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log.go
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log.go
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package zklog
import (
"crypto/rand"
"github.com/sa8/multi-party-sig/pkg/hash"
"github.com/sa8/multi-party-sig/pkg/math/curve"
"github.com/sa8/multi-party-sig/pkg/math/sample"
)
type Public struct {
// H = b⋅G
H curve.Point
// X = a⋅G
X curve.Point
// Y = a⋅H
Y curve.Point
}
type Private struct {
// A = a
A curve.Scalar
// B = b
B curve.Scalar
}
type Commitment struct {
// A = α⋅G
A curve.Point
// B = α⋅H
B curve.Point
// C = β⋅G
C curve.Point
}
type Proof struct {
group curve.Curve
*Commitment
// Z1 = α+ea (mod q)
Z1 curve.Scalar
// Z2 = β+eb (mod q)
Z2 curve.Scalar
}
func (p *Proof) IsValid() bool {
if p == nil {
return false
}
if p.A.IsIdentity() || p.B.IsIdentity() || p.C.IsIdentity() {
return false
}
if p.Z1.IsZero() || p.Z2.IsZero() {
return false
}
return true
}
func NewProof(group curve.Curve, hash *hash.Hash, public Public, private Private) *Proof {
alpha := sample.Scalar(rand.Reader, group)
beta := sample.Scalar(rand.Reader, group)
commitment := &Commitment{
A: alpha.ActOnBase(), // A = α⋅G
B: alpha.Act(public.H), // B = α⋅H
C: beta.ActOnBase(), // C = β⋅H
}
e, _ := challenge(hash, group, public, commitment)
return &Proof{
group: group,
Commitment: commitment,
Z1: group.NewScalar().Set(e).Mul(private.A).Add(alpha), // Z₁ = α+ea (mod q)
Z2: group.NewScalar().Set(e).Mul(private.B).Add(beta), // Z₂ = β+eb (mod q)
}
}
func (p Proof) Verify(hash *hash.Hash, public Public) bool {
if !p.IsValid() {
return false
}
e, err := challenge(hash, p.group, public, p.Commitment)
if err != nil {
return false
}
{
lhs := p.Z1.ActOnBase() // lhs = z₁⋅G
rhs := e.Act(public.X).Add(p.A) // rhs = A+e⋅X
if !lhs.Equal(rhs) {
return false
}
}
{
lhs := p.Z1.Act(public.H) // lhs = z₁⋅H
rhs := e.Act(public.Y).Add(p.B) // rhs = B+e⋅Y
if !lhs.Equal(rhs) {
return false
}
}
{
lhs := p.Z2.ActOnBase() // lhs = z₂⋅G
rhs := e.Act(public.H).Add(p.C) // rhs = C+e⋅H
if !lhs.Equal(rhs) {
return false
}
}
return true
}
func challenge(hash *hash.Hash, group curve.Curve, public Public, commitment *Commitment) (e curve.Scalar, err error) {
err = hash.WriteAny(public.H, public.X, public.Y,
commitment.A, commitment.B, commitment.C)
e = sample.Scalar(hash.Digest(), group)
return
}
func Empty(group curve.Curve) *Proof {
return &Proof{
group: group,
Commitment: &Commitment{
A: group.NewPoint(),
B: group.NewPoint(),
C: group.NewPoint(),
},
Z1: group.NewScalar(),
Z2: group.NewScalar(),
}
}