1 files changed, 49 insertions, 52 deletions

diff --git a/nizk/stage1.go b/nizk/stage1.go
index ff42e7f..dd4a896 100644
--- a/nizk/stage1.go
+++ b/nizk/stage1.go
@@ -2,32 +2,35 @@ package nizk
 
 import . "kesim.org/seal/common"
 
-// 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 Stage1 struct {
-	// Original Bit
-	*Bit
-
-	// New stage 1 private data
 	x *Scalar
 	y *Scalar
 	r *Scalar
+
+	com *Stage1Commitment
+	prf *Stage1Proof
+
+	bit *Bit
 }
 
 type Stage1Commitment struct {
-	// Original Commitment
-	*Commitment
-
-	// New
 	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 {
@@ -38,70 +41,64 @@ func (b *Bit) Stage1() *Stage1 {
 
 func (b *Bit) Stage1FromScalars(x, y, r *Scalar) *Stage1 {
 	return &Stage1{
-		x:   x,
-		y:   y,
-		r:   r,
-		Bit: b,
+		x: x,
+		y: y,
+		r: r,
+
+		bit: b,
 	}
 }
 
 func (s *Stage1) commit() *Stage1Commitment {
+	if s.com != nil {
+		return s.com
+	}
 	var Z *Point
-	φ := s.α.Mul(s.β)
-	if s.bitSet {
+	if s.bit.IsSet() {
 		Z = G.Exp(s.x.Mul(s.r))
-		φ = φ.Add(One)
 	} else {
 		Z = G.Exp(s.x.Mul(s.y))
 	}
 
-	return &Stage1Commitment{
+	s.com = &Stage1Commitment{
 		Z: Z,
 		X: G.Exp(s.x),
 		Y: G.Exp(s.y),
 		R: G.Exp(s.r),
-
-		Commitment: &Commitment{
-			A: G.Exp(s.α),
-			B: G.Exp(s.β),
-			C: G.Exp(φ),
-		},
 	}
+	return s.com
 }
 
-type Stage1Proof struct {
-	Ch  [2]*Scalar
-	Rho [2][2]*Scalar
-}
-
-func (s *Stage1) proof(c *Stage1Commitment) *Stage1Proof {
+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.bitSet {
+	if s.bit.IsSet() {
 		ε[0][0] = G.Exp(r1).Mul(c.X.Exp(ω))
-		ε[0][1] = G.Exp(r2).Mul(c.A.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] = c.B.Exp(r2).Mul(c.C.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] = c.B.Exp(ρ2)
+		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] = c.B.Exp(r2)
+		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(c.A.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] = c.B.Exp(ρ2).Mul(c.C.Div(G).Exp(ω))
+		ε[1][3] = bc.B.Exp(ρ2).Mul(bc.C.Div(G).Exp(ω))
 	}
 
-	p := []Bytes{G, c.A, c.B, c.C, c.R, c.X, c.Y, c.Z}
+	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)
 	}
@@ -111,19 +108,20 @@ func (s *Stage1) proof(c *Stage1Commitment) *Stage1Proof {
 
 	ch := Challenge(p...)
 	pr := &Stage1Proof{}
+	α, _ := s.bit.Scalars()
 
-	if s.bitSet {
+	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(s.α.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(s.α.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
 	}
@@ -132,23 +130,22 @@ func (s *Stage1) proof(c *Stage1Commitment) *Stage1Proof {
 }
 
 func (s *Stage1) Commit() (*Stage1Commitment, *Stage1Proof) {
-	c := s.commit()
-	return c, s.proof(c)
+	return s.commit(), s.proof()
 }
 
-func (c *Stage1Commitment) Verify(p *Stage1Proof) bool {
+func (c1 *Stage1Commitment) Verify(c *Commitment, p *Stage1Proof) bool {
 	var ε [2][4]*Point
 
-	ε[0][0] = G.Exp(p.Rho[0][0]).Mul(c.X.Exp(p.Ch[0]))
+	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] = c.Y.Exp(p.Rho[0][0]).Mul(c.Z.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(c.X.Exp(p.Ch[1]))
+	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] = c.R.Exp(p.Rho[1][0]).Mul(c.Z.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, c.R, c.X, c.Y, c.Z}
+	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)
 	}