mirror of
https://github.com/luxfi/kms.git
synced 2026-10-30 16:23:36 +00:00
zeekay
cc986c328d
Squashes all pre-rewrite history into a single root commit. Previous tree: - 14506 commits including upstream Infisical fork history - Multiple merge chains carrying pre-purge content Force-rewrite per disk-space reclamation discipline. GHCR images (1.9.9, 1.9.11) remain immutable; their git lineage is no longer materialized.
134 lines
4.1 KiB
Go
134 lines
4.1 KiB
Go
package bls12381
|
|
|
|
import "github.com/cloudflare/circl/ecc/bls12381/ff"
|
|
|
|
func doubleAndLine(P *G2, l *line) {
|
|
// Reference:
|
|
// "Faster Pairing Computations on Curves with High-Degree Twists" by
|
|
// Costello-Lange-Naehrig. [Sec. 5] (eprint.iacr.org/2009/615).
|
|
// "Complete addition formulas for prime order elliptic curves" by
|
|
// Costello-Renes-Batina. [Alg.9] (eprint.iacr.org/2015/1060).
|
|
var R G2
|
|
X, Y, Z := &P.x, &P.y, &P.z
|
|
X3, Y3, Z3 := &R.x, &R.y, &R.z
|
|
isDoubLine := l != nil
|
|
_3B := &g2Params._3b
|
|
var A, B, C, D, E, F, G, T ff.Fp2
|
|
B.Sqr(Y) // 1. B = Y1^2
|
|
C.Sqr(Z) // 2. C = Z1^2
|
|
D.Mul(_3B, &C) // 3. D = 3b*C
|
|
F.Add(Y, Z) // 4. F = (Y1+Z1)
|
|
F.Sqr(&F) // F = (Y1+Z1)^2
|
|
F.Sub(&F, &B) // F = (Y1+Z1)^2-B
|
|
F.Sub(&F, &C) // F = (Y1+Z1)^2-B-C
|
|
if isDoubLine {
|
|
A.Sqr(X) // 5. A = X1^2
|
|
E.Add(X, Y) // E = (X1+Y1)
|
|
E.Sqr(&E) // E = (X1+Y1)^2
|
|
E.Sub(&E, &A) // E = (X1+Y1)^2-A
|
|
E.Sub(&E, &B) // E = (X1+Y1)^2-A-B = 2X*Y
|
|
l[0].Add(&A, &A) // 5a. l0 = 2A
|
|
l[0].Add(&l[0], &A) // l0 = 3A = 3X1^2
|
|
l[1] = F // 5b. l1 = F
|
|
l[1].Neg() // l1 = -F = -2Y1Z1
|
|
l[2].Sub(&D, &B) // 5c. l2 = D-B = 3b*Z1^2-Y1^2
|
|
} else {
|
|
E.Mul(X, Y) // 5. E = X*Y
|
|
E.Add(&E, &E) // E = 2X*Y
|
|
}
|
|
T.Add(&D, &D) // 6. T = 2D
|
|
G.Add(&T, &D) // 7. G = 3D
|
|
X3.Sub(&B, &G) // 8. X3 = (B-G)
|
|
X3.Mul(X3, &E) // X3 = E*(B-G)
|
|
T.Sqr(&T) // 9 . T = 4D^2
|
|
Y3.Add(&B, &G) // 10. Y3 = (B+G)
|
|
Y3.Sqr(Y3) // Y3 = (B+G)^2
|
|
Y3.Sub(Y3, &T) // Y3 = (B+G)^2-4D^2
|
|
Y3.Sub(Y3, &T) // Y3 = (B+G)^2-8D^2
|
|
Y3.Sub(Y3, &T) // Y3 = (B+G)^2-12D^2
|
|
Z3.Mul(&B, &F) // 11. Z3 = B*F
|
|
Z3.Add(Z3, Z3) // Z3 = 2B*F
|
|
Z3.Add(Z3, Z3) // Z3 = 4B*F
|
|
*P = R
|
|
}
|
|
|
|
func addAndLine(PQ, P, Q *G2, l *line) {
|
|
// Reference:
|
|
// "Faster Pairing Computations on Curves with High-Degree Twists" by
|
|
// Costello-Lange-Naehrig. [Sec. 5] (eprint.iacr.org/2009/615).
|
|
// "Complete addition formulas for prime order elliptic curves" by
|
|
// Costello-Renes-Batina. [Alg.7] (eprint.iacr.org/2015/1060).
|
|
var R G2
|
|
X1, Y1, Z1 := &P.x, &P.y, &P.z
|
|
X2, Y2, Z2 := &Q.x, &Q.y, &Q.z
|
|
X3, Y3, Z3 := &R.x, &R.y, &R.z
|
|
_3B := &g2Params._3b
|
|
isAddLine := l != nil
|
|
var X1X2, Y1Y2, Z1Z2, _3bZ1Z2 ff.Fp2
|
|
var A, B, C, D, E, F, G ff.Fp2
|
|
t0, t1 := &ff.Fp2{}, &ff.Fp2{}
|
|
|
|
X1X2.Mul(X1, X2)
|
|
Y1Y2.Mul(Y1, Y2)
|
|
Z1Z2.Mul(Z1, Z2)
|
|
_3bZ1Z2.Mul(&Z1Z2, _3B)
|
|
|
|
A.Add(&X1X2, &X1X2) // A = 2X1X2
|
|
A.Add(&A, &X1X2) // = 3X1X2
|
|
B.Add(&Y1Y2, &_3bZ1Z2) // B = Y1Y2+3bZ1Z2
|
|
C.Sub(&Y1Y2, &_3bZ1Z2) // C = Y1Y2-3bZ1Z2
|
|
|
|
t0.Add(X1, Y1) // t0 = (X1 + Y1)
|
|
D.Add(X2, Y2) // D = (X2 + Y2)
|
|
D.Mul(&D, t0) // = X1X2 + X1Y2 + X2Y1 + Y1Y2
|
|
D.Sub(&D, &X1X2) // = X1Y2 + X2Y1 + Y1Y2
|
|
D.Sub(&D, &Y1Y2) // = X1Y2 + X2Y1
|
|
|
|
if isAddLine {
|
|
var EE, FF ff.Fp2
|
|
t0.Mul(Y1, Z2) // t0 = Y1Z2
|
|
t1.Mul(Y2, Z1) // t1 = Y2Z1
|
|
E.Add(t0, t1) // E = Y1Z2 + Y2Z1
|
|
EE.Sub(t0, t1) // EE = Y1Z2 - Y2Z1
|
|
|
|
t0.Mul(X1, Z2) // t0 = X1Z2
|
|
t1.Mul(X2, Z1) // t1 = X2Z1
|
|
F.Add(t0, t1) // F = X1Z2 + X2Z1
|
|
FF.Sub(t0, t1) // FF = X1Z2 - X2Z1
|
|
|
|
l[0].Mul(&EE, Z2) // l0 = (Y1Z2 - Y2Z1)*Z2
|
|
l[0].Neg() // = -(Y1Z2 - Y2Z1)*Z2
|
|
l[1].Mul(&FF, Z2) // l1 = (X1Z2 - X2Z1)*Z2
|
|
t0.Mul(&FF, Y2) // t0 = (X1Z2 - X2Z1)*Y2
|
|
l[2].Mul(&EE, X2) // l2 = (Y1Z2 - Y2Z1)*X2
|
|
l[2].Sub(&l[2], t0) // = (Y1Z2 - Y2Z1)*X2 - (X1Z2 - X2Z1)*Y2
|
|
} else {
|
|
t0.Add(Y1, Z1) // t0 = (Y1 + Z1)
|
|
t1.Add(Y2, Z2) // t1 = (Y2 + Z2)
|
|
E.Mul(t0, t1) // E = Y1Y2 + Y1Z2 + Y2Z1 + Z1Z2
|
|
E.Sub(&E, &Y1Y2) // = Y1Z2 + Y2Z1 + Z1Z2
|
|
E.Sub(&E, &Z1Z2) // = Y1Z2 + Y2Z1
|
|
|
|
t0.Add(X1, Z1) // t0 = (X1 + Z1)
|
|
t1.Add(X2, Z2) // t1 = (X2 + Z2)
|
|
F.Mul(t0, t1) // F = X1X2 + X1Z2 + X2Z1 + Z1Z2
|
|
F.Sub(&F, &X1X2) // = X1Z2 + X2Z1 + Z1Z2
|
|
F.Sub(&F, &Z1Z2) // = X1Z2 + X2Z1
|
|
}
|
|
G.Mul(&F, _3B) // G = 3b*F
|
|
|
|
t0.Mul(&E, &G) // t0 = E*G
|
|
X3.Mul(&D, &C) // X3 = D*C
|
|
X3.Sub(X3, t0) // = D*C - E*G
|
|
|
|
t0.Mul(&A, &G) // t0 = A*G
|
|
Y3.Mul(&B, &C) // Y3 = B*C
|
|
Y3.Add(Y3, t0) // = B*C + A*G
|
|
|
|
t0.Mul(&A, &D) // t0 = A*D
|
|
Z3.Mul(&E, &B) // Z3 = E*B
|
|
Z3.Add(Z3, t0) // = E*B + A*D
|
|
|
|
*PQ = R
|
|
}
|