/
g2Isog.go
170 lines (156 loc) · 6.53 KB
/
g2Isog.go
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package bls12381
import (
"fmt"
"github.com/cloudflare/circl/ecc/bls12381/ff"
)
type isogG2Point struct{ x, y, z ff.Fp2 }
func (p isogG2Point) String() string { return fmt.Sprintf("x: %v\ny: %v\nz: %v", p.x, p.y, p.z) }
// IsOnCurve returns true if g is a valid point on the curve.
func (p *isogG2Point) IsOnCurve() bool {
var x2, x3, z2, z3, y2 ff.Fp2
y2.Sqr(&p.y) // y2 = y^2
y2.Mul(&y2, &p.z) // y2 = y^2*z
z2.Sqr(&p.z) // z2 = z^2
z3.Mul(&z2, &p.z) // z3 = z^3
z3.Mul(&z3, &g2Isog3.b) // z3 = B*z^3
x2.Sqr(&p.x) // x2 = x^2
x3.Mul(&z2, &g2Isog3.a) // x3 = A*z^2
x3.Add(&x3, &x2) // x3 = x^2 + A*z^2
x3.Mul(&x3, &p.x) // x3 = x^3 + A*x*z^2
x3.Add(&x3, &z3) // x3 = x^3 + A*x*z^2 + Bz^3
return y2.IsEqual(&x3) == 1 && *p != isogG2Point{}
}
// sswu implements the Simplified Shallue-van de Woestijne-Ulas method for
// mapping a field element to a point on the isogenous curve.
func (p *isogG2Point) sswu(u *ff.Fp2) {
// Method in Appendix-G.2.3 of
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11
tv1, tv2, tv3, tv4 := &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}
tv5, xd, x1n, gxd := &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}
gx1, y, xn, gx2 := &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}
tv1.Sqr(u) // 1. tv1 = u^2
tv3.Mul(&g2sswu.Z, tv1) // 2. tv3 = Z * tv1
tv5.Sqr(tv3) // 3. tv5 = tv3^2
xd.Add(tv5, tv3) // 4. xd = tv5 + tv3
tv2.SetOne() // 5. tv2 = 1
x1n.Add(xd, tv2) // x1n = xd + tv2
x1n.Mul(x1n, &g2Isog3.b) // 6. x1n = x1n * B
xd.Mul(&g2Isog3.a, xd) // 7. xd = A * xd
xd.Neg() // xd = -xd
e1 := xd.IsZero() // 8. e1 = xd == 0
tv2.Mul(&g2sswu.Z, &g2Isog3.a) // 9. tv2 = Z * A
xd.CMov(xd, tv2, e1) // xd = CMOV(xd, tv2, e1)
tv2.Sqr(xd) // 10. tv2 = xd^2
gxd.Mul(tv2, xd) // 11. gxd = tv2 * xd
tv2.Mul(&g2Isog3.a, tv2) // 12. tv2 = A * tv2
gx1.Sqr(x1n) // 13. gx1 = x1n^2
gx1.Add(gx1, tv2) // 14. gx1 = gx1 + tv2
gx1.Mul(gx1, x1n) // 15. gx1 = gx1 * x1n
tv2.Mul(&g2Isog3.b, gxd) // 16. tv2 = B * gxd
gx1.Add(gx1, tv2) // 17. gx1 = gx1 + tv2
tv4.Sqr(gxd) // 18. tv4 = gxd^2
tv2.Mul(tv4, gxd) // 19. tv2 = tv4 * gxd
tv4.Sqr(tv4) // 20. tv4 = tv4^2
tv2.Mul(tv2, tv4) // 21. tv2 = tv2 * tv4
tv2.Mul(tv2, gx1) // 22. tv2 = tv2 * gx1
tv4.Sqr(tv4) // 23. tv4 = tv4^2
tv4.Mul(tv2, tv4) // 24. tv4 = tv2 * tv4
y.ExpVarTime(tv4, g2sswu.c1[:]) // 25. y = tv4^c1
y.Mul(y, tv2) // 26. y = y * tv2
tv4.Mul(y, &g2sswu.c2) // 27. tv4 = y * c2
tv2.Sqr(tv4) // 28. tv2 = tv4^2
tv2.Mul(tv2, gxd) // 29. tv2 = tv2 * gxd
e2 := tv2.IsEqual(gx1) // 30. e2 = tv2 == gx1
y.CMov(y, tv4, e2) // 31. y = CMOV(y, tv4, e2)
tv4.Mul(y, &g2sswu.c3) // 32. tv4 = y * c3
tv2.Sqr(tv4) // 33. tv2 = tv4^2
tv2.Mul(tv2, gxd) // 34. tv2 = tv2 * gxd
e3 := tv2.IsEqual(gx1) // 35. e3 = tv2 == gx1
y.CMov(y, tv4, e3) // 36. y = CMOV(y, tv4, e3)
tv4.Mul(tv4, &g2sswu.c2) // 37. tv4 = tv4 * c2
tv2.Sqr(tv4) // 38. tv2 = tv4^2
tv2.Mul(tv2, gxd) // 39. tv2 = tv2 * gxd
e4 := tv2.IsEqual(gx1) // 40. e4 = tv2 == gx1
y.CMov(y, tv4, e4) // 41. y = CMOV(y, tv4, e4)
gx2.Mul(gx1, tv5) // 42. gx2 = gx1 * tv5
gx2.Mul(gx2, tv3) // 43. gx2 = gx2 * tv3
tv5.Mul(y, tv1) // 44. tv5 = y * tv1
tv5.Mul(tv5, u) // 45. tv5 = tv5 * u
tv1.Mul(tv5, &g2sswu.c4) // 46. tv1 = tv5 * c4
tv4.Mul(tv1, &g2sswu.c2) // 47. tv4 = tv1 * c2
tv2.Sqr(tv4) // 48. tv2 = tv4^2
tv2.Mul(tv2, gxd) // 49. tv2 = tv2 * gxd
e5 := tv2.IsEqual(gx2) // 50. e5 = tv2 == gx2
tv1.CMov(tv1, tv4, e5) // 51. tv1 = CMOV(tv1, tv4, e5)
tv4.Mul(tv5, &g2sswu.c5) // 52. tv4 = tv5 * c5
tv2.Sqr(tv4) // 53. tv2 = tv4^2
tv2.Mul(tv2, gxd) // 54. tv2 = tv2 * gxd
e6 := tv2.IsEqual(gx2) // 55. e6 = tv2 == gx2
tv1.CMov(tv1, tv4, e6) // 56. tv1 = CMOV(tv1, tv4, e6)
tv4.Mul(tv4, &g2sswu.c2) // 57. tv4 = tv4 * c2
tv2.Sqr(tv4) // 58. tv2 = tv4^2
tv2.Mul(tv2, gxd) // 59. tv2 = tv2 * gxd
e7 := tv2.IsEqual(gx2) // 60. e7 = tv2 == gx2
tv1.CMov(tv1, tv4, e7) // 61. tv1 = CMOV(tv1, tv4, e7)
tv2.Sqr(y) // 62. tv2 = y^2
tv2.Mul(tv2, gxd) // 63. tv2 = tv2 * gxd
e8 := tv2.IsEqual(gx1) // 64. e8 = tv2 == gx1
y.CMov(tv1, y, e8) // 65. y = CMOV(tv1, y, e8)
tv2.Mul(tv3, x1n) // 66. tv2 = tv3 * x1n
xn.CMov(tv2, x1n, e8) // 67. xn = CMOV(tv2, x1n, e8)
e9 := 1 ^ u.Sgn0() ^ y.Sgn0() // 68. e9 = sgn0(u) == sgn0(y)
*tv1 = *y // 69. tv1 = y
tv1.Neg() // tv1 = -y
y.CMov(tv1, y, e9) // y = CMOV(tv1, y, e9)
p.x = *xn // 70. return
p.y.Mul(y, xd) // (x,y) = (xn/xd, y/1)
p.z = *xd // (X,Y,Z) = (xn, y*xd, xd)
}
// evalIsogG2 calculates g = g2Isog3(p), where g2Isog3 is an isogeny of
// degree 3 to the curve used in G2.
func (g *G2) evalIsogG2(p *isogG2Point) {
x, y, z := &p.x, &p.y, &p.z
t, zi := &ff.Fp2{}, &ff.Fp2{}
xNum, xDen, yNum, yDen := &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}, &ff.Fp2{}
ixn := len(g2Isog3.xNum) - 1
ixd := len(g2Isog3.xDen) - 1
iyn := len(g2Isog3.yNum) - 1
iyd := len(g2Isog3.yDen) - 1
*xNum = g2Isog3.xNum[ixn]
*xDen = g2Isog3.xDen[ixd]
*yNum = g2Isog3.yNum[iyn]
*yDen = g2Isog3.yDen[iyd]
*zi = *z
for (ixn | ixd | iyn | iyd) != 0 {
if ixn > 0 {
ixn--
t.Mul(zi, &g2Isog3.xNum[ixn])
xNum.Mul(xNum, x)
xNum.Add(xNum, t)
}
if ixd > 0 {
ixd--
t.Mul(zi, &g2Isog3.xDen[ixd])
xDen.Mul(xDen, x)
xDen.Add(xDen, t)
}
if iyn > 0 {
iyn--
t.Mul(zi, &g2Isog3.yNum[iyn])
yNum.Mul(yNum, x)
yNum.Add(yNum, t)
}
if iyd > 0 {
iyd--
t.Mul(zi, &g2Isog3.yDen[iyd])
yDen.Mul(yDen, x)
yDen.Add(yDen, t)
}
zi.Mul(zi, z)
}
g.x.Mul(xNum, yDen)
g.y.Mul(yNum, xDen)
g.y.Mul(&g.y, y)
g.z.Mul(xDen, yDen)
g.z.Mul(&g.z, z)
}