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Diffstat (limited to 'vendor/golang.org/x/crypto/bn256/curve.go')
-rw-r--r--vendor/golang.org/x/crypto/bn256/curve.go287
1 files changed, 0 insertions, 287 deletions
diff --git a/vendor/golang.org/x/crypto/bn256/curve.go b/vendor/golang.org/x/crypto/bn256/curve.go
deleted file mode 100644
index 63c052b..0000000
--- a/vendor/golang.org/x/crypto/bn256/curve.go
+++ /dev/null
@@ -1,287 +0,0 @@
-// 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
-}
-
-// MakeAffine converts c to affine form and returns c. If c is ∞, then it sets
-// c to 0 : 1 : 0.
-func (c *curvePoint) MakeAffine(pool *bnPool) *curvePoint {
- if words := c.z.Bits(); len(words) == 1 && words[0] == 1 {
- return c
- }
- if c.IsInfinity() {
- c.x.SetInt64(0)
- c.y.SetInt64(1)
- c.z.SetInt64(0)
- c.t.SetInt64(0)
- 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)
-}