m; - /** - * Tpb: The integer <code>k</code> where <code>x<sup>m</sup> + - * x<sup>k</sup> + 1</code> represents the reduction polynomial - * <code>f(z)</code>.<br/> - * Ppb: The integer <code>k1</code> where <code>x<sup>m</sup> + - * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code> - * represents the reduction polynomial <code>f(z)</code>.<br/> - */ - private int k1; - - /** - * Tpb: Always set to <code>0</code><br/> - * Ppb: The integer <code>k2</code> where <code>x<sup>m</sup> + - * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code> - * represents the reduction polynomial <code>f(z)</code>.<br/> - */ - private int k2; - - /** - * Tpb: Always set to <code>0</code><br/> - * Ppb: The integer <code>k3</code> where <code>x<sup>m</sup> + - * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code> - * represents the reduction polynomial <code>f(z)</code>.<br/> - */ - private int k3; + ///** + // * Tpb: The integer <code>k</code> where <code>x<sup>m</sup> + + // * x<sup>k</sup> + 1</code> represents the reduction polynomial + // * <code>f(z)</code>.<br/> + // * Ppb: The integer <code>k1</code> where <code>x<sup>m</sup> + + // * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code> + // * represents the reduction polynomial <code>f(z)</code>.<br/> + // */ + //private int k1; + + ///** + // * Tpb: Always set to <code>0</code><br/> + // * Ppb: The integer <code>k2</code> where <code>x<sup>m</sup> + + // * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code> + // * represents the reduction polynomial <code>f(z)</code>.<br/> + // */ + //private int k2; + + ///** + // * Tpb: Always set to <code>0</code><br/> + // * Ppb: The integer <code>k3</code> where <code>x<sup>m</sup> + + // * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code> + // * represents the reduction polynomial <code>f(z)</code>.<br/> + // */ + //private int k3; + + private int[] ks; /** - * The <code>IntArray</code> holding the bits. + * The <code>LongArray</code> holding the bits. */ - private IntArray x; - - /** - * The number of <code>int</code>s required to hold <code>m</code> bits. - */ - private readonly int t; + private LongArray x; /** * Constructor for Ppb. @@ -931,13 +928,10 @@ namespace Org.BouncyCastle.Math.EC int k3, BigInteger x) { - // t = m / 32 rounded up to the next integer - this.t = (m + 31) >> 5; - this.x = new IntArray(x, t); - if ((k2 == 0) && (k3 == 0)) { this.representation = Tpb; + this.ks = new int[] { k1 }; } else { @@ -947,15 +941,11 @@ namespace Org.BouncyCastle.Math.EC throw new ArgumentException("k2 must be larger than 0"); this.representation = Ppb; + this.ks = new int[] { k1, k2, k3 }; } - if (x.SignValue < 0) - throw new ArgumentException("x value cannot be negative"); - this.m = m; - this.k1 = k1; - this.k2 = k2; - this.k3 = k3; + this.x = new LongArray(x); } /** @@ -976,23 +966,12 @@ namespace Org.BouncyCastle.Math.EC // Set k1 to k, and set k2 and k3 to 0 } - private F2mFieldElement(int m, int k1, int k2, int k3, IntArray x) + private F2mFieldElement(int m, int[] ks, LongArray x) { - t = (m + 31) >> 5; - this.x = x; this.m = m; - this.k1 = k1; - this.k2 = k2; - this.k3 = k3; - - if ((k2 == 0) && (k3 == 0)) - { - this.representation = Tpb; - } - else - { - this.representation = Ppb; - } + this.representation = (ks.Length == 1) ? Tpb : Ppb; + this.ks = ks; + this.x = x; } public override BigInteger ToBigInteger() @@ -1034,19 +1013,15 @@ namespace Org.BouncyCastle.Math.EC F2mFieldElement aF2m = (F2mFieldElement)a; F2mFieldElement bF2m = (F2mFieldElement)b; - if ((aF2m.m != bF2m.m) || (aF2m.k1 != bF2m.k1) - || (aF2m.k2 != bF2m.k2) || (aF2m.k3 != bF2m.k3)) + if (aF2m.representation != bF2m.representation) { - throw new ArgumentException("Field elements are not " - + "elements of the same field F2m"); + // Should never occur + throw new ArgumentException("One of the F2m field elements has incorrect representation"); } - if (aF2m.representation != bF2m.representation) + if ((aF2m.m != bF2m.m) || !Arrays.AreEqual(aF2m.ks, bF2m.ks)) { - // Should never occur - throw new ArgumentException( - "One of the field " - + "elements are not elements has incorrect representation"); + throw new ArgumentException("Field elements are not elements of the same field F2m"); } } @@ -1056,10 +1031,10 @@ namespace Org.BouncyCastle.Math.EC // No check performed here for performance reasons. Instead the // elements involved are checked in ECPoint.F2m // checkFieldElements(this, b); - IntArray iarrClone = (IntArray) this.x.Copy(); - F2mFieldElement bF2m = (F2mFieldElement) b; - iarrClone.AddShifted(bF2m.x, 0); - return new F2mFieldElement(m, k1, k2, k3, iarrClone); + LongArray iarrClone = this.x.Copy(); + F2mFieldElement bF2m = (F2mFieldElement)b; + iarrClone.AddShiftedByWords(bF2m.x, 0); + return new F2mFieldElement(m, ks, iarrClone); } public override ECFieldElement Subtract( @@ -1079,10 +1054,7 @@ namespace Org.BouncyCastle.Math.EC // No check performed here for performance reasons. Instead the // elements involved are checked in ECPoint.F2m // checkFieldElements(this, b); - F2mFieldElement bF2m = (F2mFieldElement) b; - IntArray mult = x.Multiply(bF2m.x, m); - mult.Reduce(m, new int[]{k1, k2, k3}); - return new F2mFieldElement(m, k1, k2, k3, mult); + return new F2mFieldElement(m, ks, x.ModMultiply(((F2mFieldElement)b).x, m, ks)); } public override ECFieldElement Divide( @@ -1101,76 +1073,12 @@ namespace Org.BouncyCastle.Math.EC public override ECFieldElement Square() { - IntArray squared = x.Square(m); - squared.Reduce(m, new int[]{k1, k2, k3}); - return new F2mFieldElement(m, k1, k2, k3, squared); + return new F2mFieldElement(m, ks, x.ModSquare(m, ks)); } public override ECFieldElement Invert() { - // Inversion in F2m using the extended Euclidean algorithm - // Input: A nonzero polynomial a(z) of degree at most m-1 - // Output: a(z)^(-1) mod f(z) - - // u(z) := a(z) - IntArray uz = (IntArray)this.x.Copy(); - - // v(z) := f(z) - IntArray vz = new IntArray(t); - vz.SetBit(m); - vz.SetBit(0); - vz.SetBit(this.k1); - if (this.representation == Ppb) - { - vz.SetBit(this.k2); - vz.SetBit(this.k3); - } - - // g1(z) := 1, g2(z) := 0 - IntArray g1z = new IntArray(t); - g1z.SetBit(0); - IntArray g2z = new IntArray(t); - - // while u != 0 - while (uz.GetUsedLength() > 0) -// while (uz.bitLength() > 1) - { - // j := deg(u(z)) - deg(v(z)) - int j = uz.BitLength - vz.BitLength; - - // If j < 0 then: u(z) <-> v(z), g1(z) <-> g2(z), j := -j - if (j < 0) - { - IntArray uzCopy = uz; - uz = vz; - vz = uzCopy; - - IntArray g1zCopy = g1z; - g1z = g2z; - g2z = g1zCopy; - - j = -j; - } - - // u(z) := u(z) + z^j * v(z) - // Note, that no reduction modulo f(z) is required, because - // deg(u(z) + z^j * v(z)) <= max(deg(u(z)), j + deg(v(z))) - // = max(deg(u(z)), deg(u(z)) - deg(v(z)) + deg(v(z)) - // = deg(u(z)) - // uz = uz.xor(vz.ShiftLeft(j)); - // jInt = n / 32 - int jInt = j >> 5; - // jInt = n % 32 - int jBit = j & 0x1F; - IntArray vzShift = vz.ShiftLeft(jBit); - uz.AddShifted(vzShift, jInt); - - // g1(z) := g1(z) + z^j * g2(z) -// g1z = g1z.xor(g2z.ShiftLeft(j)); - IntArray g2zShift = g2z.ShiftLeft(jBit); - g1z.AddShifted(g2zShift, jInt); - } - return new F2mFieldElement(this.m, this.k1, this.k2, this.k3, g2z); + return new F2mFieldElement(this.m, this.ks, this.x.ModInverse(m, ks)); } public override ECFieldElement Sqrt() @@ -1210,7 +1118,7 @@ namespace Org.BouncyCastle.Math.EC */ public int K1 { - get { return this.k1; } + get { return this.ks[0]; } } /** @@ -1221,7 +1129,7 @@ namespace Org.BouncyCastle.Math.EC */ public int K2 { - get { return this.k2; } + get { return this.ks.Length >= 2 ? this.ks[1] : 0; } } /** @@ -1232,7 +1140,7 @@ namespace Org.BouncyCastle.Math.EC */ public int K3 { - get { return this.k3; } + get { return this.ks.Length >= 3 ? this.ks[2] : 0; } } public override bool Equals( @@ -1252,22 +1160,15 @@ namespace Org.BouncyCastle.Math.EC public virtual bool Equals( F2mFieldElement other) { - return m == other.m - && k1 == other.k1 - && k2 == other.k2 - && k3 == other.k3 - && representation == other.representation - && base.Equals(other); + return ((this.m == other.m) + && (this.representation == other.representation) + && Arrays.AreEqual(this.ks, other.ks) + && (this.x.Equals(other.x))); } public override int GetHashCode() { - return m.GetHashCode() - ^ k1.GetHashCode() - ^ k2.GetHashCode() - ^ k3.GetHashCode() - ^ representation.GetHashCode() - ^ base.GetHashCode(); + return x.GetHashCode() ^ m ^ Arrays.GetHashCode(ks); } } } diff --git a/crypto/src/math/ec/LongArray.cs b/crypto/src/math/ec/LongArray.cs new file mode 100644 index 000000000..d694f0cf0 --- /dev/null +++ b/crypto/src/math/ec/LongArray.cs @@ -0,0 +1,2023 @@ +using System; +using System.Text; + +using Org.BouncyCastle.Utilities; + +namespace Org.BouncyCastle.Math.EC +{ + internal class LongArray + { + //private static long DEInterleave_MASK = 0x5555555555555555L; + + /* + * This expands 8 bit indices into 16 bit contents (high bit 14), by inserting 0s between bits. + * In a binary field, this operation is the same as squaring an 8 bit number. + */ + private static readonly int[] INTERLEAVE2_TABLE = new int[] + { + 0x0000, 0x0001, 0x0004, 0x0005, 0x0010, 0x0011, 0x0014, 0x0015, + 0x0040, 0x0041, 0x0044, 0x0045, 0x0050, 0x0051, 0x0054, 0x0055, + 0x0100, 0x0101, 0x0104, 0x0105, 0x0110, 0x0111, 0x0114, 0x0115, + 0x0140, 0x0141, 0x0144, 0x0145, 0x0150, 0x0151, 0x0154, 0x0155, + 0x0400, 0x0401, 0x0404, 0x0405, 0x0410, 0x0411, 0x0414, 0x0415, + 0x0440, 0x0441, 0x0444, 0x0445, 0x0450, 0x0451, 0x0454, 0x0455, + 0x0500, 0x0501, 0x0504, 0x0505, 0x0510, 0x0511, 0x0514, 0x0515, + 0x0540, 0x0541, 0x0544, 0x0545, 0x0550, 0x0551, 0x0554, 0x0555, + 0x1000, 0x1001, 0x1004, 0x1005, 0x1010, 0x1011, 0x1014, 0x1015, + 0x1040, 0x1041, 0x1044, 0x1045, 0x1050, 0x1051, 0x1054, 0x1055, + 0x1100, 0x1101, 0x1104, 0x1105, 0x1110, 0x1111, 0x1114, 0x1115, + 0x1140, 0x1141, 0x1144, 0x1145, 0x1150, 0x1151, 0x1154, 0x1155, + 0x1400, 0x1401, 0x1404, 0x1405, 0x1410, 0x1411, 0x1414, 0x1415, + 0x1440, 0x1441, 0x1444, 0x1445, 0x1450, 0x1451, 0x1454, 0x1455, + 0x1500, 0x1501, 0x1504, 0x1505, 0x1510, 0x1511, 0x1514, 0x1515, + 0x1540, 0x1541, 0x1544, 0x1545, 0x1550, 0x1551, 0x1554, 0x1555, + 0x4000, 0x4001, 0x4004, 0x4005, 0x4010, 0x4011, 0x4014, 0x4015, + 0x4040, 0x4041, 0x4044, 0x4045, 0x4050, 0x4051, 0x4054, 0x4055, + 0x4100, 0x4101, 0x4104, 0x4105, 0x4110, 0x4111, 0x4114, 0x4115, + 0x4140, 0x4141, 0x4144, 0x4145, 0x4150, 0x4151, 0x4154, 0x4155, + 0x4400, 0x4401, 0x4404, 0x4405, 0x4410, 0x4411, 0x4414, 0x4415, + 0x4440, 0x4441, 0x4444, 0x4445, 0x4450, 0x4451, 0x4454, 0x4455, + 0x4500, 0x4501, 0x4504, 0x4505, 0x4510, 0x4511, 0x4514, 0x4515, + 0x4540, 0x4541, 0x4544, 0x4545, 0x4550, 0x4551, 0x4554, 0x4555, + 0x5000, 0x5001, 0x5004, 0x5005, 0x5010, 0x5011, 0x5014, 0x5015, + 0x5040, 0x5041, 0x5044, 0x5045, 0x5050, 0x5051, 0x5054, 0x5055, + 0x5100, 0x5101, 0x5104, 0x5105, 0x5110, 0x5111, 0x5114, 0x5115, + 0x5140, 0x5141, 0x5144, 0x5145, 0x5150, 0x5151, 0x5154, 0x5155, + 0x5400, 0x5401, 0x5404, 0x5405, 0x5410, 0x5411, 0x5414, 0x5415, + 0x5440, 0x5441, 0x5444, 0x5445, 0x5450, 0x5451, 0x5454, 0x5455, + 0x5500, 0x5501, 0x5504, 0x5505, 0x5510, 0x5511, 0x5514, 0x5515, + 0x5540, 0x5541, 0x5544, 0x5545, 0x5550, 0x5551, 0x5554, 0x5555 + }; + + /* + * This expands 7 bit indices into 21 bit contents (high bit 18), by inserting 0s between bits. + */ + private static readonly int[] INTERLEAVE3_TABLE = new int[] + { + 0x00000, 0x00001, 0x00008, 0x00009, 0x00040, 0x00041, 0x00048, 0x00049, + 0x00200, 0x00201, 0x00208, 0x00209, 0x00240, 0x00241, 0x00248, 0x00249, + 0x01000, 0x01001, 0x01008, 0x01009, 0x01040, 0x01041, 0x01048, 0x01049, + 0x01200, 0x01201, 0x01208, 0x01209, 0x01240, 0x01241, 0x01248, 0x01249, + 0x08000, 0x08001, 0x08008, 0x08009, 0x08040, 0x08041, 0x08048, 0x08049, + 0x08200, 0x08201, 0x08208, 0x08209, 0x08240, 0x08241, 0x08248, 0x08249, + 0x09000, 0x09001, 0x09008, 0x09009, 0x09040, 0x09041, 0x09048, 0x09049, + 0x09200, 0x09201, 0x09208, 0x09209, 0x09240, 0x09241, 0x09248, 0x09249, + 0x40000, 0x40001, 0x40008, 0x40009, 0x40040, 0x40041, 0x40048, 0x40049, + 0x40200, 0x40201, 0x40208, 0x40209, 0x40240, 0x40241, 0x40248, 0x40249, + 0x41000, 0x41001, 0x41008, 0x41009, 0x41040, 0x41041, 0x41048, 0x41049, + 0x41200, 0x41201, 0x41208, 0x41209, 0x41240, 0x41241, 0x41248, 0x41249, + 0x48000, 0x48001, 0x48008, 0x48009, 0x48040, 0x48041, 0x48048, 0x48049, + 0x48200, 0x48201, 0x48208, 0x48209, 0x48240, 0x48241, 0x48248, 0x48249, + 0x49000, 0x49001, 0x49008, 0x49009, 0x49040, 0x49041, 0x49048, 0x49049, + 0x49200, 0x49201, 0x49208, 0x49209, 0x49240, 0x49241, 0x49248, 0x49249 + }; + + /* + * This expands 8 bit indices into 32 bit contents (high bit 28), by inserting 0s between bits. + */ + private static readonly int[] INTERLEAVE4_TABLE = new int[] + { + 0x00000000, 0x00000001, 0x00000010, 0x00000011, 0x00000100, 0x00000101, 0x00000110, 0x00000111, + 0x00001000, 0x00001001, 0x00001010, 0x00001011, 0x00001100, 0x00001101, 0x00001110, 0x00001111, + 0x00010000, 0x00010001, 0x00010010, 0x00010011, 0x00010100, 0x00010101, 0x00010110, 0x00010111, + 0x00011000, 0x00011001, 0x00011010, 0x00011011, 0x00011100, 0x00011101, 0x00011110, 0x00011111, + 0x00100000, 0x00100001, 0x00100010, 0x00100011, 0x00100100, 0x00100101, 0x00100110, 0x00100111, + 0x00101000, 0x00101001, 0x00101010, 0x00101011, 0x00101100, 0x00101101, 0x00101110, 0x00101111, + 0x00110000, 0x00110001, 0x00110010, 0x00110011, 0x00110100, 0x00110101, 0x00110110, 0x00110111, + 0x00111000, 0x00111001, 0x00111010, 0x00111011, 0x00111100, 0x00111101, 0x00111110, 0x00111111, + 0x01000000, 0x01000001, 0x01000010, 0x01000011, 0x01000100, 0x01000101, 0x01000110, 0x01000111, + 0x01001000, 0x01001001, 0x01001010, 0x01001011, 0x01001100, 0x01001101, 0x01001110, 0x01001111, + 0x01010000, 0x01010001, 0x01010010, 0x01010011, 0x01010100, 0x01010101, 0x01010110, 0x01010111, + 0x01011000, 0x01011001, 0x01011010, 0x01011011, 0x01011100, 0x01011101, 0x01011110, 0x01011111, + 0x01100000, 0x01100001, 0x01100010, 0x01100011, 0x01100100, 0x01100101, 0x01100110, 0x01100111, + 0x01101000, 0x01101001, 0x01101010, 0x01101011, 0x01101100, 0x01101101, 0x01101110, 0x01101111, + 0x01110000, 0x01110001, 0x01110010, 0x01110011, 0x01110100, 0x01110101, 0x01110110, 0x01110111, + 0x01111000, 0x01111001, 0x01111010, 0x01111011, 0x01111100, 0x01111101, 0x01111110, 0x01111111, + 0x10000000, 0x10000001, 0x10000010, 0x10000011, 0x10000100, 0x10000101, 0x10000110, 0x10000111, + 0x10001000, 0x10001001, 0x10001010, 0x10001011, 0x10001100, 0x10001101, 0x10001110, 0x10001111, + 0x10010000, 0x10010001, 0x10010010, 0x10010011, 0x10010100, 0x10010101, 0x10010110, 0x10010111, + 0x10011000, 0x10011001, 0x10011010, 0x10011011, 0x10011100, 0x10011101, 0x10011110, 0x10011111, + 0x10100000, 0x10100001, 0x10100010, 0x10100011, 0x10100100, 0x10100101, 0x10100110, 0x10100111, + 0x10101000, 0x10101001, 0x10101010, 0x10101011, 0x10101100, 0x10101101, 0x10101110, 0x10101111, + 0x10110000, 0x10110001, 0x10110010, 0x10110011, 0x10110100, 0x10110101, 0x10110110, 0x10110111, + 0x10111000, 0x10111001, 0x10111010, 0x10111011, 0x10111100, 0x10111101, 0x10111110, 0x10111111, + 0x11000000, 0x11000001, 0x11000010, 0x11000011, 0x11000100, 0x11000101, 0x11000110, 0x11000111, + 0x11001000, 0x11001001, 0x11001010, 0x11001011, 0x11001100, 0x11001101, 0x11001110, 0x11001111, + 0x11010000, 0x11010001, 0x11010010, 0x11010011, 0x11010100, 0x11010101, 0x11010110, 0x11010111, + 0x11011000, 0x11011001, 0x11011010, 0x11011011, 0x11011100, 0x11011101, 0x11011110, 0x11011111, + 0x11100000, 0x11100001, 0x11100010, 0x11100011, 0x11100100, 0x11100101, 0x11100110, 0x11100111, + 0x11101000, 0x11101001, 0x11101010, 0x11101011, 0x11101100, 0x11101101, 0x11101110, 0x11101111, + 0x11110000, 0x11110001, 0x11110010, 0x11110011, 0x11110100, 0x11110101, 0x11110110, 0x11110111, + 0x11111000, 0x11111001, 0x11111010, 0x11111011, 0x11111100, 0x11111101, 0x11111110, 0x11111111 + }; + + /* + * This expands 7 bit indices into 35 bit contents (high bit 30), by inserting 0s between bits. + */ + private static readonly int[] INTERLEAVE5_TABLE = new int[] { + 0x00000000, 0x00000001, 0x00000020, 0x00000021, 0x00000400, 0x00000401, 0x00000420, 0x00000421, + 0x00008000, 0x00008001, 0x00008020, 0x00008021, 0x00008400, 0x00008401, 0x00008420, 0x00008421, + 0x00100000, 0x00100001, 0x00100020, 0x00100021, 0x00100400, 0x00100401, 0x00100420, 0x00100421, + 0x00108000, 0x00108001, 0x00108020, 0x00108021, 0x00108400, 0x00108401, 0x00108420, 0x00108421, + 0x02000000, 0x02000001, 0x02000020, 0x02000021, 0x02000400, 0x02000401, 0x02000420, 0x02000421, + 0x02008000, 0x02008001, 0x02008020, 0x02008021, 0x02008400, 0x02008401, 0x02008420, 0x02008421, + 0x02100000, 0x02100001, 0x02100020, 0x02100021, 0x02100400, 0x02100401, 0x02100420, 0x02100421, + 0x02108000, 0x02108001, 0x02108020, 0x02108021, 0x02108400, 0x02108401, 0x02108420, 0x02108421, + 0x40000000, 0x40000001, 0x40000020, 0x40000021, 0x40000400, 0x40000401, 0x40000420, 0x40000421, + 0x40008000, 0x40008001, 0x40008020, 0x40008021, 0x40008400, 0x40008401, 0x40008420, 0x40008421, + 0x40100000, 0x40100001, 0x40100020, 0x40100021, 0x40100400, 0x40100401, 0x40100420, 0x40100421, + 0x40108000, 0x40108001, 0x40108020, 0x40108021, 0x40108400, 0x40108401, 0x40108420, 0x40108421, + 0x42000000, 0x42000001, 0x42000020, 0x42000021, 0x42000400, 0x42000401, 0x42000420, 0x42000421, + 0x42008000, 0x42008001, 0x42008020, 0x42008021, 0x42008400, 0x42008401, 0x42008420, 0x42008421, + 0x42100000, 0x42100001, 0x42100020, 0x42100021, 0x42100400, 0x42100401, 0x42100420, 0x42100421, + 0x42108000, 0x42108001, 0x42108020, 0x42108021, 0x42108400, 0x42108401, 0x42108420, 0x42108421 + }; + + /* + * This expands 9 bit indices into 63 bit (long) contents (high bit 56), by inserting 0s between bits. + */ + private static readonly long[] INTERLEAVE7_TABLE = new long[] + { + 0x0000000000000000L, 0x0000000000000001L, 0x0000000000000080L, 0x0000000000000081L, + 0x0000000000004000L, 0x0000000000004001L, 0x0000000000004080L, 0x0000000000004081L, + 0x0000000000200000L, 0x0000000000200001L, 0x0000000000200080L, 0x0000000000200081L, + 0x0000000000204000L, 0x0000000000204001L, 0x0000000000204080L, 0x0000000000204081L, + 0x0000000010000000L, 0x0000000010000001L, 0x0000000010000080L, 0x0000000010000081L, + 0x0000000010004000L, 0x0000000010004001L, 0x0000000010004080L, 0x0000000010004081L, + 0x0000000010200000L, 0x0000000010200001L, 0x0000000010200080L, 0x0000000010200081L, + 0x0000000010204000L, 0x0000000010204001L, 0x0000000010204080L, 0x0000000010204081L, + 0x0000000800000000L, 0x0000000800000001L, 0x0000000800000080L, 0x0000000800000081L, + 0x0000000800004000L, 0x0000000800004001L, 0x0000000800004080L, 0x0000000800004081L, + 0x0000000800200000L, 0x0000000800200001L, 0x0000000800200080L, 0x0000000800200081L, + 0x0000000800204000L, 0x0000000800204001L, 0x0000000800204080L, 0x0000000800204081L, + 0x0000000810000000L, 0x0000000810000001L, 0x0000000810000080L, 0x0000000810000081L, + 0x0000000810004000L, 0x0000000810004001L, 0x0000000810004080L, 0x0000000810004081L, + 0x0000000810200000L, 0x0000000810200001L, 0x0000000810200080L, 0x0000000810200081L, + 0x0000000810204000L, 0x0000000810204001L, 0x0000000810204080L, 0x0000000810204081L, + 0x0000040000000000L, 0x0000040000000001L, 0x0000040000000080L, 0x0000040000000081L, + 0x0000040000004000L, 0x0000040000004001L, 0x0000040000004080L, 0x0000040000004081L, + 0x0000040000200000L, 0x0000040000200001L, 0x0000040000200080L, 0x0000040000200081L, + 0x0000040000204000L, 0x0000040000204001L, 0x0000040000204080L, 0x0000040000204081L, + 0x0000040010000000L, 0x0000040010000001L, 0x0000040010000080L, 0x0000040010000081L, + 0x0000040010004000L, 0x0000040010004001L, 0x0000040010004080L, 0x0000040010004081L, + 0x0000040010200000L, 0x0000040010200001L, 0x0000040010200080L, 0x0000040010200081L, + 0x0000040010204000L, 0x0000040010204001L, 0x0000040010204080L, 0x0000040010204081L, + 0x0000040800000000L, 0x0000040800000001L, 0x0000040800000080L, 0x0000040800000081L, + 0x0000040800004000L, 0x0000040800004001L, 0x0000040800004080L, 0x0000040800004081L, + 0x0000040800200000L, 0x0000040800200001L, 0x0000040800200080L, 0x0000040800200081L, + 0x0000040800204000L, 0x0000040800204001L, 0x0000040800204080L, 0x0000040800204081L, + 0x0000040810000000L, 0x0000040810000001L, 0x0000040810000080L, 0x0000040810000081L, + 0x0000040810004000L, 0x0000040810004001L, 0x0000040810004080L, 0x0000040810004081L, + 0x0000040810200000L, 0x0000040810200001L, 0x0000040810200080L, 0x0000040810200081L, + 0x0000040810204000L, 0x0000040810204001L, 0x0000040810204080L, 0x0000040810204081L, + 0x0002000000000000L, 0x0002000000000001L, 0x0002000000000080L, 0x0002000000000081L, + 0x0002000000004000L, 0x0002000000004001L, 0x0002000000004080L, 0x0002000000004081L, + 0x0002000000200000L, 0x0002000000200001L, 0x0002000000200080L, 0x0002000000200081L, + 0x0002000000204000L, 0x0002000000204001L, 0x0002000000204080L, 0x0002000000204081L, + 0x0002000010000000L, 0x0002000010000001L, 0x0002000010000080L, 0x0002000010000081L, + 0x0002000010004000L, 0x0002000010004001L, 0x0002000010004080L, 0x0002000010004081L, + 0x0002000010200000L, 0x0002000010200001L, 0x0002000010200080L, 0x0002000010200081L, + 0x0002000010204000L, 0x0002000010204001L, 0x0002000010204080L, 0x0002000010204081L, + 0x0002000800000000L, 0x0002000800000001L, 0x0002000800000080L, 0x0002000800000081L, + 0x0002000800004000L, 0x0002000800004001L, 0x0002000800004080L, 0x0002000800004081L, + 0x0002000800200000L, 0x0002000800200001L, 0x0002000800200080L, 0x0002000800200081L, + 0x0002000800204000L, 0x0002000800204001L, 0x0002000800204080L, 0x0002000800204081L, + 0x0002000810000000L, 0x0002000810000001L, 0x0002000810000080L, 0x0002000810000081L, + 0x0002000810004000L, 0x0002000810004001L, 0x0002000810004080L, 0x0002000810004081L, + 0x0002000810200000L, 0x0002000810200001L, 0x0002000810200080L, 0x0002000810200081L, + 0x0002000810204000L, 0x0002000810204001L, 0x0002000810204080L, 0x0002000810204081L, + 0x0002040000000000L, 0x0002040000000001L, 0x0002040000000080L, 0x0002040000000081L, + 0x0002040000004000L, 0x0002040000004001L, 0x0002040000004080L, 0x0002040000004081L, + 0x0002040000200000L, 0x0002040000200001L, 0x0002040000200080L, 0x0002040000200081L, + 0x0002040000204000L, 0x0002040000204001L, 0x0002040000204080L, 0x0002040000204081L, + 0x0002040010000000L, 0x0002040010000001L, 0x0002040010000080L, 0x0002040010000081L, + 0x0002040010004000L, 0x0002040010004001L, 0x0002040010004080L, 0x0002040010004081L, + 0x0002040010200000L, 0x0002040010200001L, 0x0002040010200080L, 0x0002040010200081L, + 0x0002040010204000L, 0x0002040010204001L, 0x0002040010204080L, 0x0002040010204081L, + 0x0002040800000000L, 0x0002040800000001L, 0x0002040800000080L, 0x0002040800000081L, + 0x0002040800004000L, 0x0002040800004001L, 0x0002040800004080L, 0x0002040800004081L, + 0x0002040800200000L, 0x0002040800200001L, 0x0002040800200080L, 0x0002040800200081L, + 0x0002040800204000L, 0x0002040800204001L, 0x0002040800204080L, 0x0002040800204081L, + 0x0002040810000000L, 0x0002040810000001L, 0x0002040810000080L, 0x0002040810000081L, + 0x0002040810004000L, 0x0002040810004001L, 0x0002040810004080L, 0x0002040810004081L, + 0x0002040810200000L, 0x0002040810200001L, 0x0002040810200080L, 0x0002040810200081L, + 0x0002040810204000L, 0x0002040810204001L, 0x0002040810204080L, 0x0002040810204081L, + 0x0100000000000000L, 0x0100000000000001L, 0x0100000000000080L, 0x0100000000000081L, + 0x0100000000004000L, 0x0100000000004001L, 0x0100000000004080L, 0x0100000000004081L, + 0x0100000000200000L, 0x0100000000200001L, 0x0100000000200080L, 0x0100000000200081L, + 0x0100000000204000L, 0x0100000000204001L, 0x0100000000204080L, 0x0100000000204081L, + 0x0100000010000000L, 0x0100000010000001L, 0x0100000010000080L, 0x0100000010000081L, + 0x0100000010004000L, 0x0100000010004001L, 0x0100000010004080L, 0x0100000010004081L, + 0x0100000010200000L, 0x0100000010200001L, 0x0100000010200080L, 0x0100000010200081L, + 0x0100000010204000L, 0x0100000010204001L, 0x0100000010204080L, 0x0100000010204081L, + 0x0100000800000000L, 0x0100000800000001L, 0x0100000800000080L, 0x0100000800000081L, + 0x0100000800004000L, 0x0100000800004001L, 0x0100000800004080L, 0x0100000800004081L, + 0x0100000800200000L, 0x0100000800200001L, 0x0100000800200080L, 0x0100000800200081L, + 0x0100000800204000L, 0x0100000800204001L, 0x0100000800204080L, 0x0100000800204081L, + 0x0100000810000000L, 0x0100000810000001L, 0x0100000810000080L, 0x0100000810000081L, + 0x0100000810004000L, 0x0100000810004001L, 0x0100000810004080L, 0x0100000810004081L, + 0x0100000810200000L, 0x0100000810200001L, 0x0100000810200080L, 0x0100000810200081L, + 0x0100000810204000L, 0x0100000810204001L, 0x0100000810204080L, 0x0100000810204081L, + 0x0100040000000000L, 0x0100040000000001L, 0x0100040000000080L, 0x0100040000000081L, + 0x0100040000004000L, 0x0100040000004001L, 0x0100040000004080L, 0x0100040000004081L, + 0x0100040000200000L, 0x0100040000200001L, 0x0100040000200080L, 0x0100040000200081L, + 0x0100040000204000L, 0x0100040000204001L, 0x0100040000204080L, 0x0100040000204081L, + 0x0100040010000000L, 0x0100040010000001L, 0x0100040010000080L, 0x0100040010000081L, + 0x0100040010004000L, 0x0100040010004001L, 0x0100040010004080L, 0x0100040010004081L, + 0x0100040010200000L, 0x0100040010200001L, 0x0100040010200080L, 0x0100040010200081L, + 0x0100040010204000L, 0x0100040010204001L, 0x0100040010204080L, 0x0100040010204081L, + 0x0100040800000000L, 0x0100040800000001L, 0x0100040800000080L, 0x0100040800000081L, + 0x0100040800004000L, 0x0100040800004001L, 0x0100040800004080L, 0x0100040800004081L, + 0x0100040800200000L, 0x0100040800200001L, 0x0100040800200080L, 0x0100040800200081L, + 0x0100040800204000L, 0x0100040800204001L, 0x0100040800204080L, 0x0100040800204081L, + 0x0100040810000000L, 0x0100040810000001L, 0x0100040810000080L, 0x0100040810000081L, + 0x0100040810004000L, 0x0100040810004001L, 0x0100040810004080L, 0x0100040810004081L, + 0x0100040810200000L, 0x0100040810200001L, 0x0100040810200080L, 0x0100040810200081L, + 0x0100040810204000L, 0x0100040810204001L, 0x0100040810204080L, 0x0100040810204081L, + 0x0102000000000000L, 0x0102000000000001L, 0x0102000000000080L, 0x0102000000000081L, + 0x0102000000004000L, 0x0102000000004001L, 0x0102000000004080L, 0x0102000000004081L, + 0x0102000000200000L, 0x0102000000200001L, 0x0102000000200080L, 0x0102000000200081L, + 0x0102000000204000L, 0x0102000000204001L, 0x0102000000204080L, 0x0102000000204081L, + 0x0102000010000000L, 0x0102000010000001L, 0x0102000010000080L, 0x0102000010000081L, + 0x0102000010004000L, 0x0102000010004001L, 0x0102000010004080L, 0x0102000010004081L, + 0x0102000010200000L, 0x0102000010200001L, 0x0102000010200080L, 0x0102000010200081L, + 0x0102000010204000L, 0x0102000010204001L, 0x0102000010204080L, 0x0102000010204081L, + 0x0102000800000000L, 0x0102000800000001L, 0x0102000800000080L, 0x0102000800000081L, + 0x0102000800004000L, 0x0102000800004001L, 0x0102000800004080L, 0x0102000800004081L, + 0x0102000800200000L, 0x0102000800200001L, 0x0102000800200080L, 0x0102000800200081L, + 0x0102000800204000L, 0x0102000800204001L, 0x0102000800204080L, 0x0102000800204081L, + 0x0102000810000000L, 0x0102000810000001L, 0x0102000810000080L, 0x0102000810000081L, + 0x0102000810004000L, 0x0102000810004001L, 0x0102000810004080L, 0x0102000810004081L, + 0x0102000810200000L, 0x0102000810200001L, 0x0102000810200080L, 0x0102000810200081L, + 0x0102000810204000L, 0x0102000810204001L, 0x0102000810204080L, 0x0102000810204081L, + 0x0102040000000000L, 0x0102040000000001L, 0x0102040000000080L, 0x0102040000000081L, + 0x0102040000004000L, 0x0102040000004001L, 0x0102040000004080L, 0x0102040000004081L, + 0x0102040000200000L, 0x0102040000200001L, 0x0102040000200080L, 0x0102040000200081L, + 0x0102040000204000L, 0x0102040000204001L, 0x0102040000204080L, 0x0102040000204081L, + 0x0102040010000000L, 0x0102040010000001L, 0x0102040010000080L, 0x0102040010000081L, + 0x0102040010004000L, 0x0102040010004001L, 0x0102040010004080L, 0x0102040010004081L, + 0x0102040010200000L, 0x0102040010200001L, 0x0102040010200080L, 0x0102040010200081L, + 0x0102040010204000L, 0x0102040010204001L, 0x0102040010204080L, 0x0102040010204081L, + 0x0102040800000000L, 0x0102040800000001L, 0x0102040800000080L, 0x0102040800000081L, + 0x0102040800004000L, 0x0102040800004001L, 0x0102040800004080L, 0x0102040800004081L, + 0x0102040800200000L, 0x0102040800200001L, 0x0102040800200080L, 0x0102040800200081L, + 0x0102040800204000L, 0x0102040800204001L, 0x0102040800204080L, 0x0102040800204081L, + 0x0102040810000000L, 0x0102040810000001L, 0x0102040810000080L, 0x0102040810000081L, + 0x0102040810004000L, 0x0102040810004001L, 0x0102040810004080L, 0x0102040810004081L, + 0x0102040810200000L, 0x0102040810200001L, 0x0102040810200080L, 0x0102040810200081L, + 0x0102040810204000L, 0x0102040810204001L, 0x0102040810204080L, 0x0102040810204081L + }; + + // For toString(); must have length 64 + private const string ZEROES = "0000000000000000000000000000000000000000000000000000000000000000"; + + internal static readonly byte[] BitLengths = + { + 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, + 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, + 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, + 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, + 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, + 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, + 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, + 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, + 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, + 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, + 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, + 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, + 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, + 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, + 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, + 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 + }; + + // TODO make m fixed for the LongArray, and hence compute T once and for all + + private long[] m_ints; + + public LongArray(int intLen) + { + m_ints = new long[intLen]; + } + + public LongArray(long[] ints) + { + m_ints = ints; + } + + public LongArray(long[] ints, int off, int len) + { + if (off == 0 && len == ints.Length) + { + m_ints = ints; + } + else + { + m_ints = new long[len]; + Array.Copy(ints, off, m_ints, 0, len); + } + } + + public LongArray(BigInteger bigInt) + { + if (bigInt == null || bigInt.SignValue < 0) + { + throw new ArgumentException("invalid F2m field value", "bigInt"); + } + + if (bigInt.SignValue == 0) + { + m_ints = new long[] { 0L }; + return; + } + + byte[] barr = bigInt.ToByteArray(); + int barrLen = barr.Length; + int barrStart = 0; + if (barr[0] == 0) + { + // First byte is 0 to enforce highest (=sign) bit is zero. + // In this case ignore barr[0]. + barrLen--; + barrStart = 1; + } + int intLen = (barrLen + 7) / 8; + m_ints = new long[intLen]; + + int iarrJ = intLen - 1; + int rem = barrLen % 8 + barrStart; + long temp = 0; + int barrI = barrStart; + if (barrStart < rem) + { + for (; barrI < rem; barrI++) + { + temp <<= 8; + uint barrBarrI = barr[barrI]; + temp |= barrBarrI; + } + m_ints[iarrJ--] = temp; + } + + for (; iarrJ >= 0; iarrJ--) + { + temp = 0; + for (int i = 0; i < 8; i++) + { + temp <<= 8; + uint barrBarrI = barr[barrI++]; + temp |= barrBarrI; + } + m_ints[iarrJ] = temp; + } + } + + public bool IsOne() + { + long[] a = m_ints; + if (a[0] != 1L) + { + return false; + } + for (int i = 1; i < a.Length; ++i) + { + if (a[i] != 0L) + { + return false; + } + } + return true; + } + + public bool IsZero() + { + long[] a = m_ints; + for (int i = 0; i < a.Length; ++i) + { + if (a[i] != 0L) + { + return false; + } + } + return true; + } + + public int GetUsedLength() + { + return GetUsedLengthFrom(m_ints.Length); + } + + public int GetUsedLengthFrom(int from) + { + long[] a = m_ints; + from = System.Math.Min(from, a.Length); + + if (from < 1) + { + return 0; + } + + // Check if first element will act as sentinel + if (a[0] != 0) + { + while (a[--from] == 0) + { + } + return from + 1; + } + + do + { + if (a[--from] != 0) + { + return from + 1; + } + } + while (from > 0); + + return 0; + } + + public int Degree() + { + int i = m_ints.Length; + long w; + do + { + if (i == 0) + { + return 0; + } + w = m_ints[--i]; + } + while (w == 0); + + return (i << 6) + BitLength(w); + } + + private int DegreeFrom(int limit) + { + int i = (int)(((uint)limit + 62) >> 6); + long w; + do + { + if (i == 0) + { + return 0; + } + w = m_ints[--i]; + } + while (w == 0); + + return (i << 6) + BitLength(w); + } + + // private int lowestCoefficient() + // { + // for (int i = 0; i < m_ints.Length; ++i) + // { + // long mi = m_ints[i]; + // if (mi != 0) + // { + // int j = 0; + // while ((mi & 0xFFL) == 0) + // { + // j += 8; + // mi >>>= 8; + // } + // while ((mi & 1L) == 0) + // { + // ++j; + // mi >>>= 1; + // } + // return (i << 6) + j; + // } + // } + // return -1; + // } + + private static int BitLength(long w) + { + int u = (int)((ulong)w >> 32), b; + if (u == 0) + { + u = (int)w; + b = 0; + } + else + { + b = 32; + } + + int t = (int)((uint)u >> 16), k; + if (t == 0) + { + t = (int)((uint)u >> 8); + k = (t == 0) ? BitLengths[u] : 8 + BitLengths[t]; + } + else + { + int v = (int)((uint)t >> 8); + k = (v == 0) ? 16 + BitLengths[t] : 24 + BitLengths[v]; + } + + return b + k; + } + + private long[] ResizedInts(int newLen) + { + long[] newInts = new long[newLen]; + Array.Copy(m_ints, 0, newInts, 0, System.Math.Min(m_ints.Length, newLen)); + return newInts; + } + + public BigInteger ToBigInteger() + { + int usedLen = GetUsedLength(); + if (usedLen == 0) + { + return BigInteger.Zero; + } + + long highestInt = m_ints[usedLen - 1]; + byte[] temp = new byte[8]; + int barrI = 0; + bool trailingZeroBytesDone = false; + for (int j = 7; j >= 0; j--) + { + byte thisByte = (byte)((ulong)highestInt >> (8 * j)); + if (trailingZeroBytesDone || (thisByte != 0)) + { + trailingZeroBytesDone = true; + temp[barrI++] = thisByte; + } + } + + int barrLen = 8 * (usedLen - 1) + barrI; + byte[] barr = new byte[barrLen]; + for (int j = 0; j < barrI; j++) + { + barr[j] = temp[j]; + } + // Highest value int is done now + + for (int iarrJ = usedLen - 2; iarrJ >= 0; iarrJ--) + { + long mi = m_ints[iarrJ]; + for (int j = 7; j >= 0; j--) + { + barr[barrI++] = (byte)((ulong)mi >> (8 * j)); + } + } + return new BigInteger(1, barr); + } + + // private static long shiftUp(long[] x, int xOff, int count) + // { + // long prev = 0; + // for (int i = 0; i < count; ++i) + // { + // long next = x[xOff + i]; + // x[xOff + i] = (next << 1) | prev; + // prev = next >>> 63; + // } + // return prev; + // } + + private static long ShiftUp(long[] x, int xOff, int count, int shift) + { + int shiftInv = 64 - shift; + long prev = 0; + for (int i = 0; i < count; ++i) + { + long next = x[xOff + i]; + x[xOff + i] = (next << shift) | prev; + prev = (long)((ulong)next >> shiftInv); + } + return prev; + } + + private static long ShiftUp(long[] x, int xOff, long[] z, int zOff, int count, int shift) + { + int shiftInv = 64 - shift; + long prev = 0; + for (int i = 0; i < count; ++i) + { + long next = x[xOff + i]; + z[zOff + i] = (next << shift) | prev; + prev = (long)((ulong)next >> shiftInv); + } + return prev; + } + + public LongArray AddOne() + { + if (m_ints.Length == 0) + { + return new LongArray(new long[]{ 1L }); + } + + int resultLen = System.Math.Max(1, GetUsedLength()); + long[] ints = ResizedInts(resultLen); + ints[0] ^= 1L; + return new LongArray(ints); + } + + // private void addShiftedByBits(LongArray other, int bits) + // { + // int words = bits >>> 6; + // int shift = bits & 0x3F; + // + // if (shift == 0) + // { + // addShiftedByWords(other, words); + // return; + // } + // + // int otherUsedLen = other.GetUsedLength(); + // if (otherUsedLen == 0) + // { + // return; + // } + // + // int minLen = otherUsedLen + words + 1; + // if (minLen > m_ints.Length) + // { + // m_ints = resizedInts(minLen); + // } + // + // long carry = addShiftedByBits(m_ints, words, other.m_ints, 0, otherUsedLen, shift); + // m_ints[otherUsedLen + words] ^= carry; + // } + + private void AddShiftedByBitsSafe(LongArray other, int otherDegree, int bits) + { + int otherLen = (int)((uint)(otherDegree + 63) >> 6); + + int words = (int)((uint)bits >> 6); + int shift = bits & 0x3F; + + if (shift == 0) + { + Add(m_ints, words, other.m_ints, 0, otherLen); + return; + } + + long carry = AddShiftedUp(m_ints, words, other.m_ints, 0, otherLen, shift); + if (carry != 0L) + { + m_ints[otherLen + words] ^= carry; + } + } + + private static long AddShiftedUp(long[] x, int xOff, long[] y, int yOff, int count, int shift) + { + int shiftInv = 64 - shift; + long prev = 0; + for (int i = 0; i < count; ++i) + { + long next = y[yOff + i]; + x[xOff + i] ^= (next << shift) | prev; + prev = (long)((ulong)next >> shiftInv); + } + return prev; + } + + private static long AddShiftedDown(long[] x, int xOff, long[] y, int yOff, int count, int shift) + { + int shiftInv = 64 - shift; + long prev = 0; + int i = count; + while (--i >= 0) + { + long next = y[yOff + i]; + x[xOff + i] ^= (long)((ulong)next >> shift) | prev; + prev = next << shiftInv; + } + return prev; + } + + public void AddShiftedByWords(LongArray other, int words) + { + int otherUsedLen = other.GetUsedLength(); + if (otherUsedLen == 0) + { + return; + } + + int minLen = otherUsedLen + words; + if (minLen > m_ints.Length) + { + m_ints = ResizedInts(minLen); + } + + Add(m_ints, words, other.m_ints, 0, otherUsedLen); + } + + private static void Add(long[] x, int xOff, long[] y, int yOff, int count) + { + for (int i = 0; i < count; ++i) + { + x[xOff + i] ^= y[yOff + i]; + } + } + + private static void Add(long[] x, int xOff, long[] y, int yOff, long[] z, int zOff, int count) + { + for (int i = 0; i < count; ++i) + { + z[zOff + i] = x[xOff + i] ^ y[yOff + i]; + } + } + + private static void AddBoth(long[] x, int xOff, long[] y1, int y1Off, long[] y2, int y2Off, int count) + { + for (int i = 0; i < count; ++i) + { + x[xOff + i] ^= y1[y1Off + i] ^ y2[y2Off + i]; + } + } + + private static void Distribute(long[] x, int src, int dst1, int dst2, int count) + { + for (int i = 0; i < count; ++i) + { + long v = x[src + i]; + x[dst1 + i] ^= v; + x[dst2 + i] ^= v; + } + } + + public int Length + { + get { return m_ints.Length; } + } + + private static void FlipWord(long[] buf, int off, int bit, long word) + { + int n = off + (int)((uint)bit >> 6); + int shift = bit & 0x3F; + if (shift == 0) + { + buf[n] ^= word; + } + else + { + buf[n] ^= word << shift; + word = (long)((ulong)word >> (64 - shift)); + if (word != 0) + { + buf[++n] ^= word; + } + } + } + + // private static long getWord(long[] buf, int off, int len, int bit) + // { + // int n = off + (bit >>> 6); + // int shift = bit & 0x3F; + // if (shift == 0) + // { + // return buf[n]; + // } + // long result = buf[n] >>> shift; + // if (++n < len) + // { + // result |= buf[n] << (64 - shift); + // } + // return result; + // } + + public bool TestBitZero() + { + return m_ints.Length > 0 && (m_ints[0] & 1L) != 0; + } + + private static bool TestBit(long[] buf, int off, int n) + { + // theInt = n / 64 + int theInt = (int)((uint)n >> 6); + // theBit = n % 64 + int theBit = n & 0x3F; + long tester = 1L << theBit; + return (buf[off + theInt] & tester) != 0; + } + + private static void FlipBit(long[] buf, int off, int n) + { + // theInt = n / 64 + int theInt = (int)((uint)n >> 6); + // theBit = n % 64 + int theBit = n & 0x3F; + long flipper = 1L << theBit; + buf[off + theInt] ^= flipper; + } + + // private static void SetBit(long[] buf, int off, int n) + // { + // // theInt = n / 64 + // int theInt = n >>> 6; + // // theBit = n % 64 + // int theBit = n & 0x3F; + // long setter = 1L << theBit; + // buf[off + theInt] |= setter; + // } + // + // private static void ClearBit(long[] buf, int off, int n) + // { + // // theInt = n / 64 + // int theInt = n >>> 6; + // // theBit = n % 64 + // int theBit = n & 0x3F; + // long setter = 1L << theBit; + // buf[off + theInt] &= ~setter; + // } + + private static void MultiplyWord(long a, long[] b, int bLen, long[] c, int cOff) + { + if ((a & 1L) != 0L) + { + Add(c, cOff, b, 0, bLen); + } + int k = 1; + while ((a = (long)((ulong)a >> 1)) != 0L) + { + if ((a & 1L) != 0L) + { + long carry = AddShiftedUp(c, cOff, b, 0, bLen, k); + if (carry != 0L) + { + c[cOff + bLen] ^= carry; + } + } + ++k; + } + } + + public LongArray ModMultiplyLD(LongArray other, int m, int[] ks) + { + /* + * Find out the degree of each argument and handle the zero cases + */ + int aDeg = Degree(); + if (aDeg == 0) + { + return this; + } + int bDeg = other.Degree(); + if (bDeg == 0) + { + return other; + } + + /* + * Swap if necessary so that A is the smaller argument + */ + LongArray A = this, B = other; + if (aDeg > bDeg) + { + A = other; B = this; + int tmp = aDeg; aDeg = bDeg; bDeg = tmp; + } + + /* + * Establish the word lengths of the arguments and result + */ + int aLen = (int)((uint)(aDeg + 63) >> 6); + int bLen = (int)((uint)(bDeg + 63) >> 6); + int cLen = (int)((uint)(aDeg + bDeg + 62) >> 6); + + if (aLen == 1) + { + long a0 = A.m_ints[0]; + if (a0 == 1L) + { + return B; + } + + /* + * Fast path for small A, with performance dependent only on the number of set bits + */ + long[] c0 = new long[cLen]; + MultiplyWord(a0, B.m_ints, bLen, c0, 0); + + /* + * Reduce the raw answer against the reduction coefficients + */ + return ReduceResult(c0, 0, cLen, m, ks); + } + + /* + * Determine if B will get bigger during shifting + */ + int bMax = (int)((uint)(bDeg + 7 + 63) >> 6); + + /* + * Lookup table for the offset of each B in the tables + */ + int[] ti = new int[16]; + + /* + * Precompute table of all 4-bit products of B + */ + long[] T0 = new long[bMax << 4]; + int tOff = bMax; + ti[1] = tOff; + Array.Copy(B.m_ints, 0, T0, tOff, bLen); + for (int i = 2; i < 16; ++i) + { + ti[i] = (tOff += bMax); + if ((i & 1) == 0) + { + ShiftUp(T0, (int)((uint)tOff >> 1), T0, tOff, bMax, 1); + } + else + { + Add(T0, bMax, T0, tOff - bMax, T0, tOff, bMax); + } + } + + /* + * Second table with all 4-bit products of B shifted 4 bits + */ + long[] T1 = new long[T0.Length]; + ShiftUp(T0, 0, T1, 0, T0.Length, 4); + // shiftUp(T0, bMax, T1, bMax, tOff, 4); + + long[] a = A.m_ints; + long[] c = new long[cLen]; + + int MASK = 0xF; + + /* + * Lopez-Dahab algorithm + */ + + for (int k = 56; k >= 0; k -= 8) + { + for (int j = 1; j < aLen; j += 2) + { + int aVal = (int)((ulong)a[j] >> k); + int u = aVal & MASK; + int v = (int)((uint)aVal >> 4) & MASK; + AddBoth(c, j - 1, T0, ti[u], T1, ti[v], bMax); + } + ShiftUp(c, 0, cLen, 8); + } + + for (int k = 56; k >= 0; k -= 8) + { + for (int j = 0; j < aLen; j += 2) + { + int aVal = (int)((ulong)a[j] >> k); + int u = aVal & MASK; + int v = (int)((uint)aVal >> 4) & MASK; + AddBoth(c, j, T0, ti[u], T1, ti[v], bMax); + } + if (k > 0) + { + ShiftUp(c, 0, cLen, 8); + } + } + + /* + * Finally the raw answer is collected, reduce it against the reduction coefficients + */ + return ReduceResult(c, 0, cLen, m, ks); + } + + public LongArray ModMultiply(LongArray other, int m, int[] ks) + { + /* + * Find out the degree of each argument and handle the zero cases + */ + int aDeg = Degree(); + if (aDeg == 0) + { + return this; + } + int bDeg = other.Degree(); + if (bDeg == 0) + { + return other; + } + + /* + * Swap if necessary so that A is the smaller argument + */ + LongArray A = this, B = other; + if (aDeg > bDeg) + { + A = other; B = this; + int tmp = aDeg; aDeg = bDeg; bDeg = tmp; + } + + /* + * Establish the word lengths of the arguments and result + */ + int aLen = (int)((uint)(aDeg + 63) >> 6); + int bLen = (int)((uint)(bDeg + 63) >> 6); + int cLen = (int)((uint)(aDeg + bDeg + 62) >> 6); + + if (aLen == 1) + { + long a0 = A.m_ints[0]; + if (a0 == 1L) + { + return B; + } + + /* + * Fast path for small A, with performance dependent only on the number of set bits + */ + long[] c0 = new long[cLen]; + MultiplyWord(a0, B.m_ints, bLen, c0, 0); + + /* + * Reduce the raw answer against the reduction coefficients + */ + return ReduceResult(c0, 0, cLen, m, ks); + } + + /* + * Determine if B will get bigger during shifting + */ + int bMax = (int)((uint)(bDeg + 7 + 63) >> 6); + + /* + * Lookup table for the offset of each B in the tables + */ + int[] ti = new int[16]; + + /* + * Precompute table of all 4-bit products of B + */ + long[] T0 = new long[bMax << 4]; + int tOff = bMax; + ti[1] = tOff; + Array.Copy(B.m_ints, 0, T0, tOff, bLen); + for (int i = 2; i < 16; ++i) + { + ti[i] = (tOff += bMax); + if ((i & 1) == 0) + { + ShiftUp(T0, (int)((uint)tOff >> 1), T0, tOff, bMax, 1); + } + else + { + Add(T0, bMax, T0, tOff - bMax, T0, tOff, bMax); + } + } + + /* + * Second table with all 4-bit products of B shifted 4 bits + */ + long[] T1 = new long[T0.Length]; + ShiftUp(T0, 0, T1, 0, T0.Length, 4); + // ShiftUp(T0, bMax, T1, bMax, tOff, 4); + + long[] a = A.m_ints; + long[] c = new long[cLen << 3]; + + int MASK = 0xF; + + /* + * Lopez-Dahab (Modified) algorithm + */ + + for (int aPos = 0; aPos < aLen; ++aPos) + { + long aVal = a[aPos]; + int cOff = aPos; + for (;;) + { + int u = (int)aVal & MASK; + aVal = (long)((ulong)aVal >> 4); + int v = (int)aVal & MASK; + AddBoth(c, cOff, T0, ti[u], T1, ti[v], bMax); + aVal = (long)((ulong)aVal >> 4); + if (aVal == 0L) + { + break; + } + cOff += cLen; + } + } + + { + int cOff = c.Length; + while ((cOff -= cLen) != 0) + { + AddShiftedUp(c, cOff - cLen, c, cOff, cLen, 8); + } + } + + /* + * Finally the raw answer is collected, reduce it against the reduction coefficients + */ + return ReduceResult(c, 0, cLen, m, ks); + } + + public LongArray ModMultiplyAlt(LongArray other, int m, int[] ks) + { + /* + * Find out the degree of each argument and handle the zero cases + */ + int aDeg = Degree(); + if (aDeg == 0) + { + return this; + } + int bDeg = other.Degree(); + if (bDeg == 0) + { + return other; + } + + /* + * Swap if necessary so that A is the smaller argument + */ + LongArray A = this, B = other; + if (aDeg > bDeg) + { + A = other; B = this; + int tmp = aDeg; aDeg = bDeg; bDeg = tmp; + } + + /* + * Establish the word lengths of the arguments and result + */ + int aLen = (int)((uint)(aDeg + 63) >> 6); + int bLen = (int)((uint)(bDeg + 63) >> 6); + int cLen = (int)((uint)(aDeg + bDeg + 62) >> 6); + + if (aLen == 1) + { + long a0 = A.m_ints[0]; + if (a0 == 1L) + { + return B; + } + + /* + * Fast path for small A, with performance dependent only on the number of set bits + */ + long[] c0 = new long[cLen]; + MultiplyWord(a0, B.m_ints, bLen, c0, 0); + + /* + * Reduce the raw answer against the reduction coefficients + */ + return ReduceResult(c0, 0, cLen, m, ks); + } + + // NOTE: This works, but is slower than width 4 processing + // if (aLen == 2) + // { + // /* + // * Use common-multiplicand optimization to save ~1/4 of the adds + // */ + // long a1 = A.m_ints[0], a2 = A.m_ints[1]; + // long aa = a1 & a2; a1 ^= aa; a2 ^= aa; + // + // long[] b = B.m_ints; + // long[] c = new long[cLen]; + // multiplyWord(aa, b, bLen, c, 1); + // add(c, 0, c, 1, cLen - 1); + // multiplyWord(a1, b, bLen, c, 0); + // multiplyWord(a2, b, bLen, c, 1); + // + // /* + // * Reduce the raw answer against the reduction coefficients + // */ + // return ReduceResult(c, 0, cLen, m, ks); + // } + + /* + * Determine the parameters of the Interleaved window algorithm: the 'width' in bits to + * process together, the number of evaluation 'positions' implied by that width, and the + * 'top' position at which the regular window algorithm stops. + */ + int width, positions, top, banks; + + // NOTE: width 4 is the fastest over the entire range of sizes used in current crypto + // width = 1; positions = 64; top = 64; banks = 4; + // width = 2; positions = 32; top = 64; banks = 4; + // width = 3; positions = 21; top = 63; banks = 3; + width = 4; positions = 16; top = 64; banks = 8; + // width = 5; positions = 13; top = 65; banks = 7; + // width = 7; positions = 9; top = 63; banks = 9; + // width = 8; positions = 8; top = 64; banks = 8; + + /* + * Determine if B will get bigger during shifting + */ + int shifts = top < 64 ? positions : positions - 1; + int bMax = (int)((uint)(bDeg + shifts + 63) >> 6); + + int bTotal = bMax * banks, stride = width * banks; + + /* + * Create a single temporary buffer, with an offset table to find the positions of things in it + */ + int[] ci = new int[1 << width]; + int cTotal = aLen; + { + ci[0] = cTotal; + cTotal += bTotal; + ci[1] = cTotal; + for (int i = 2; i < ci.Length; ++i) + { + cTotal += cLen; + ci[i] = cTotal; + } + cTotal += cLen; + } + // NOTE: Provide a safe dump for "high zeroes" since we are adding 'bMax' and not 'bLen' + ++cTotal; + + long[] c = new long[cTotal]; + + // Prepare A in Interleaved form, according to the chosen width + Interleave(A.m_ints, 0, c, 0, aLen, width); + + // Make a working copy of B, since we will be shifting it + { + int bOff = aLen; + Array.Copy(B.m_ints, 0, c, bOff, bLen); + for (int bank = 1; bank < banks; ++bank) + { + ShiftUp(c, aLen, c, bOff += bMax, bMax, bank); + } + } + + /* + * The main loop analyzes the Interleaved windows in A, and for each non-zero window + * a single word-array XOR is performed to a carefully selected slice of 'c'. The loop is + * breadth-first, checking the lowest window in each word, then looping again for the + * next higher window position. + */ + int MASK = (1 << width) - 1; + + int k = 0; + for (;;) + { + int aPos = 0; + do + { + long aVal = (long)((ulong)c[aPos] >> k); + int bank = 0, bOff = aLen; + for (;;) + { + int index = (int)(aVal) & MASK; + if (index != 0) + { + /* + * Add to a 'c' buffer based on the bit-pattern of 'index'. Since A is in + * Interleaved form, the bits represent the current B shifted by 0, 'positions', + * 'positions' * 2, ..., 'positions' * ('width' - 1) + */ + Add(c, aPos + ci[index], c, bOff, bMax); + } + if (++bank == banks) + { + break; + } + bOff += bMax; + aVal = (long)((ulong)aVal >> width); + } + } + while (++aPos < aLen); + + if ((k += stride) >= top) + { + if (k >= 64) + { + break; + } + + /* + * Adjustment for window setups with top == 63, the final bit (if any) is processed + * as the top-bit of a window + */ + k = 64 - width; + MASK &= MASK << (top - k); + } + + /* + * After each position has been checked for all words of A, B is shifted up 1 place + */ + ShiftUp(c, aLen, bTotal, banks); + } + + int ciPos = ci.Length; + while (--ciPos > 1) + { + if ((ciPos & 1L) == 0L) + { + /* + * For even numbers, shift contents and add to the half-position + */ + AddShiftedUp(c, ci[(uint)ciPos >> 1], c, ci[ciPos], cLen, positions); + } + else + { + /* + * For odd numbers, 'distribute' contents to the result and the next-lowest position + */ + Distribute(c, ci[ciPos], ci[ciPos - 1], ci[1], cLen); + } + } + + /* + * Finally the raw answer is collected, reduce it against the reduction coefficients + */ + return ReduceResult(c, ci[1], cLen, m, ks); + } + + private static LongArray ReduceResult(long[] buf, int off, int len, int m, int[] ks) + { + int rLen = ReduceInPlace(buf, off, len, m, ks); + return new LongArray(buf, off, rLen); + } + + // private static void deInterleave(long[] x, int xOff, long[] z, int zOff, int count, int rounds) + // { + // for (int i = 0; i < count; ++i) + // { + // z[zOff + i] = deInterleave(x[zOff + i], rounds); + // } + // } + // + // private static long deInterleave(long x, int rounds) + // { + // while (--rounds >= 0) + // { + // x = deInterleave32(x & DEInterleave_MASK) | (deInterleave32((x >>> 1) & DEInterleave_MASK) << 32); + // } + // return x; + // } + // + // private static long deInterleave32(long x) + // { + // x = (x | (x >>> 1)) & 0x3333333333333333L; + // x = (x | (x >>> 2)) & 0x0F0F0F0F0F0F0F0FL; + // x = (x | (x >>> 4)) & 0x00FF00FF00FF00FFL; + // x = (x | (x >>> 8)) & 0x0000FFFF0000FFFFL; + // x = (x | (x >>> 16)) & 0x00000000FFFFFFFFL; + // return x; + // } + + private static int ReduceInPlace(long[] buf, int off, int len, int m, int[] ks) + { + int mLen = (int)((uint)(m + 63) >> 6); + if (len < mLen) + { + return len; + } + + int numBits = System.Math.Min(len << 6, (m << 1) - 1); // TODO use actual degree? + int excessBits = (len << 6) - numBits; + while (excessBits >= 64) + { + --len; + excessBits -= 64; + } + + int kLen = ks.Length, kMax = ks[kLen - 1], kNext = kLen > 1 ? ks[kLen - 2] : 0; + int wordWiseLimit = System.Math.Max(m, kMax + 64); + int vectorableWords = (excessBits + System.Math.Min(numBits - wordWiseLimit, m - kNext)) >> 6; + if (vectorableWords > 1) + { + int vectorWiseWords = len - vectorableWords; + ReduceVectorWise(buf, off, len, vectorWiseWords, m, ks); + while (len > vectorWiseWords) + { + buf[off + --len] = 0L; + } + numBits = vectorWiseWords << 6; + } + + if (numBits > wordWiseLimit) + { + ReduceWordWise(buf, off, len, wordWiseLimit, m, ks); + numBits = wordWiseLimit; + } + + if (numBits > m) + { + ReduceBitWise(buf, off, numBits, m, ks); + } + + return mLen; + } + + private static void ReduceBitWise(long[] buf, int off, int BitLength, int m, int[] ks) + { + while (--BitLength >= m) + { + if (TestBit(buf, off, BitLength)) + { + ReduceBit(buf, off, BitLength, m, ks); + } + } + } + + private static void ReduceBit(long[] buf, int off, int bit, int m, int[] ks) + { + FlipBit(buf, off, bit); + int n = bit - m; + int j = ks.Length; + while (--j >= 0) + { + FlipBit(buf, off, ks[j] + n); + } + FlipBit(buf, off, n); + } + + private static void ReduceWordWise(long[] buf, int off, int len, int toBit, int m, int[] ks) + { + int toPos = (int)((uint)toBit >> 6); + + while (--len > toPos) + { + long word = buf[off + len]; + if (word != 0) + { + buf[off + len] = 0; + ReduceWord(buf, off, (len << 6), word, m, ks); + } + } + + { + int partial = toBit & 0x3F; + long word = (long)((ulong)buf[off + toPos] >> partial); + if (word != 0) + { + buf[off + toPos] ^= word << partial; + ReduceWord(buf, off, toBit, word, m, ks); + } + } + } + + private static void ReduceWord(long[] buf, int off, int bit, long word, int m, int[] ks) + { + int offset = bit - m; + int j = ks.Length; + while (--j >= 0) + { + FlipWord(buf, off, offset + ks[j], word); + } + FlipWord(buf, off, offset, word); + } + + private static void ReduceVectorWise(long[] buf, int off, int len, int words, int m, int[] ks) + { + /* + * NOTE: It's important we go from highest coefficient to lowest, because for the highest + * one (only) we allow the ranges to partially overlap, and therefore any changes must take + * effect for the subsequent lower coefficients. + */ + int baseBit = (words << 6) - m; + int j = ks.Length; + while (--j >= 0) + { + FlipVector(buf, off, buf, off + words, len - words, baseBit + ks[j]); + } + FlipVector(buf, off, buf, off + words, len - words, baseBit); + } + + private static void FlipVector(long[] x, int xOff, long[] y, int yOff, int yLen, int bits) + { + xOff += (int)((uint)bits >> 6); + bits &= 0x3F; + + if (bits == 0) + { + Add(x, xOff, y, yOff, yLen); + } + else + { + long carry = AddShiftedDown(x, xOff + 1, y, yOff, yLen, 64 - bits); + x[xOff] ^= carry; + } + } + + public LongArray ModSquare(int m, int[] ks) + { + int len = GetUsedLength(); + if (len == 0) + { + return this; + } + + int _2len = len << 1; + long[] r = new long[_2len]; + + int pos = 0; + while (pos < _2len) + { + long mi = m_ints[(uint)pos >> 1]; + r[pos++] = Interleave2_32to64((int)mi); + r[pos++] = Interleave2_32to64((int)((ulong)mi >> 32)); + } + + return new LongArray(r, 0, ReduceInPlace(r, 0, r.Length, m, ks)); + } + + // private LongArray modSquareN(int n, int m, int[] ks) + // { + // int len = GetUsedLength(); + // if (len == 0) + // { + // return this; + // } + // + // int mLen = (m + 63) >>> 6; + // long[] r = new long[mLen << 1]; + // Array.Copy(m_ints, 0, r, 0, len); + // + // while (--n >= 0) + // { + // squareInPlace(r, len, m, ks); + // len = reduceInPlace(r, 0, r.Length, m, ks); + // } + // + // return new LongArray(r, 0, len); + // } + // + // private static void squareInPlace(long[] x, int xLen, int m, int[] ks) + // { + // int pos = xLen << 1; + // while (--xLen >= 0) + // { + // long xVal = x[xLen]; + // x[--pos] = Interleave2_32to64((int)(xVal >>> 32)); + // x[--pos] = Interleave2_32to64((int)xVal); + // } + // } + + private static void Interleave(long[] x, int xOff, long[] z, int zOff, int count, int width) + { + switch (width) + { + case 3: + Interleave3(x, xOff, z, zOff, count); + break; + case 5: + Interleave5(x, xOff, z, zOff, count); + break; + case 7: + Interleave7(x, xOff, z, zOff, count); + break; + default: + Interleave2_n(x, xOff, z, zOff, count, BitLengths[width] - 1); + break; + } + } + + private static void Interleave3(long[] x, int xOff, long[] z, int zOff, int count) + { + for (int i = 0; i < count; ++i) + { + z[zOff + i] = Interleave3(x[xOff + i]); + } + } + + private static long Interleave3(long x) + { + long z = x & (1L << 63); + return z + | Interleave3_21to63((int)x & 0x1FFFFF) + | Interleave3_21to63((int)((ulong)x >> 21) & 0x1FFFFF) << 1 + | Interleave3_21to63((int)((ulong)x >> 42) & 0x1FFFFF) << 2; + + // int zPos = 0, wPos = 0, xPos = 0; + // for (;;) + // { + // z |= ((x >>> xPos) & 1L) << zPos; + // if (++zPos == 63) + // { + // String sz2 = Long.toBinaryString(z); + // return z; + // } + // if ((xPos += 21) >= 63) + // { + // xPos = ++wPos; + // } + // } + } + + private static long Interleave3_21to63(int x) + { + int r00 = INTERLEAVE3_TABLE[x & 0x7F]; + int r21 = INTERLEAVE3_TABLE[((uint)x >> 7) & 0x7F]; + int r42 = INTERLEAVE3_TABLE[(uint)x >> 14]; + return (r42 & 0xFFFFFFFFL) << 42 | (r21 & 0xFFFFFFFFL) << 21 | (r00 & 0xFFFFFFFFL); + } + + private static void Interleave5(long[] x, int xOff, long[] z, int zOff, int count) + { + for (int i = 0; i < count; ++i) + { + z[zOff + i] = Interleave5(x[xOff + i]); + } + } + + private static long Interleave5(long x) + { + return Interleave3_13to65((int)x & 0x1FFF) + | Interleave3_13to65((int)((ulong)x >> 13) & 0x1FFF) << 1 + | Interleave3_13to65((int)((ulong)x >> 26) & 0x1FFF) << 2 + | Interleave3_13to65((int)((ulong)x >> 39) & 0x1FFF) << 3 + | Interleave3_13to65((int)((ulong)x >> 52) & 0x1FFF) << 4; + + // long z = 0; + // int zPos = 0, wPos = 0, xPos = 0; + // for (;;) + // { + // z |= ((x >>> xPos) & 1L) << zPos; + // if (++zPos == 64) + // { + // return z; + // } + // if ((xPos += 13) >= 64) + // { + // xPos = ++wPos; + // } + // } + } + + private static long Interleave3_13to65(int x) + { + int r00 = INTERLEAVE5_TABLE[x & 0x7F]; + int r35 = INTERLEAVE5_TABLE[(uint)x >> 7]; + return (r35 & 0xFFFFFFFFL) << 35 | (r00 & 0xFFFFFFFFL); + } + + private static void Interleave7(long[] x, int xOff, long[] z, int zOff, int count) + { + for (int i = 0; i < count; ++i) + { + z[zOff + i] = Interleave7(x[xOff + i]); + } + } + + private static long Interleave7(long x) + { + long z = x & (1L << 63); + return z + | INTERLEAVE7_TABLE[(int)x & 0x1FF] + | INTERLEAVE7_TABLE[(int)((ulong)x >> 9) & 0x1FF] << 1 + | INTERLEAVE7_TABLE[(int)((ulong)x >> 18) & 0x1FF] << 2 + | INTERLEAVE7_TABLE[(int)((ulong)x >> 27) & 0x1FF] << 3 + | INTERLEAVE7_TABLE[(int)((ulong)x >> 36) & 0x1FF] << 4 + | INTERLEAVE7_TABLE[(int)((ulong)x >> 45) & 0x1FF] << 5 + | INTERLEAVE7_TABLE[(int)((ulong)x >> 54) & 0x1FF] << 6; + + // int zPos = 0, wPos = 0, xPos = 0; + // for (;;) + // { + // z |= ((x >>> xPos) & 1L) << zPos; + // if (++zPos == 63) + // { + // return z; + // } + // if ((xPos += 9) >= 63) + // { + // xPos = ++wPos; + // } + // } + } + + private static void Interleave2_n(long[] x, int xOff, long[] z, int zOff, int count, int rounds) + { + for (int i = 0; i < count; ++i) + { + z[zOff + i] = Interleave2_n(x[xOff + i], rounds); + } + } + + private static long Interleave2_n(long x, int rounds) + { + while (rounds > 1) + { + rounds -= 2; + x = Interleave4_16to64((int)x & 0xFFFF) + | Interleave4_16to64((int)((ulong)x >> 16) & 0xFFFF) << 1 + | Interleave4_16to64((int)((ulong)x >> 32) & 0xFFFF) << 2 + | Interleave4_16to64((int)((ulong)x >> 48) & 0xFFFF) << 3; + } + if (rounds > 0) + { + x = Interleave2_32to64((int)x) | Interleave2_32to64((int)((ulong)x >> 32)) << 1; + } + return x; + } + + private static long Interleave4_16to64(int x) + { + int r00 = INTERLEAVE4_TABLE[x & 0xFF]; + int r32 = INTERLEAVE4_TABLE[(uint)x >> 8]; + return (r32 & 0xFFFFFFFFL) << 32 | (r00 & 0xFFFFFFFFL); + } + + private static long Interleave2_32to64(int x) + { + int r00 = INTERLEAVE2_TABLE[x & 0xFF] | INTERLEAVE2_TABLE[((uint)x >> 8) & 0xFF] << 16; + int r32 = INTERLEAVE2_TABLE[((uint)x >> 16) & 0xFF] | INTERLEAVE2_TABLE[(uint)x >> 24] << 16; + return (r32 & 0xFFFFFFFFL) << 32 | (r00 & 0xFFFFFFFFL); + } + + // private static LongArray ExpItohTsujii2(LongArray B, int n, int m, int[] ks) + // { + // LongArray t1 = B, t3 = new LongArray(new long[]{ 1L }); + // int scale = 1; + // + // int numTerms = n; + // while (numTerms > 1) + // { + // if ((numTerms & 1) != 0) + // { + // t3 = t3.ModMultiply(t1, m, ks); + // t1 = t1.modSquareN(scale, m, ks); + // } + // + // LongArray t2 = t1.modSquareN(scale, m, ks); + // t1 = t1.ModMultiply(t2, m, ks); + // numTerms >>>= 1; scale <<= 1; + // } + // + // return t3.ModMultiply(t1, m, ks); + // } + // + // private static LongArray ExpItohTsujii23(LongArray B, int n, int m, int[] ks) + // { + // LongArray t1 = B, t3 = new LongArray(new long[]{ 1L }); + // int scale = 1; + // + // int numTerms = n; + // while (numTerms > 1) + // { + // bool m03 = numTerms % 3 == 0; + // bool m14 = !m03 && (numTerms & 1) != 0; + // + // if (m14) + // { + // t3 = t3.ModMultiply(t1, m, ks); + // t1 = t1.modSquareN(scale, m, ks); + // } + // + // LongArray t2 = t1.modSquareN(scale, m, ks); + // t1 = t1.ModMultiply(t2, m, ks); + // + // if (m03) + // { + // t2 = t2.modSquareN(scale, m, ks); + // t1 = t1.ModMultiply(t2, m, ks); + // numTerms /= 3; scale *= 3; + // } + // else + // { + // numTerms >>>= 1; scale <<= 1; + // } + // } + // + // return t3.ModMultiply(t1, m, ks); + // } + // + // private static LongArray ExpItohTsujii235(LongArray B, int n, int m, int[] ks) + // { + // LongArray t1 = B, t4 = new LongArray(new long[]{ 1L }); + // int scale = 1; + // + // int numTerms = n; + // while (numTerms > 1) + // { + // if (numTerms % 5 == 0) + // { + //// t1 = ExpItohTsujii23(t1, 5, m, ks); + // + // LongArray t3 = t1; + // t1 = t1.modSquareN(scale, m, ks); + // + // LongArray t2 = t1.modSquareN(scale, m, ks); + // t1 = t1.ModMultiply(t2, m, ks); + // t2 = t1.modSquareN(scale << 1, m, ks); + // t1 = t1.ModMultiply(t2, m, ks); + // + // t1 = t1.ModMultiply(t3, m, ks); + // + // numTerms /= 5; scale *= 5; + // continue; + // } + // + // bool m03 = numTerms % 3 == 0; + // bool m14 = !m03 && (numTerms & 1) != 0; + // + // if (m14) + // { + // t4 = t4.ModMultiply(t1, m, ks); + // t1 = t1.modSquareN(scale, m, ks); + // } + // + // LongArray t2 = t1.modSquareN(scale, m, ks); + // t1 = t1.ModMultiply(t2, m, ks); + // + // if (m03) + // { + // t2 = t2.modSquareN(scale, m, ks); + // t1 = t1.ModMultiply(t2, m, ks); + // numTerms /= 3; scale *= 3; + // } + // else + // { + // numTerms >>>= 1; scale <<= 1; + // } + // } + // + // return t4.ModMultiply(t1, m, ks); + // } + + public LongArray ModInverse(int m, int[] ks) + { + /* + * Fermat's Little Theorem + */ + // LongArray A = this; + // LongArray B = A.modSquare(m, ks); + // LongArray R0 = B, R1 = B; + // for (int i = 2; i < m; ++i) + // { + // R1 = R1.modSquare(m, ks); + // R0 = R0.ModMultiply(R1, m, ks); + // } + // + // return R0; + + /* + * Itoh-Tsujii + */ + // LongArray B = modSquare(m, ks); + // switch (m) + // { + // case 409: + // return ExpItohTsujii23(B, m - 1, m, ks); + // case 571: + // return ExpItohTsujii235(B, m - 1, m, ks); + // case 163: + // case 233: + // case 283: + // default: + // return ExpItohTsujii2(B, m - 1, m, ks); + // } + + /* + * Inversion in F2m using the extended Euclidean algorithm + * + * Input: A nonzero polynomial a(z) of degree at most m-1 + * Output: a(z)^(-1) mod f(z) + */ + int uzDegree = Degree(); + if (uzDegree == 1) + { + return this; + } + + // u(z) := a(z) + LongArray uz = (LongArray)Copy(); + + int t = (int)((uint)(m + 63) >> 6); + + // v(z) := f(z) + LongArray vz = new LongArray(t); + ReduceBit(vz.m_ints, 0, m, m, ks); + + // g1(z) := 1, g2(z) := 0 + LongArray g1z = new LongArray(t); + g1z.m_ints[0] = 1L; + LongArray g2z = new LongArray(t); + + int[] uvDeg = new int[]{ uzDegree, m + 1 }; + LongArray[] uv = new LongArray[]{ uz, vz }; + + int[] ggDeg = new int[]{ 1, 0 }; + LongArray[] gg = new LongArray[]{ g1z, g2z }; + + int b = 1; + int duv1 = uvDeg[b]; + int dgg1 = ggDeg[b]; + int j = duv1 - uvDeg[1 - b]; + + for (;;) + { + if (j < 0) + { + j = -j; + uvDeg[b] = duv1; + ggDeg[b] = dgg1; + b = 1 - b; + duv1 = uvDeg[b]; + dgg1 = ggDeg[b]; + } + + uv[b].AddShiftedByBitsSafe(uv[1 - b], uvDeg[1 - b], j); + + int duv2 = uv[b].DegreeFrom(duv1); + if (duv2 == 0) + { + return gg[1 - b]; + } + + { + int dgg2 = ggDeg[1 - b]; + gg[b].AddShiftedByBitsSafe(gg[1 - b], dgg2, j); + dgg2 += j; + + if (dgg2 > dgg1) + { + dgg1 = dgg2; + } + else if (dgg2 == dgg1) + { + dgg1 = gg[b].DegreeFrom(dgg1); + } + } + + j += (duv2 - duv1); + duv1 = duv2; + } + } + + public override bool Equals(object obj) + { + return Equals(obj as LongArray); + } + + public virtual bool Equals(LongArray other) + { + if (this == other) + return true; + if (null == other) + return false; + int usedLen = GetUsedLength(); + if (other.GetUsedLength() != usedLen) + { + return false; + } + for (int i = 0; i < usedLen; i++) + { + if (m_ints[i] != other.m_ints[i]) + { + return false; + } + } + return true; + } + + public override int GetHashCode() + { + int usedLen = GetUsedLength(); + int hash = 1; + for (int i = 0; i < usedLen; i++) + { + long mi = m_ints[i]; + hash *= 31; + hash ^= (int)mi; + hash *= 31; + hash ^= (int)((ulong)mi >> 32); + } + return hash; + } + + public LongArray Copy() + { + return new LongArray(Arrays.Clone(m_ints)); + } + + public override string ToString() + { + int i = GetUsedLength(); + if (i == 0) + { + return "0"; + } + + StringBuilder sb = new StringBuilder(Convert.ToString(m_ints[--i], 2)); + while (--i >= 0) + { + string s = Convert.ToString(m_ints[i], 2); + + // Add leading zeroes, except for highest significant word + int len = s.Length; + if (len < 64) + { + sb.Append(ZEROES.Substring(len)); + } + + sb.Append(s); + } + return sb.ToString(); + } + } +} |