From 38ee83e45b4de7edf89bf9f0ef629eb4c6ad0fa8 Mon Sep 17 00:00:00 2001 From: Christopher Speller Date: Thu, 12 May 2016 23:56:07 -0400 Subject: Moving to glide --- vendor/golang.org/x/crypto/bn256/curve.go | 278 ++++++++++++++++++++++++++++++ 1 file changed, 278 insertions(+) create mode 100644 vendor/golang.org/x/crypto/bn256/curve.go (limited to 'vendor/golang.org/x/crypto/bn256/curve.go') diff --git a/vendor/golang.org/x/crypto/bn256/curve.go b/vendor/golang.org/x/crypto/bn256/curve.go new file mode 100644 index 000000000..55b7063f1 --- /dev/null +++ b/vendor/golang.org/x/crypto/bn256/curve.go @@ -0,0 +1,278 @@ +// Copyright 2012 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package bn256 + +import ( + "math/big" +) + +// curvePoint implements the elliptic curve y²=x³+3. Points are kept in +// Jacobian form and t=z² when valid. G₁ is the set of points of this curve on +// GF(p). +type curvePoint struct { + x, y, z, t *big.Int +} + +var curveB = new(big.Int).SetInt64(3) + +// curveGen is the generator of G₁. +var curveGen = &curvePoint{ + new(big.Int).SetInt64(1), + new(big.Int).SetInt64(-2), + new(big.Int).SetInt64(1), + new(big.Int).SetInt64(1), +} + +func newCurvePoint(pool *bnPool) *curvePoint { + return &curvePoint{ + pool.Get(), + pool.Get(), + pool.Get(), + pool.Get(), + } +} + +func (c *curvePoint) String() string { + c.MakeAffine(new(bnPool)) + return "(" + c.x.String() + ", " + c.y.String() + ")" +} + +func (c *curvePoint) Put(pool *bnPool) { + pool.Put(c.x) + pool.Put(c.y) + pool.Put(c.z) + pool.Put(c.t) +} + +func (c *curvePoint) Set(a *curvePoint) { + c.x.Set(a.x) + c.y.Set(a.y) + c.z.Set(a.z) + c.t.Set(a.t) +} + +// IsOnCurve returns true iff c is on the curve where c must be in affine form. +func (c *curvePoint) IsOnCurve() bool { + yy := new(big.Int).Mul(c.y, c.y) + xxx := new(big.Int).Mul(c.x, c.x) + xxx.Mul(xxx, c.x) + yy.Sub(yy, xxx) + yy.Sub(yy, curveB) + if yy.Sign() < 0 || yy.Cmp(p) >= 0 { + yy.Mod(yy, p) + } + return yy.Sign() == 0 +} + +func (c *curvePoint) SetInfinity() { + c.z.SetInt64(0) +} + +func (c *curvePoint) IsInfinity() bool { + return c.z.Sign() == 0 +} + +func (c *curvePoint) Add(a, b *curvePoint, pool *bnPool) { + if a.IsInfinity() { + c.Set(b) + return + } + if b.IsInfinity() { + c.Set(a) + return + } + + // See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/addition/add-2007-bl.op3 + + // Normalize the points by replacing a = [x1:y1:z1] and b = [x2:y2:z2] + // by [u1:s1:z1·z2] and [u2:s2:z1·z2] + // where u1 = x1·z2², s1 = y1·z2³ and u1 = x2·z1², s2 = y2·z1³ + z1z1 := pool.Get().Mul(a.z, a.z) + z1z1.Mod(z1z1, p) + z2z2 := pool.Get().Mul(b.z, b.z) + z2z2.Mod(z2z2, p) + u1 := pool.Get().Mul(a.x, z2z2) + u1.Mod(u1, p) + u2 := pool.Get().Mul(b.x, z1z1) + u2.Mod(u2, p) + + t := pool.Get().Mul(b.z, z2z2) + t.Mod(t, p) + s1 := pool.Get().Mul(a.y, t) + s1.Mod(s1, p) + + t.Mul(a.z, z1z1) + t.Mod(t, p) + s2 := pool.Get().Mul(b.y, t) + s2.Mod(s2, p) + + // Compute x = (2h)²(s²-u1-u2) + // where s = (s2-s1)/(u2-u1) is the slope of the line through + // (u1,s1) and (u2,s2). The extra factor 2h = 2(u2-u1) comes from the value of z below. + // This is also: + // 4(s2-s1)² - 4h²(u1+u2) = 4(s2-s1)² - 4h³ - 4h²(2u1) + // = r² - j - 2v + // with the notations below. + h := pool.Get().Sub(u2, u1) + xEqual := h.Sign() == 0 + + t.Add(h, h) + // i = 4h² + i := pool.Get().Mul(t, t) + i.Mod(i, p) + // j = 4h³ + j := pool.Get().Mul(h, i) + j.Mod(j, p) + + t.Sub(s2, s1) + yEqual := t.Sign() == 0 + if xEqual && yEqual { + c.Double(a, pool) + return + } + r := pool.Get().Add(t, t) + + v := pool.Get().Mul(u1, i) + v.Mod(v, p) + + // t4 = 4(s2-s1)² + t4 := pool.Get().Mul(r, r) + t4.Mod(t4, p) + t.Add(v, v) + t6 := pool.Get().Sub(t4, j) + c.x.Sub(t6, t) + + // Set y = -(2h)³(s1 + s*(x/4h²-u1)) + // This is also + // y = - 2·s1·j - (s2-s1)(2x - 2i·u1) = r(v-x) - 2·s1·j + t.Sub(v, c.x) // t7 + t4.Mul(s1, j) // t8 + t4.Mod(t4, p) + t6.Add(t4, t4) // t9 + t4.Mul(r, t) // t10 + t4.Mod(t4, p) + c.y.Sub(t4, t6) + + // Set z = 2(u2-u1)·z1·z2 = 2h·z1·z2 + t.Add(a.z, b.z) // t11 + t4.Mul(t, t) // t12 + t4.Mod(t4, p) + t.Sub(t4, z1z1) // t13 + t4.Sub(t, z2z2) // t14 + c.z.Mul(t4, h) + c.z.Mod(c.z, p) + + pool.Put(z1z1) + pool.Put(z2z2) + pool.Put(u1) + pool.Put(u2) + pool.Put(t) + pool.Put(s1) + pool.Put(s2) + pool.Put(h) + pool.Put(i) + pool.Put(j) + pool.Put(r) + pool.Put(v) + pool.Put(t4) + pool.Put(t6) +} + +func (c *curvePoint) Double(a *curvePoint, pool *bnPool) { + // See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3 + A := pool.Get().Mul(a.x, a.x) + A.Mod(A, p) + B := pool.Get().Mul(a.y, a.y) + B.Mod(B, p) + C := pool.Get().Mul(B, B) + C.Mod(C, p) + + t := pool.Get().Add(a.x, B) + t2 := pool.Get().Mul(t, t) + t2.Mod(t2, p) + t.Sub(t2, A) + t2.Sub(t, C) + d := pool.Get().Add(t2, t2) + t.Add(A, A) + e := pool.Get().Add(t, A) + f := pool.Get().Mul(e, e) + f.Mod(f, p) + + t.Add(d, d) + c.x.Sub(f, t) + + t.Add(C, C) + t2.Add(t, t) + t.Add(t2, t2) + c.y.Sub(d, c.x) + t2.Mul(e, c.y) + t2.Mod(t2, p) + c.y.Sub(t2, t) + + t.Mul(a.y, a.z) + t.Mod(t, p) + c.z.Add(t, t) + + pool.Put(A) + pool.Put(B) + pool.Put(C) + pool.Put(t) + pool.Put(t2) + pool.Put(d) + pool.Put(e) + pool.Put(f) +} + +func (c *curvePoint) Mul(a *curvePoint, scalar *big.Int, pool *bnPool) *curvePoint { + sum := newCurvePoint(pool) + sum.SetInfinity() + t := newCurvePoint(pool) + + for i := scalar.BitLen(); i >= 0; i-- { + t.Double(sum, pool) + if scalar.Bit(i) != 0 { + sum.Add(t, a, pool) + } else { + sum.Set(t) + } + } + + c.Set(sum) + sum.Put(pool) + t.Put(pool) + return c +} + +func (c *curvePoint) MakeAffine(pool *bnPool) *curvePoint { + if words := c.z.Bits(); len(words) == 1 && words[0] == 1 { + return c + } + + zInv := pool.Get().ModInverse(c.z, p) + t := pool.Get().Mul(c.y, zInv) + t.Mod(t, p) + zInv2 := pool.Get().Mul(zInv, zInv) + zInv2.Mod(zInv2, p) + c.y.Mul(t, zInv2) + c.y.Mod(c.y, p) + t.Mul(c.x, zInv2) + t.Mod(t, p) + c.x.Set(t) + c.z.SetInt64(1) + c.t.SetInt64(1) + + pool.Put(zInv) + pool.Put(t) + pool.Put(zInv2) + + return c +} + +func (c *curvePoint) Negative(a *curvePoint) { + c.x.Set(a.x) + c.y.Neg(a.y) + c.z.Set(a.z) + c.t.SetInt64(0) +} -- cgit v1.2.3-1-g7c22