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156 lines
2.8 KiB
156 lines
2.8 KiB
package bn256
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// For details of the algorithms used, see "Multiplication and Squaring on
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// Pairing-Friendly Fields, Devegili et al.
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// http://eprint.iacr.org/2006/471.pdf.
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// gfP2 implements a field of size p² as a quadratic extension of the base field
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// where i²=-1.
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type gfP2 struct {
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x, y gfP // value is xi+y.
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}
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func gfP2Decode(in *gfP2) *gfP2 {
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out := &gfP2{}
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montDecode(&out.x, &in.x)
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montDecode(&out.y, &in.y)
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return out
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}
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func (e *gfP2) String() string {
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return "(" + e.x.String() + ", " + e.y.String() + ")"
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}
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func (e *gfP2) Set(a *gfP2) *gfP2 {
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e.x.Set(&a.x)
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e.y.Set(&a.y)
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return e
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}
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func (e *gfP2) SetZero() *gfP2 {
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e.x = gfP{0}
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e.y = gfP{0}
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return e
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}
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func (e *gfP2) SetOne() *gfP2 {
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e.x = gfP{0}
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e.y = *newGFp(1)
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return e
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}
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func (e *gfP2) IsZero() bool {
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zero := gfP{0}
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return e.x == zero && e.y == zero
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}
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func (e *gfP2) IsOne() bool {
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zero, one := gfP{0}, *newGFp(1)
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return e.x == zero && e.y == one
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}
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func (e *gfP2) Conjugate(a *gfP2) *gfP2 {
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e.y.Set(&a.y)
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gfpNeg(&e.x, &a.x)
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return e
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}
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func (e *gfP2) Neg(a *gfP2) *gfP2 {
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gfpNeg(&e.x, &a.x)
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gfpNeg(&e.y, &a.y)
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return e
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}
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func (e *gfP2) Add(a, b *gfP2) *gfP2 {
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gfpAdd(&e.x, &a.x, &b.x)
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gfpAdd(&e.y, &a.y, &b.y)
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return e
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}
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func (e *gfP2) Sub(a, b *gfP2) *gfP2 {
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gfpSub(&e.x, &a.x, &b.x)
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gfpSub(&e.y, &a.y, &b.y)
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return e
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}
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// See "Multiplication and Squaring in Pairing-Friendly Fields",
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// http://eprint.iacr.org/2006/471.pdf
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func (e *gfP2) Mul(a, b *gfP2) *gfP2 {
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tx, t := &gfP{}, &gfP{}
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gfpMul(tx, &a.x, &b.y)
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gfpMul(t, &b.x, &a.y)
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gfpAdd(tx, tx, t)
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ty := &gfP{}
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gfpMul(ty, &a.y, &b.y)
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gfpMul(t, &a.x, &b.x)
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gfpSub(ty, ty, t)
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e.x.Set(tx)
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e.y.Set(ty)
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return e
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}
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func (e *gfP2) MulScalar(a *gfP2, b *gfP) *gfP2 {
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gfpMul(&e.x, &a.x, b)
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gfpMul(&e.y, &a.y, b)
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return e
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}
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// MulXi sets e=ξa where ξ=i+9 and then returns e.
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func (e *gfP2) MulXi(a *gfP2) *gfP2 {
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// (xi+y)(i+9) = (9x+y)i+(9y-x)
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tx := &gfP{}
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gfpAdd(tx, &a.x, &a.x)
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gfpAdd(tx, tx, tx)
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gfpAdd(tx, tx, tx)
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gfpAdd(tx, tx, &a.x)
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gfpAdd(tx, tx, &a.y)
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ty := &gfP{}
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gfpAdd(ty, &a.y, &a.y)
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gfpAdd(ty, ty, ty)
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gfpAdd(ty, ty, ty)
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gfpAdd(ty, ty, &a.y)
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gfpSub(ty, ty, &a.x)
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e.x.Set(tx)
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e.y.Set(ty)
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return e
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}
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func (e *gfP2) Square(a *gfP2) *gfP2 {
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// Complex squaring algorithm:
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// (xi+y)² = (x+y)(y-x) + 2*i*x*y
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tx, ty := &gfP{}, &gfP{}
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gfpSub(tx, &a.y, &a.x)
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gfpAdd(ty, &a.x, &a.y)
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gfpMul(ty, tx, ty)
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gfpMul(tx, &a.x, &a.y)
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gfpAdd(tx, tx, tx)
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e.x.Set(tx)
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e.y.Set(ty)
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return e
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}
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func (e *gfP2) Invert(a *gfP2) *gfP2 {
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// See "Implementing cryptographic pairings", M. Scott, section 3.2.
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// ftp://136.206.11.249/pub/crypto/pairings.pdf
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t1, t2 := &gfP{}, &gfP{}
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gfpMul(t1, &a.x, &a.x)
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gfpMul(t2, &a.y, &a.y)
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gfpAdd(t1, t1, t2)
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inv := &gfP{}
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inv.Invert(t1)
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gfpNeg(t1, &a.x)
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gfpMul(&e.x, t1, inv)
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gfpMul(&e.y, &a.y, inv)
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return e
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}
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