diff options
Diffstat (limited to 'vendor/github.com/miekg/dns/vendor/golang.org/x/crypto/bn256/gfp6.go')
| -rw-r--r-- | vendor/github.com/miekg/dns/vendor/golang.org/x/crypto/bn256/gfp6.go | 296 |
1 files changed, 0 insertions, 296 deletions
diff --git a/vendor/github.com/miekg/dns/vendor/golang.org/x/crypto/bn256/gfp6.go b/vendor/github.com/miekg/dns/vendor/golang.org/x/crypto/bn256/gfp6.go deleted file mode 100644 index f98ae782c..000000000 --- a/vendor/github.com/miekg/dns/vendor/golang.org/x/crypto/bn256/gfp6.go +++ /dev/null @@ -1,296 +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 - -// For details of the algorithms used, see "Multiplication and Squaring on -// Pairing-Friendly Fields, Devegili et al. -// http://eprint.iacr.org/2006/471.pdf. - -import ( - "math/big" -) - -// gfP6 implements the field of size p⁶ as a cubic extension of gfP2 where τ³=ξ -// and ξ=i+3. -type gfP6 struct { - x, y, z *gfP2 // value is xτ² + yτ + z -} - -func newGFp6(pool *bnPool) *gfP6 { - return &gfP6{newGFp2(pool), newGFp2(pool), newGFp2(pool)} -} - -func (e *gfP6) String() string { - return "(" + e.x.String() + "," + e.y.String() + "," + e.z.String() + ")" -} - -func (e *gfP6) Put(pool *bnPool) { - e.x.Put(pool) - e.y.Put(pool) - e.z.Put(pool) -} - -func (e *gfP6) Set(a *gfP6) *gfP6 { - e.x.Set(a.x) - e.y.Set(a.y) - e.z.Set(a.z) - return e -} - -func (e *gfP6) SetZero() *gfP6 { - e.x.SetZero() - e.y.SetZero() - e.z.SetZero() - return e -} - -func (e *gfP6) SetOne() *gfP6 { - e.x.SetZero() - e.y.SetZero() - e.z.SetOne() - return e -} - -func (e *gfP6) Minimal() { - e.x.Minimal() - e.y.Minimal() - e.z.Minimal() -} - -func (e *gfP6) IsZero() bool { - return e.x.IsZero() && e.y.IsZero() && e.z.IsZero() -} - -func (e *gfP6) IsOne() bool { - return e.x.IsZero() && e.y.IsZero() && e.z.IsOne() -} - -func (e *gfP6) Negative(a *gfP6) *gfP6 { - e.x.Negative(a.x) - e.y.Negative(a.y) - e.z.Negative(a.z) - return e -} - -func (e *gfP6) Frobenius(a *gfP6, pool *bnPool) *gfP6 { - e.x.Conjugate(a.x) - e.y.Conjugate(a.y) - e.z.Conjugate(a.z) - - e.x.Mul(e.x, xiTo2PMinus2Over3, pool) - e.y.Mul(e.y, xiToPMinus1Over3, pool) - return e -} - -// FrobeniusP2 computes (xτ²+yτ+z)^(p²) = xτ^(2p²) + yτ^(p²) + z -func (e *gfP6) FrobeniusP2(a *gfP6) *gfP6 { - // τ^(2p²) = τ²τ^(2p²-2) = τ²ξ^((2p²-2)/3) - e.x.MulScalar(a.x, xiTo2PSquaredMinus2Over3) - // τ^(p²) = ττ^(p²-1) = τξ^((p²-1)/3) - e.y.MulScalar(a.y, xiToPSquaredMinus1Over3) - e.z.Set(a.z) - return e -} - -func (e *gfP6) Add(a, b *gfP6) *gfP6 { - e.x.Add(a.x, b.x) - e.y.Add(a.y, b.y) - e.z.Add(a.z, b.z) - return e -} - -func (e *gfP6) Sub(a, b *gfP6) *gfP6 { - e.x.Sub(a.x, b.x) - e.y.Sub(a.y, b.y) - e.z.Sub(a.z, b.z) - return e -} - -func (e *gfP6) Double(a *gfP6) *gfP6 { - e.x.Double(a.x) - e.y.Double(a.y) - e.z.Double(a.z) - return e -} - -func (e *gfP6) Mul(a, b *gfP6, pool *bnPool) *gfP6 { - // "Multiplication and Squaring on Pairing-Friendly Fields" - // Section 4, Karatsuba method. - // http://eprint.iacr.org/2006/471.pdf - - v0 := newGFp2(pool) - v0.Mul(a.z, b.z, pool) - v1 := newGFp2(pool) - v1.Mul(a.y, b.y, pool) - v2 := newGFp2(pool) - v2.Mul(a.x, b.x, pool) - - t0 := newGFp2(pool) - t0.Add(a.x, a.y) - t1 := newGFp2(pool) - t1.Add(b.x, b.y) - tz := newGFp2(pool) - tz.Mul(t0, t1, pool) - - tz.Sub(tz, v1) - tz.Sub(tz, v2) - tz.MulXi(tz, pool) - tz.Add(tz, v0) - - t0.Add(a.y, a.z) - t1.Add(b.y, b.z) - ty := newGFp2(pool) - ty.Mul(t0, t1, pool) - ty.Sub(ty, v0) - ty.Sub(ty, v1) - t0.MulXi(v2, pool) - ty.Add(ty, t0) - - t0.Add(a.x, a.z) - t1.Add(b.x, b.z) - tx := newGFp2(pool) - tx.Mul(t0, t1, pool) - tx.Sub(tx, v0) - tx.Add(tx, v1) - tx.Sub(tx, v2) - - e.x.Set(tx) - e.y.Set(ty) - e.z.Set(tz) - - t0.Put(pool) - t1.Put(pool) - tx.Put(pool) - ty.Put(pool) - tz.Put(pool) - v0.Put(pool) - v1.Put(pool) - v2.Put(pool) - return e -} - -func (e *gfP6) MulScalar(a *gfP6, b *gfP2, pool *bnPool) *gfP6 { - e.x.Mul(a.x, b, pool) - e.y.Mul(a.y, b, pool) - e.z.Mul(a.z, b, pool) - return e -} - -func (e *gfP6) MulGFP(a *gfP6, b *big.Int) *gfP6 { - e.x.MulScalar(a.x, b) - e.y.MulScalar(a.y, b) - e.z.MulScalar(a.z, b) - return e -} - -// MulTau computes τ·(aτ²+bτ+c) = bτ²+cτ+aξ -func (e *gfP6) MulTau(a *gfP6, pool *bnPool) { - tz := newGFp2(pool) - tz.MulXi(a.x, pool) - ty := newGFp2(pool) - ty.Set(a.y) - e.y.Set(a.z) - e.x.Set(ty) - e.z.Set(tz) - tz.Put(pool) - ty.Put(pool) -} - -func (e *gfP6) Square(a *gfP6, pool *bnPool) *gfP6 { - v0 := newGFp2(pool).Square(a.z, pool) - v1 := newGFp2(pool).Square(a.y, pool) - v2 := newGFp2(pool).Square(a.x, pool) - - c0 := newGFp2(pool).Add(a.x, a.y) - c0.Square(c0, pool) - c0.Sub(c0, v1) - c0.Sub(c0, v2) - c0.MulXi(c0, pool) - c0.Add(c0, v0) - - c1 := newGFp2(pool).Add(a.y, a.z) - c1.Square(c1, pool) - c1.Sub(c1, v0) - c1.Sub(c1, v1) - xiV2 := newGFp2(pool).MulXi(v2, pool) - c1.Add(c1, xiV2) - - c2 := newGFp2(pool).Add(a.x, a.z) - c2.Square(c2, pool) - c2.Sub(c2, v0) - c2.Add(c2, v1) - c2.Sub(c2, v2) - - e.x.Set(c2) - e.y.Set(c1) - e.z.Set(c0) - - v0.Put(pool) - v1.Put(pool) - v2.Put(pool) - c0.Put(pool) - c1.Put(pool) - c2.Put(pool) - xiV2.Put(pool) - - return e -} - -func (e *gfP6) Invert(a *gfP6, pool *bnPool) *gfP6 { - // See "Implementing cryptographic pairings", M. Scott, section 3.2. - // ftp://136.206.11.249/pub/crypto/pairings.pdf - - // Here we can give a short explanation of how it works: let j be a cubic root of - // unity in GF(p²) so that 1+j+j²=0. - // Then (xτ² + yτ + z)(xj²τ² + yjτ + z)(xjτ² + yj²τ + z) - // = (xτ² + yτ + z)(Cτ²+Bτ+A) - // = (x³ξ²+y³ξ+z³-3ξxyz) = F is an element of the base field (the norm). - // - // On the other hand (xj²τ² + yjτ + z)(xjτ² + yj²τ + z) - // = τ²(y²-ξxz) + τ(ξx²-yz) + (z²-ξxy) - // - // So that's why A = (z²-ξxy), B = (ξx²-yz), C = (y²-ξxz) - t1 := newGFp2(pool) - - A := newGFp2(pool) - A.Square(a.z, pool) - t1.Mul(a.x, a.y, pool) - t1.MulXi(t1, pool) - A.Sub(A, t1) - - B := newGFp2(pool) - B.Square(a.x, pool) - B.MulXi(B, pool) - t1.Mul(a.y, a.z, pool) - B.Sub(B, t1) - - C := newGFp2(pool) - C.Square(a.y, pool) - t1.Mul(a.x, a.z, pool) - C.Sub(C, t1) - - F := newGFp2(pool) - F.Mul(C, a.y, pool) - F.MulXi(F, pool) - t1.Mul(A, a.z, pool) - F.Add(F, t1) - t1.Mul(B, a.x, pool) - t1.MulXi(t1, pool) - F.Add(F, t1) - - F.Invert(F, pool) - - e.x.Mul(C, F, pool) - e.y.Mul(B, F, pool) - e.z.Mul(A, F, pool) - - t1.Put(pool) - A.Put(pool) - B.Put(pool) - C.Put(pool) - F.Put(pool) - - return e -} |