diff options
Diffstat (limited to 'stage2.go')
| -rw-r--r-- | stage2.go | 221 |
1 files changed, 221 insertions, 0 deletions
diff --git a/stage2.go b/stage2.go new file mode 100644 index 0000000..7d82d89 --- /dev/null +++ b/stage2.go @@ -0,0 +1,221 @@ +package seal + +import ( + . "kesim.org/seal/common" +) + +// Represents the proof of a statement of the following form: +// +// ( Z=g^(x*y) && X=g^x && Y=g^y && Z_=g^(x_*y_) && X_=g^x_ && Y_=g^y_ ) // case "lost" +// || ( Z=g^(x*y) && X=g^x && Y=g^y && Z_=g^(x_*r_) && X_=g^x_ && R_=g^r_ && C=g^(a*b) && A=g^a && B=g^b ) // case "unset" +// || ( Z=g^(x*r) && X=g^x && R=g^r && Z_=g^(x_*r_) && X_=g^x_ && R_=g^r_ && C=g^(a*b+1) && A=g^a && B=g^b ) // case "set" +// +// for given A, B, C, R, X, Y, Z, R_, X_, Y_, Z_ on the curve +type Stage2Proof struct { + Ch [3]*Scalar + R1 [3]*Scalar + R2 [3]*Scalar + R3 [2]*Scalar +} + +func (b *Bit) RevealStage2(lost bool, prev *Bit, Xs ...*Point) (rv2 *StageReveal, pr *Stage2Proof) { + if b.Stage == nil { + b.StageCommit() + } + s := b.Stage + + var ( + ε1, ε1_ [3]Bytes + ε2, ε2_ [3]Bytes + ε3, ε3_ [2]Bytes + + ρ1, ρ2 [3]*Scalar + ρ3 [2]*Scalar + ω [2]*Scalar + ) + + for _, s := range [][]*Scalar{ρ1[:], ρ2[:], ρ3[:], ω[:]} { + for i := range s { + s[i] = Curve.RandomScalar() + } + } + + c1 := prev.StageCommitment + c2 := s.StageCommitment + rv1 := prev.StageReveal + b.StageReveal = b.reveal(prev.Sent, Xs...) + rv2 = b.StageReveal + + if lost { + ε1[0] = G.Exp(ρ1[0]).Mul(c2.X.Exp(ω[0])) + ε1[1] = G.Exp(ρ1[1]).Mul(c1.X.Exp(ω[0])) + ε1[2] = G.Exp(ρ1[2]).Mul(b.A.Exp(ω[0])) + + ε1_[0] = c2.R.Exp(ρ1[0]).Mul(rv2.Z.Exp(ω[0])) + ε1_[1] = c1.R.Exp(ρ1[1]).Mul(rv1.Z.Exp(ω[0])) + ε1_[2] = b.B.Exp(ρ1[2]).Mul(b.C.Div(G).Exp(ω[0])) + + ε2[0] = G.Exp(ρ2[0]).Mul(c2.X.Exp(ω[1])) + ε2[1] = G.Exp(ρ2[1]).Mul(c1.X.Exp(ω[1])) + ε2[2] = G.Exp(ρ2[2]).Mul(b.A.Exp(ω[1])) + + ε2_[0] = rv2.Y.Exp(ρ2[0]).Mul(rv2.Z.Exp(ω[1])) + ε2_[1] = c1.R.Exp(ρ2[1]).Mul(rv1.Z.Exp(ω[1])) + ε2_[2] = b.B.Exp(ρ2[2]).Mul(b.C.Exp(ω[1])) + + ε3[0] = G.Exp(ρ3[0]) + ε3[1] = G.Exp(ρ3[1]) + + ε3_[0] = rv2.Y.Exp(ρ3[0]) + ε3_[1] = rv1.Y.Exp(ρ3[1]) + } else { + if b.IsSet() { + ε1[0] = G.Exp(ρ1[0]) + ε1[1] = G.Exp(ρ1[1]) + ε1[2] = G.Exp(ρ1[2]) + + ε1_[0] = c2.R.Exp(ρ1[0]) + ε1_[1] = c1.R.Exp(ρ1[1]) + ε1_[2] = b.B.Exp(ρ1[2]) + + ε2[0] = G.Exp(ρ2[0]).Mul(c2.X.Exp(ω[0])) + ε2[1] = G.Exp(ρ2[1]).Mul(c1.X.Exp(ω[0])) + ε2[2] = G.Exp(ρ2[2]).Mul(b.A.Exp(ω[0])) + + ε2_[0] = rv2.Y.Exp(ρ2[0]).Mul(rv2.Z.Exp(ω[0])) + ε2_[1] = c1.R.Exp(ρ2[1]).Mul(rv1.Z.Exp(ω[0])) + ε2_[2] = b.B.Exp(ρ2[2]).Mul(b.C.Exp(ω[0])) + + ε3[0] = G.Exp(ρ3[0]).Mul(c2.X.Exp(ω[1])) + ε3[1] = G.Exp(ρ3[1]).Mul(c1.X.Exp(ω[1])) + + ε3_[0] = rv2.Y.Exp(ρ3[0]).Mul(rv2.Z.Exp(ω[1])) + ε3_[1] = rv1.Y.Exp(ρ3[1]).Mul(rv1.Z.Exp(ω[1])) + } else { + ε1[0] = G.Exp(ρ1[0]).Mul(c2.X.Exp(ω[0])) + ε1[1] = G.Exp(ρ1[1]).Mul(c1.X.Exp(ω[0])) + ε1[2] = G.Exp(ρ1[2]).Mul(b.A.Exp(ω[0])) + + ε1_[0] = c2.R.Exp(ρ1[0]).Mul(rv2.Z.Exp(ω[0])) + ε1_[1] = c1.R.Exp(ρ1[1]).Mul(rv1.Z.Exp(ω[0])) + ε1_[2] = b.B.Exp(ρ1[2]).Mul(b.C.Div(G).Exp(ω[0])) + + ε2[0] = G.Exp(ρ2[0]) + ε2[1] = G.Exp(ρ2[1]) + ε2[2] = G.Exp(ρ2[2]) + + ε2_[0] = rv2.Y.Exp(ρ2[0]) + ε2_[1] = c1.R.Exp(ρ2[1]) + ε2_[2] = b.B.Exp(ρ2[2]) + + ε3[0] = G.Exp(ρ3[0]).Mul(c2.X.Exp(ω[1])) + ε3[1] = G.Exp(ρ3[1]).Mul(c1.X.Exp(ω[1])) + + ε3_[0] = rv2.Y.Exp(ρ3[0]).Mul(rv2.Z.Exp(ω[1])) + ε3_[1] = rv1.Y.Exp(ρ3[1]).Mul(rv1.Z.Exp(ω[1])) + } + } + + points := []Bytes{G, b.A, b.B, b.C, c2.R, c2.X, rv2.Y, rv2.Z, c1.R, c1.X, rv1.Y, rv1.Z} + points = append(points, ε1[:]...) + points = append(points, ε2[:]...) + points = append(points, ε3[:]...) + points = append(points, ε1_[:]...) + points = append(points, ε2_[:]...) + points = append(points, ε3_[:]...) + + ch := Challenge(points...) + pr = &Stage2Proof{} + + if lost { + pr.Ch[0] = ω[0] + pr.Ch[1] = ω[1] + pr.Ch[2] = ch.Sub(ω[0]).Sub(ω[1]) + + pr.R1[0] = ρ1[0] + pr.R1[1] = ρ1[1] + pr.R1[2] = ρ1[2] + + pr.R2[0] = ρ2[0] + pr.R2[1] = ρ2[1] + pr.R2[2] = ρ2[2] + + pr.R3[0] = ρ3[0].Sub(s.x.Mul(pr.Ch[2])) + pr.R3[1] = ρ3[1].Sub(prev.x.Mul(pr.Ch[2])) + } else { + if b.IsSet() { + pr.Ch[0] = ch.Sub(ω[0]).Sub(ω[1]) + pr.Ch[1] = ω[0] + pr.Ch[2] = ω[1] + + pr.R1[0] = ρ1[0].Sub(s.x.Mul(pr.Ch[0])) + pr.R1[1] = ρ1[1].Sub(prev.x.Mul(pr.Ch[0])) + pr.R1[2] = ρ1[2].Sub(b.α.Mul(pr.Ch[0])) + + pr.R2[0] = ρ2[0] + pr.R2[1] = ρ2[1] + pr.R2[2] = ρ2[2] + + pr.R3[0] = ρ3[0] + pr.R3[1] = ρ3[1] + } else { + pr.Ch[0] = ω[0] + pr.Ch[1] = ch.Sub(ω[0]).Sub(ω[1]) + pr.Ch[2] = ω[1] + + pr.R1[0] = ρ1[0] + pr.R1[1] = ρ1[1] + pr.R1[2] = ρ1[2] + + pr.R2[0] = ρ2[0].Sub(s.x.Mul(pr.Ch[1])) + pr.R2[1] = ρ2[1].Sub(prev.x.Mul(pr.Ch[1])) + pr.R2[2] = ρ2[2].Sub(b.α.Mul(pr.Ch[1])) + + pr.R3[0] = ρ3[0] + pr.R3[1] = ρ3[1] + } + } + + return rv2, pr +} + +func (c *Commitment) VerifyStage2(c1, c2 *StageCommitment, r1, r2 *StageReveal, p *Stage2Proof) bool { + var ( + e1, e1_ [3]Bytes + e2, e2_ [3]Bytes + e3, e3_ [2]Bytes + ) + e1[0] = G.Exp(p.R1[0]).Mul(c2.X.Exp(p.Ch[0])) + e1[1] = G.Exp(p.R1[1]).Mul(c1.X.Exp(p.Ch[0])) + e1[2] = G.Exp(p.R1[2]).Mul(c.A.Exp(p.Ch[0])) + + e1_[0] = c2.R.Exp(p.R1[0]).Mul(r2.Z.Exp(p.Ch[0])) + e1_[1] = c1.R.Exp(p.R1[1]).Mul(r1.Z.Exp(p.Ch[0])) + e1_[2] = c.B.Exp(p.R1[2]).Mul(c.C.Div(G).Exp(p.Ch[0])) + + e2[0] = G.Exp(p.R2[0]).Mul(c2.X.Exp(p.Ch[1])) + e2[1] = G.Exp(p.R2[1]).Mul(c1.X.Exp(p.Ch[1])) + e2[2] = G.Exp(p.R2[2]).Mul(c.A.Exp(p.Ch[1])) + + e2_[0] = r2.Y.Exp(p.R2[0]).Mul(r2.Z.Exp(p.Ch[1])) + e2_[1] = c1.R.Exp(p.R2[1]).Mul(r1.Z.Exp(p.Ch[1])) + e2_[2] = c.B.Exp(p.R2[2]).Mul(c.C.Exp(p.Ch[1])) + + e3[0] = G.Exp(p.R3[0]).Mul(c2.X.Exp(p.Ch[2])) + e3[1] = G.Exp(p.R3[1]).Mul(c1.X.Exp(p.Ch[2])) + + e3_[0] = r2.Y.Exp(p.R3[0]).Mul(r2.Z.Exp(p.Ch[2])) + e3_[1] = r1.Y.Exp(p.R3[1]).Mul(r1.Z.Exp(p.Ch[2])) + + points := []Bytes{G, c.A, c.B, c.C, c2.R, c2.X, r2.Y, r2.Z, c1.R, c1.X, r1.Y, r1.Z} + points = append(points, e1[:]...) + points = append(points, e2[:]...) + points = append(points, e3[:]...) + points = append(points, e1_[:]...) + points = append(points, e2_[:]...) + points = append(points, e3_[:]...) + + ch := Challenge(points...) + + return p.Ch[0].Add(p.Ch[1]).Add(p.Ch[2]).Equal(ch) +} |