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Diffstat (limited to 'vendor/golang.org/x/crypto/bn256/twist.go')
-rw-r--r--vendor/golang.org/x/crypto/bn256/twist.go258
1 files changed, 0 insertions, 258 deletions
diff --git a/vendor/golang.org/x/crypto/bn256/twist.go b/vendor/golang.org/x/crypto/bn256/twist.go
deleted file mode 100644
index 056d80f..0000000
--- a/vendor/golang.org/x/crypto/bn256/twist.go
+++ /dev/null
@@ -1,258 +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"
-)
-
-// twistPoint implements the elliptic curve y²=x³+3/ξ over GF(p²). Points are
-// kept in Jacobian form and t=z² when valid. The group G₂ is the set of
-// n-torsion points of this curve over GF(p²) (where n = Order)
-type twistPoint struct {
- x, y, z, t *gfP2
-}
-
-var twistB = &gfP2{
- bigFromBase10("6500054969564660373279643874235990574282535810762300357187714502686418407178"),
- bigFromBase10("45500384786952622612957507119651934019977750675336102500314001518804928850249"),
-}
-
-// twistGen is the generator of group G₂.
-var twistGen = &twistPoint{
- &gfP2{
- bigFromBase10("21167961636542580255011770066570541300993051739349375019639421053990175267184"),
- bigFromBase10("64746500191241794695844075326670126197795977525365406531717464316923369116492"),
- },
- &gfP2{
- bigFromBase10("20666913350058776956210519119118544732556678129809273996262322366050359951122"),
- bigFromBase10("17778617556404439934652658462602675281523610326338642107814333856843981424549"),
- },
- &gfP2{
- bigFromBase10("0"),
- bigFromBase10("1"),
- },
- &gfP2{
- bigFromBase10("0"),
- bigFromBase10("1"),
- },
-}
-
-func newTwistPoint(pool *bnPool) *twistPoint {
- return &twistPoint{
- newGFp2(pool),
- newGFp2(pool),
- newGFp2(pool),
- newGFp2(pool),
- }
-}
-
-func (c *twistPoint) String() string {
- return "(" + c.x.String() + ", " + c.y.String() + ", " + c.z.String() + ")"
-}
-
-func (c *twistPoint) Put(pool *bnPool) {
- c.x.Put(pool)
- c.y.Put(pool)
- c.z.Put(pool)
- c.t.Put(pool)
-}
-
-func (c *twistPoint) Set(a *twistPoint) {
- 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 *twistPoint) IsOnCurve() bool {
- pool := new(bnPool)
- yy := newGFp2(pool).Square(c.y, pool)
- xxx := newGFp2(pool).Square(c.x, pool)
- xxx.Mul(xxx, c.x, pool)
- yy.Sub(yy, xxx)
- yy.Sub(yy, twistB)
- yy.Minimal()
- return yy.x.Sign() == 0 && yy.y.Sign() == 0
-}
-
-func (c *twistPoint) SetInfinity() {
- c.z.SetZero()
-}
-
-func (c *twistPoint) IsInfinity() bool {
- return c.z.IsZero()
-}
-
-func (c *twistPoint) Add(a, b *twistPoint, pool *bnPool) {
- // For additional comments, see the same function in curve.go.
-
- 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
- z1z1 := newGFp2(pool).Square(a.z, pool)
- z2z2 := newGFp2(pool).Square(b.z, pool)
- u1 := newGFp2(pool).Mul(a.x, z2z2, pool)
- u2 := newGFp2(pool).Mul(b.x, z1z1, pool)
-
- t := newGFp2(pool).Mul(b.z, z2z2, pool)
- s1 := newGFp2(pool).Mul(a.y, t, pool)
-
- t.Mul(a.z, z1z1, pool)
- s2 := newGFp2(pool).Mul(b.y, t, pool)
-
- h := newGFp2(pool).Sub(u2, u1)
- xEqual := h.IsZero()
-
- t.Add(h, h)
- i := newGFp2(pool).Square(t, pool)
- j := newGFp2(pool).Mul(h, i, pool)
-
- t.Sub(s2, s1)
- yEqual := t.IsZero()
- if xEqual && yEqual {
- c.Double(a, pool)
- return
- }
- r := newGFp2(pool).Add(t, t)
-
- v := newGFp2(pool).Mul(u1, i, pool)
-
- t4 := newGFp2(pool).Square(r, pool)
- t.Add(v, v)
- t6 := newGFp2(pool).Sub(t4, j)
- c.x.Sub(t6, t)
-
- t.Sub(v, c.x) // t7
- t4.Mul(s1, j, pool) // t8
- t6.Add(t4, t4) // t9
- t4.Mul(r, t, pool) // t10
- c.y.Sub(t4, t6)
-
- t.Add(a.z, b.z) // t11
- t4.Square(t, pool) // t12
- t.Sub(t4, z1z1) // t13
- t4.Sub(t, z2z2) // t14
- c.z.Mul(t4, h, pool)
-
- z1z1.Put(pool)
- z2z2.Put(pool)
- u1.Put(pool)
- u2.Put(pool)
- t.Put(pool)
- s1.Put(pool)
- s2.Put(pool)
- h.Put(pool)
- i.Put(pool)
- j.Put(pool)
- r.Put(pool)
- v.Put(pool)
- t4.Put(pool)
- t6.Put(pool)
-}
-
-func (c *twistPoint) Double(a *twistPoint, pool *bnPool) {
- // See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3
- A := newGFp2(pool).Square(a.x, pool)
- B := newGFp2(pool).Square(a.y, pool)
- C := newGFp2(pool).Square(B, pool)
-
- t := newGFp2(pool).Add(a.x, B)
- t2 := newGFp2(pool).Square(t, pool)
- t.Sub(t2, A)
- t2.Sub(t, C)
- d := newGFp2(pool).Add(t2, t2)
- t.Add(A, A)
- e := newGFp2(pool).Add(t, A)
- f := newGFp2(pool).Square(e, pool)
-
- 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, pool)
- c.y.Sub(t2, t)
-
- t.Mul(a.y, a.z, pool)
- c.z.Add(t, t)
-
- A.Put(pool)
- B.Put(pool)
- C.Put(pool)
- t.Put(pool)
- t2.Put(pool)
- d.Put(pool)
- e.Put(pool)
- f.Put(pool)
-}
-
-func (c *twistPoint) Mul(a *twistPoint, scalar *big.Int, pool *bnPool) *twistPoint {
- sum := newTwistPoint(pool)
- sum.SetInfinity()
- t := newTwistPoint(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 *twistPoint) MakeAffine(pool *bnPool) *twistPoint {
- if c.z.IsOne() {
- return c
- }
- if c.IsInfinity() {
- c.x.SetZero()
- c.y.SetOne()
- c.z.SetZero()
- c.t.SetZero()
- return c
- }
-
- zInv := newGFp2(pool).Invert(c.z, pool)
- t := newGFp2(pool).Mul(c.y, zInv, pool)
- zInv2 := newGFp2(pool).Square(zInv, pool)
- c.y.Mul(t, zInv2, pool)
- t.Mul(c.x, zInv2, pool)
- c.x.Set(t)
- c.z.SetOne()
- c.t.SetOne()
-
- zInv.Put(pool)
- t.Put(pool)
- zInv2.Put(pool)
-
- return c
-}
-
-func (c *twistPoint) Negative(a *twistPoint, pool *bnPool) {
- c.x.Set(a.x)
- c.y.SetZero()
- c.y.Sub(c.y, a.y)
- c.z.Set(a.z)
- c.t.SetZero()
-}