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Diffstat (limited to 'crypto/secp256k1/curve.go')
| -rw-r--r-- | crypto/secp256k1/curve.go | 299 |
1 files changed, 299 insertions, 0 deletions
diff --git a/crypto/secp256k1/curve.go b/crypto/secp256k1/curve.go new file mode 100644 index 000000000..59e7100c5 --- /dev/null +++ b/crypto/secp256k1/curve.go @@ -0,0 +1,299 @@ +// Copyright 2010 The Go Authors. All rights reserved. +// Copyright 2011 ThePiachu. All rights reserved. +// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved. +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above +// copyright notice, this list of conditions and the following disclaimer +// in the documentation and/or other materials provided with the +// distribution. +// * Neither the name of Google Inc. nor the names of its +// contributors may be used to endorse or promote products derived from +// this software without specific prior written permission. +// * The name of ThePiachu may not be used to endorse or promote products +// derived from this software without specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +package secp256k1 + +import ( + "crypto/elliptic" + "math/big" +) + +const ( + // number of bits in a big.Word + wordBits = 32 << (uint64(^big.Word(0)) >> 63) + // number of bytes in a big.Word + wordBytes = wordBits / 8 +) + +// readBits encodes the absolute value of bigint as big-endian bytes. Callers +// must ensure that buf has enough space. If buf is too short the result will +// be incomplete. +func readBits(bigint *big.Int, buf []byte) { + i := len(buf) + for _, d := range bigint.Bits() { + for j := 0; j < wordBytes && i > 0; j++ { + i-- + buf[i] = byte(d) + d >>= 8 + } + } +} + +// This code is from https://github.com/ThePiachu/GoBit and implements +// several Koblitz elliptic curves over prime fields. +// +// The curve methods, internally, on Jacobian coordinates. For a given +// (x, y) position on the curve, the Jacobian coordinates are (x1, y1, +// z1) where x = x1/z1² and y = y1/z1³. The greatest speedups come +// when the whole calculation can be performed within the transform +// (as in ScalarMult and ScalarBaseMult). But even for Add and Double, +// it's faster to apply and reverse the transform than to operate in +// affine coordinates. + +// A BitCurve represents a Koblitz Curve with a=0. +// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html +type BitCurve struct { + P *big.Int // the order of the underlying field + N *big.Int // the order of the base point + B *big.Int // the constant of the BitCurve equation + Gx, Gy *big.Int // (x,y) of the base point + BitSize int // the size of the underlying field +} + +// Params returns param +func (BitCurve *BitCurve) Params() *elliptic.CurveParams { + return &elliptic.CurveParams{ + P: BitCurve.P, + N: BitCurve.N, + B: BitCurve.B, + Gx: BitCurve.Gx, + Gy: BitCurve.Gy, + BitSize: BitCurve.BitSize, + } +} + +// IsOnCurve returns true if the given (x,y) lies on the BitCurve. +func (BitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool { + // y² = x³ + b + y2 := new(big.Int).Mul(y, y) //y² + y2.Mod(y2, BitCurve.P) //y²%P + + x3 := new(big.Int).Mul(x, x) //x² + x3.Mul(x3, x) //x³ + + x3.Add(x3, BitCurve.B) //x³+B + x3.Mod(x3, BitCurve.P) //(x³+B)%P + + return x3.Cmp(y2) == 0 +} + +//TODO: double check if the function is okay +// affineFromJacobian reverses the Jacobian transform. See the comment at the +// top of the file. +func (BitCurve *BitCurve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) { + if z.Sign() == 0 { + return new(big.Int), new(big.Int) + } + + zinv := new(big.Int).ModInverse(z, BitCurve.P) + zinvsq := new(big.Int).Mul(zinv, zinv) + + xOut = new(big.Int).Mul(x, zinvsq) + xOut.Mod(xOut, BitCurve.P) + zinvsq.Mul(zinvsq, zinv) + yOut = new(big.Int).Mul(y, zinvsq) + yOut.Mod(yOut, BitCurve.P) + return +} + +// Add returns the sum of (x1,y1) and (x2,y2) +func (BitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { + // If one point is at infinity, return the other point. + // Adding the point at infinity to any point will preserve the other point. + if x1.Sign() == 0 && y1.Sign() == 0 { + return x2, y2 + } + if x2.Sign() == 0 && y2.Sign() == 0 { + return x1, y1 + } + z := new(big.Int).SetInt64(1) + if x1.Cmp(x2) == 0 && y1.Cmp(y2) == 0 { + return BitCurve.affineFromJacobian(BitCurve.doubleJacobian(x1, y1, z)) + } + return BitCurve.affineFromJacobian(BitCurve.addJacobian(x1, y1, z, x2, y2, z)) +} + +// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and +// (x2, y2, z2) and returns their sum, also in Jacobian form. +func (BitCurve *BitCurve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) { + // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl + z1z1 := new(big.Int).Mul(z1, z1) + z1z1.Mod(z1z1, BitCurve.P) + z2z2 := new(big.Int).Mul(z2, z2) + z2z2.Mod(z2z2, BitCurve.P) + + u1 := new(big.Int).Mul(x1, z2z2) + u1.Mod(u1, BitCurve.P) + u2 := new(big.Int).Mul(x2, z1z1) + u2.Mod(u2, BitCurve.P) + h := new(big.Int).Sub(u2, u1) + if h.Sign() == -1 { + h.Add(h, BitCurve.P) + } + i := new(big.Int).Lsh(h, 1) + i.Mul(i, i) + j := new(big.Int).Mul(h, i) + + s1 := new(big.Int).Mul(y1, z2) + s1.Mul(s1, z2z2) + s1.Mod(s1, BitCurve.P) + s2 := new(big.Int).Mul(y2, z1) + s2.Mul(s2, z1z1) + s2.Mod(s2, BitCurve.P) + r := new(big.Int).Sub(s2, s1) + if r.Sign() == -1 { + r.Add(r, BitCurve.P) + } + r.Lsh(r, 1) + v := new(big.Int).Mul(u1, i) + + x3 := new(big.Int).Set(r) + x3.Mul(x3, x3) + x3.Sub(x3, j) + x3.Sub(x3, v) + x3.Sub(x3, v) + x3.Mod(x3, BitCurve.P) + + y3 := new(big.Int).Set(r) + v.Sub(v, x3) + y3.Mul(y3, v) + s1.Mul(s1, j) + s1.Lsh(s1, 1) + y3.Sub(y3, s1) + y3.Mod(y3, BitCurve.P) + + z3 := new(big.Int).Add(z1, z2) + z3.Mul(z3, z3) + z3.Sub(z3, z1z1) + if z3.Sign() == -1 { + z3.Add(z3, BitCurve.P) + } + z3.Sub(z3, z2z2) + if z3.Sign() == -1 { + z3.Add(z3, BitCurve.P) + } + z3.Mul(z3, h) + z3.Mod(z3, BitCurve.P) + + return x3, y3, z3 +} + +// Double returns 2*(x,y) +func (BitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { + z1 := new(big.Int).SetInt64(1) + return BitCurve.affineFromJacobian(BitCurve.doubleJacobian(x1, y1, z1)) +} + +// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and +// returns its double, also in Jacobian form. +func (BitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) { + // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l + + a := new(big.Int).Mul(x, x) //X1² + b := new(big.Int).Mul(y, y) //Y1² + c := new(big.Int).Mul(b, b) //B² + + d := new(big.Int).Add(x, b) //X1+B + d.Mul(d, d) //(X1+B)² + d.Sub(d, a) //(X1+B)²-A + d.Sub(d, c) //(X1+B)²-A-C + d.Mul(d, big.NewInt(2)) //2*((X1+B)²-A-C) + + e := new(big.Int).Mul(big.NewInt(3), a) //3*A + f := new(big.Int).Mul(e, e) //E² + + x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D + x3.Sub(f, x3) //F-2*D + x3.Mod(x3, BitCurve.P) + + y3 := new(big.Int).Sub(d, x3) //D-X3 + y3.Mul(e, y3) //E*(D-X3) + y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C + y3.Mod(y3, BitCurve.P) + + z3 := new(big.Int).Mul(y, z) //Y1*Z1 + z3.Mul(big.NewInt(2), z3) //3*Y1*Z1 + z3.Mod(z3, BitCurve.P) + + return x3, y3, z3 +} + +// ScalarBaseMult returns k*G, where G is the base point of the group and k is +// an integer in big-endian form. +func (BitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) { + return BitCurve.ScalarMult(BitCurve.Gx, BitCurve.Gy, k) +} + +// Marshal converts a point into the form specified in section 4.3.6 of ANSI +// X9.62. +func (BitCurve *BitCurve) Marshal(x, y *big.Int) []byte { + byteLen := (BitCurve.BitSize + 7) >> 3 + ret := make([]byte, 1+2*byteLen) + ret[0] = 4 // uncompressed point flag + readBits(x, ret[1:1+byteLen]) + readBits(y, ret[1+byteLen:]) + return ret +} + +// Unmarshal converts a point, serialised by Marshal, into an x, y pair. On +// error, x = nil. +func (BitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int) { + byteLen := (BitCurve.BitSize + 7) >> 3 + if len(data) != 1+2*byteLen { + return + } + if data[0] != 4 { // uncompressed form + return + } + x = new(big.Int).SetBytes(data[1 : 1+byteLen]) + y = new(big.Int).SetBytes(data[1+byteLen:]) + return +} + +var theCurve = new(BitCurve) + +func init() { + // See SEC 2 section 2.7.1 + // curve parameters taken from: + // http://www.secg.org/sec2-v2.pdf + theCurve.P, _ = new(big.Int).SetString("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 0) + theCurve.N, _ = new(big.Int).SetString("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 0) + theCurve.B, _ = new(big.Int).SetString("0x0000000000000000000000000000000000000000000000000000000000000007", 0) + theCurve.Gx, _ = new(big.Int).SetString("0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 0) + theCurve.Gy, _ = new(big.Int).SetString("0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 0) + theCurve.BitSize = 256 +} + +// S256 returns a BitCurve which implements secp256k1. +func S256() *BitCurve { + return theCurve +} |