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package nizk
import . "kesim.org/seal/common"
type Stage1 struct {
x *Scalar
y *Scalar
r *Scalar
com *Stage1Commitment
prf *Stage1Proof
bit *Bit
}
type Stage1Commitment struct {
R *Point
X *Point
Y *Point
Z *Point
}
// Represents the proof of statements of the following form:
//
// [ Z=g^(xy) && X=g^x && Y=g^y && C=g^(αβ) && A=g^α && B=g^β ]
// || [ Z=g^(xr) && X=g^x && R=g^r && C=g^(αβ+1) && A=g^α && B=g^β ]
//
// for given Z, X, Y, R, C, A and B
type Stage1Proof struct {
Ch [2]*Scalar
Rho [2][2]*Scalar
}
func (b *Bit) Stage1() *Stage1 {
var x [3]*Scalar
for i := range x {
x[i] = Curve.RandomScalar()
}
return b.Stage1FromScalars(x[0], x[1], x[2])
}
func (b *Bit) Stage1FromScalars(x, y, r *Scalar) *Stage1 {
return &Stage1{
x: x,
y: y,
r: r,
bit: b,
}
}
func (s *Stage1) commit() *Stage1Commitment {
if s.com != nil {
return s.com
}
var Z *Point
if s.bit.IsSet() {
Z = G.Exp(s.x.Mul(s.r))
} else {
Z = G.Exp(s.x.Mul(s.y))
}
s.com = &Stage1Commitment{
Z: Z,
X: G.Exp(s.x),
Y: G.Exp(s.y),
R: G.Exp(s.r),
}
return s.com
}
func (s *Stage1) proof() *Stage1Proof {
var ε [2][4]*Point
var r1, r2, ρ1, ρ2, ω *Scalar
for _, s := range []**Scalar{&r1, &r2, &ρ1, &ρ2, &ω} {
*s = Curve.RandomScalar()
}
c := s.commit()
bc, _ := s.bit.Commit()
if s.bit.IsSet() {
ε[0][0] = G.Exp(r1).Mul(c.X.Exp(ω))
ε[0][1] = G.Exp(r2).Mul(bc.A.Exp(ω))
ε[0][2] = c.Y.Exp(r1).Mul(c.Z.Exp(ω))
ε[0][3] = bc.B.Exp(r2).Mul(bc.C.Exp(ω))
ε[1][0] = G.Exp(ρ1)
ε[1][1] = G.Exp(ρ2)
ε[1][2] = c.R.Exp(ρ1)
ε[1][3] = bc.B.Exp(ρ2)
} else {
ε[0][0] = G.Exp(r1)
ε[0][1] = G.Exp(r2)
ε[0][2] = c.Y.Exp(r1)
ε[0][3] = bc.B.Exp(r2)
ε[1][0] = G.Exp(ρ1).Mul(c.X.Exp(ω))
ε[1][1] = G.Exp(ρ2).Mul(bc.A.Exp(ω))
ε[1][2] = c.R.Exp(ρ1).Mul(c.Z.Exp(ω))
ε[1][3] = bc.B.Exp(ρ2).Mul(bc.C.Div(G).Exp(ω))
}
p := []Bytes{G, bc.A, bc.B, bc.C, c.R, c.X, c.Y, c.Z}
for _, e := range ε[0] {
p = append(p, e)
}
for _, e := range ε[1] {
p = append(p, e)
}
ch := Challenge(p...)
pr := &Stage1Proof{}
α, _ := s.bit.Scalars()
if s.bit.IsSet() {
pr.Ch[0] = ω
pr.Ch[1] = ch.Sub(ω)
pr.Rho[0][0] = r1
pr.Rho[0][1] = r2
pr.Rho[1][0] = ρ1.Sub(s.x.Mul(pr.Ch[1]))
pr.Rho[1][1] = ρ2.Sub(α.Mul(pr.Ch[1]))
} else {
pr.Ch[0] = ch.Sub(ω)
pr.Ch[1] = ω
pr.Rho[0][0] = r1.Sub(s.x.Mul(pr.Ch[0]))
pr.Rho[0][1] = r2.Sub(α.Mul(pr.Ch[0]))
pr.Rho[1][0] = ρ1
pr.Rho[1][1] = ρ2
}
return pr
}
func (s *Stage1) Commit() (*Stage1Commitment, *Stage1Proof) {
return s.commit(), s.proof()
}
func (c1 *Stage1Commitment) Verify(c *Commitment, p *Stage1Proof) bool {
var ε [2][4]*Point
ε[0][0] = G.Exp(p.Rho[0][0]).Mul(c1.X.Exp(p.Ch[0]))
ε[0][1] = G.Exp(p.Rho[0][1]).Mul(c.A.Exp(p.Ch[0]))
ε[0][2] = c1.Y.Exp(p.Rho[0][0]).Mul(c1.Z.Exp(p.Ch[0]))
ε[0][3] = c.B.Exp(p.Rho[0][1]).Mul(c.C.Exp(p.Ch[0]))
ε[1][0] = G.Exp(p.Rho[1][0]).Mul(c1.X.Exp(p.Ch[1]))
ε[1][1] = G.Exp(p.Rho[1][1]).Mul(c.A.Exp(p.Ch[1]))
ε[1][2] = c1.R.Exp(p.Rho[1][0]).Mul(c1.Z.Exp(p.Ch[1]))
ε[1][3] = c.B.Exp(p.Rho[1][1]).Mul(c.C.Div(G).Exp(p.Ch[1]))
points := []Bytes{G, c.A, c.B, c.C, c1.R, c1.X, c1.Y, c1.Z}
for _, e := range ε[0] {
points = append(points, e)
}
for _, e := range ε[1] {
points = append(points, e)
}
ch := Challenge(points...)
return p.Ch[0].Add(p.Ch[1]).Equal(ch)
}
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