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package stage1
import (
. "kesim.org/seal/nizk"
)
// Implements the proof and verification 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 Statement struct {
x *Scalar
y *Scalar
r *Scalar
α *Scalar
β *Scalar
bitSet bool
*Commitment
}
type Commitment struct {
A *Point
B *Point
C *Point
R *Point
X *Point
Y *Point
Z *Point
}
func NewStatement(bitSet bool) *Statement {
var x [5]*Scalar
for i := range x {
x[i] = Curve.RandomScalar()
}
return NewStatementFromScalars(bitSet, x[0], x[1], x[2], x[3], x[4])
}
func NewStatementFromScalars(bitSet bool, x, y, r, α, β *Scalar) *Statement {
return &Statement{
x: x,
y: y,
r: r,
α: α,
β: β,
bitSet: bitSet,
Commitment: commitment(x, y, r, α, β, bitSet),
}
}
func commitment(x, y, r, α, β *Scalar, bitSet bool) *Commitment {
var Z *Point
φ := α.Mul(β)
if bitSet {
Z = G.Exp(x.Mul(r))
φ = φ.Add(One)
} else {
Z = G.Exp(x.Mul(y))
}
return &Commitment{
Z: Z,
X: G.Exp(x),
Y: G.Exp(y),
R: G.Exp(r),
A: G.Exp(α),
B: G.Exp(β),
C: G.Exp(φ),
}
}
func (s *Statement) Commit() *Commitment {
return s.Commitment
}
type Proof struct {
Ch [2]*Scalar
Rho [2][2]*Scalar
}
func (s *Statement) Proof() *Proof {
var ε [2][4]*Point
var r1, r2, ρ1, ρ2, ω *Scalar
for _, s := range []**Scalar{&r1, &r2, &ρ1, &ρ2, &ω} {
*s = Curve.RandomScalar()
}
if s.bitSet {
ε[0][0] = G.Exp(r1).Mul(s.X.Exp(ω))
ε[0][1] = G.Exp(r2).Mul(s.A.Exp(ω))
ε[0][2] = s.Y.Exp(r1).Mul(s.Z.Exp(ω))
ε[0][3] = s.B.Exp(r2).Mul(s.C.Exp(ω))
ε[1][0] = G.Exp(ρ1)
ε[1][1] = G.Exp(ρ2)
ε[1][2] = s.R.Exp(ρ1)
ε[1][3] = s.B.Exp(ρ2)
} else {
ε[0][0] = G.Exp(r1)
ε[0][1] = G.Exp(r2)
ε[0][2] = s.Y.Exp(r1)
ε[0][3] = s.B.Exp(r2)
ε[1][0] = G.Exp(ρ1).Mul(s.X.Exp(ω))
ε[1][1] = G.Exp(ρ2).Mul(s.A.Exp(ω))
ε[1][2] = s.R.Exp(ρ1).Mul(s.Z.Exp(ω))
ε[1][3] = s.B.Exp(ρ2).Mul(s.C.Div(G).Exp(ω))
}
p := []Bytes{G, s.A, s.B, s.C, s.R, s.X, s.Y, s.Z}
for _, e := range ε[0] {
p = append(p, e)
}
for _, e := range ε[1] {
p = append(p, e)
}
ch := Challenge(p...)
pr := &Proof{}
if s.bitSet {
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(s.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(s.α.Mul(pr.Ch[0]))
pr.Rho[1][0] = ρ1
pr.Rho[1][1] = ρ2
}
return pr
}
func (c *Commitment) Verify(p *Proof) bool {
var ε [2][4]*Point
ε[0][0] = G.Exp(p.Rho[0][0]).Mul(c.X.Exp(p.Ch[0]))
ε[0][1] = G.Exp(p.Rho[0][1]).Mul(c.A.Exp(p.Ch[0]))
ε[0][2] = c.Y.Exp(p.Rho[0][0]).Mul(c.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(c.X.Exp(p.Ch[1]))
ε[1][1] = G.Exp(p.Rho[1][1]).Mul(c.A.Exp(p.Ch[1]))
ε[1][2] = c.R.Exp(p.Rho[1][0]).Mul(c.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, c.R, c.X, c.Y, c.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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