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author | Peter Dettman <peter.dettman@bouncycastle.org> | 2014-01-30 15:15:14 +0700 |
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committer | Peter Dettman <peter.dettman@bouncycastle.org> | 2014-01-30 15:15:14 +0700 |
commit | d9501d9ea10c353e267142b94507e7a065ca75f7 (patch) | |
tree | 33c49d11ac65db2b78d3313c5e30a69f1f1bb160 /crypto/src/math/ec/custom | |
parent | Add SquareN to perform repeated modular squaring (diff) | |
download | BouncyCastle.NET-ed25519-d9501d9ea10c353e267142b94507e7a065ca75f7.tar.xz |
Take advantage of special prime modulus to optimize sqrt
Diffstat (limited to 'crypto/src/math/ec/custom')
-rw-r--r-- | crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs | 73 | ||||
-rw-r--r-- | crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs | 38 |
2 files changed, 107 insertions, 4 deletions
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs index 11cf6ff6a..a5481c925 100644 --- a/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs +++ b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs @@ -126,8 +126,77 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec */ public override ECFieldElement Sqrt() { - ECFieldElement root = new FpFieldElement(Q, ToBigInteger()).Sqrt(); - return root == null ? null : new SecP256K1FieldElement(root.ToBigInteger()); + /* + * Raise this element to the exponent 2^254 - 2^30 - 2^7 - 2^6 - 2^5 - 2^4 - 2^2 + * + * Breaking up the exponent's binary representation into "repunits", we get: + * { 223 1s } { 1 0s } { 22 1s } { 4 0s } { 2 1s } { 2 0s} + * + * Therefore we need an addition chain containing 2, 22, 223 (the lengths of the repunits) + * We use: 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223] + */ + + uint[] x1 = this.x; + if (Nat256.IsZero(x1) || Nat256.IsOne(x1)) + { + return this; + } + + uint[] x2 = Nat256.Create(); + SecP256K1Field.Square(x1, x2); + SecP256K1Field.Multiply(x2, x1, x2); + + uint[] x3 = Nat256.Create(); + SecP256K1Field.Square(x2, x3); + SecP256K1Field.Multiply(x3, x1, x3); + + uint[] x6 = Nat256.Create(); + SecP256K1Field.SquareN(x3, 3, x6); + SecP256K1Field.Multiply(x6, x3, x6); + + uint[] x9 = x6; + SecP256K1Field.SquareN(x6, 3, x9); + SecP256K1Field.Multiply(x9, x3, x9); + + uint[] x11 = x9; + SecP256K1Field.SquareN(x9, 2, x11); + SecP256K1Field.Multiply(x11, x2, x11); + + uint[] x22 = Nat256.Create(); + SecP256K1Field.SquareN(x11, 11, x22); + SecP256K1Field.Multiply(x22, x11, x22); + + uint[] x44 = x11; + SecP256K1Field.SquareN(x22, 22, x44); + SecP256K1Field.Multiply(x44, x22, x44); + + uint[] x88 = Nat256.Create(); + SecP256K1Field.SquareN(x44, 44, x88); + SecP256K1Field.Multiply(x88, x44, x88); + + uint[] x176 = Nat256.Create(); + SecP256K1Field.SquareN(x88, 88, x176); + SecP256K1Field.Multiply(x176, x88, x176); + + uint[] x220 = x88; + SecP256K1Field.SquareN(x176, 44, x220); + SecP256K1Field.Multiply(x220, x44, x220); + + uint[] x223 = x44; + SecP256K1Field.SquareN(x220, 3, x223); + SecP256K1Field.Multiply(x223, x3, x223); + + uint[] t1 = x223; + SecP256K1Field.SquareN(t1, 23, t1); + SecP256K1Field.Multiply(t1, x22, t1); + SecP256K1Field.SquareN(t1, 6, t1); + SecP256K1Field.Multiply(t1, x2, t1); + SecP256K1Field.SquareN(t1, 2, t1); + + uint[] t2 = x2; + SecP256K1Field.Square(t1, t2); + + return Arrays.AreEqual(x1, t2) ? new SecP256K1FieldElement(t1) : null; } public override bool Equals(object obj) diff --git a/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs index a4a7004c0..650f12aaf 100644 --- a/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs +++ b/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs @@ -126,8 +126,42 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec */ public override ECFieldElement Sqrt() { - ECFieldElement root = new FpFieldElement(Q, ToBigInteger()).Sqrt(); - return root == null ? null : new SecP256R1FieldElement(root.ToBigInteger()); + // Raise this element to the exponent 2^254 - 2^222 + 2^190 + 2^94 + + uint[] x1 = this.x; + if (Nat256.IsZero(x1) || Nat256.IsOne(x1)) + { + return this; + } + + uint[] t1 = Nat256.Create(); + uint[] t2 = Nat256.Create(); + + SecP256R1Field.Square(x1, t1); + SecP256R1Field.Multiply(t1, x1, t1); + + SecP256R1Field.SquareN(t1, 2, t2); + SecP256R1Field.Multiply(t2, t1, t2); + + SecP256R1Field.SquareN(t2, 4, t1); + SecP256R1Field.Multiply(t1, t2, t1); + + SecP256R1Field.SquareN(t1, 8, t2); + SecP256R1Field.Multiply(t2, t1, t2); + + SecP256R1Field.SquareN(t2, 16, t1); + SecP256R1Field.Multiply(t1, t2, t1); + + SecP256R1Field.SquareN(t1, 32, t1); + SecP256R1Field.Multiply(t1, x1, t1); + + SecP256R1Field.SquareN(t1, 96, t1); + SecP256R1Field.Multiply(t1, x1, t1); + + SecP256R1Field.SquareN(t1, 94, t1); + SecP256R1Field.Multiply(t1, t1, t2); + + return Arrays.AreEqual(x1, t2) ? new SecP256R1FieldElement(t1) : null; } public override bool Equals(object obj) |