1 files changed, 47 insertions, 46 deletions
diff --git a/nizk/commit/commit.go b/nizk/commit/commit.go
index 5238c15..085d9a2 100644
--- a/nizk/commit/commit.go
+++ b/nizk/commit/commit.go
@@ -5,45 +5,46 @@ import (
 )
 
 // This is a construction of a proof of a statement of the form
-// σ ==	   [(Φ = g^(αβ))   && (A = g^α) && (Β = g^β)]
-//		|| [(Φ = g^(αβ+1)) && (A = g^α) && (Β = g^β)]
-// for given Φ, A and B
+//    [(C = g^(ab))   && (A = g^a) && (Β = g^b)]
+// || [(C = g^(ab+1)) && (A = g^a) && (Β = g^b)]
+//
+// for given C, A and B
 
 type Statement struct {
-	α    *Scalar
-	β    *Scalar
+	a    *Scalar
+	b    *Scalar
 	plus bool
 	*Commitment
 }
 
 type Commitment struct {
-	Φ *Point
+	C *Point
 	A *Point
 	B *Point
 }
 
-func NewStatement(α, β *Scalar, plus bool) *Statement {
+func NewStatement(a, b *Scalar, plus bool) *Statement {
 	return &Statement{
-		α:          α,
-		β:          β,
+		a:          a,
+		b:          b,
 		plus:       plus,
-		Commitment: commitment(α, β, plus),
+		Commitment: commitment(a, b, plus),
 	}
 }
 
-func commitment(α, β *Scalar, plus bool) *Commitment {
-	var Φ *Point
-	φ := α.Mul(β)
+func commitment(a, b *Scalar, plus bool) *Commitment {
+	var C *Point
+	c := a.Mul(b)
 
 	if plus {
-		Φ = G.Exp(φ.Add(One))
+		C = G.Exp(c.Add(One))
 	} else {
-		Φ = G.Exp(φ)
+		C = G.Exp(c)
 	}
 	return &Commitment{
-		Φ: Φ,
-		A: G.Exp(α),
-		B: G.Exp(β),
+		C: C,
+		A: G.Exp(a),
+		B: G.Exp(b),
 	}
 }
 
@@ -52,53 +53,53 @@ func (s *Statement) Commit() *Commitment {
 }
 
 type Proof struct {
-	Ch  [2]*Scalar
-	Rho [2]*Scalar
+	Ch [2]*Scalar
+	R  [2]*Scalar
 }
 
 func (s *Statement) Proof() *Proof {
-	var ε [2][2]*Point
-	var r1, r2, ω *Scalar
+	var e [2][2]*Point
+	var r1, r2, w *Scalar
 	r1 = Curve.RandomScalar()
 	r2 = Curve.RandomScalar()
-	ω = Curve.RandomScalar()
+	w = Curve.RandomScalar()
 
 	if s.plus {
-		ε[0][0] = G.Exp(r1)
-		ε[0][1] = s.B.Exp(r1).Mul(G.Exp(ω))
-		ε[1][0] = G.Exp(r2)
-		ε[1][1] = s.B.Exp(r2)
+		e[0][0] = G.Exp(r1)
+		e[0][1] = s.B.Exp(r1).Mul(G.Exp(w))
+		e[1][0] = G.Exp(r2)
+		e[1][1] = s.B.Exp(r2)
 	} else {
-		ε[0][0] = G.Exp(r1)
-		ε[0][1] = s.B.Exp(r1)
-		ε[1][0] = G.Exp(r2).Mul(s.A.Exp(ω))
-		ε[1][1] = s.B.Exp(r2).Mul(s.Φ.Div(G).Exp(ω))
+		e[0][0] = G.Exp(r1)
+		e[0][1] = s.B.Exp(r1)
+		e[1][0] = G.Exp(r2).Mul(s.A.Exp(w))
+		e[1][1] = s.B.Exp(r2).Mul(s.C.Div(G).Exp(w))
 	}
 
-	ch := Challenge(G, s.Φ, s.A, s.B, ε[0][0], ε[0][1], ε[1][0], ε[1][1])
+	ch := Challenge(G, s.C, s.A, s.B, e[0][0], e[0][1], e[1][0], e[1][1])
 	pr := &Proof{}
 
 	if s.plus {
-		pr.Ch[0] = ω
-		pr.Ch[1] = ch.Sub(ω)
-		pr.Rho[0] = r1.Sub(s.α.Mul(pr.Ch[0]))
-		pr.Rho[1] = r2.Sub(s.α.Mul(pr.Ch[1]))
+		pr.Ch[0] = w
+		pr.Ch[1] = ch.Sub(w)
+		pr.R[0] = r1.Sub(s.a.Mul(pr.Ch[0]))
+		pr.R[1] = r2.Sub(s.a.Mul(pr.Ch[1]))
 	} else {
-		pr.Ch[0] = ch.Sub(ω)
-		pr.Ch[1] = ω
-		pr.Rho[0] = r1.Sub(s.α.Mul(pr.Ch[0]))
-		pr.Rho[1] = r2
+		pr.Ch[0] = ch.Sub(w)
+		pr.Ch[1] = w
+		pr.R[0] = r1.Sub(s.a.Mul(pr.Ch[0]))
+		pr.R[1] = r2
 	}
 
 	return pr
 }
 
 func (c *Commitment) Verify(p *Proof) bool {
-	var ε [2][2]*Point
-	ε[0][0] = G.Exp(p.Rho[0]).Mul(c.A.Exp(p.Ch[0]))
-	ε[0][1] = c.B.Exp(p.Rho[0]).Mul(c.Φ.Exp(p.Ch[0]))
-	ε[1][0] = G.Exp(p.Rho[1]).Mul(c.A.Exp(p.Ch[1]))
-	ε[1][1] = c.B.Exp(p.Rho[1]).Mul(c.Φ.Div(G).Exp(p.Ch[1]))
-	ch := Challenge(G, c.Φ, c.A, c.B, ε[0][0], ε[0][1], ε[1][0], ε[1][1])
+	var e [2][2]*Point
+	e[0][0] = G.Exp(p.R[0]).Mul(c.A.Exp(p.Ch[0]))
+	e[0][1] = c.B.Exp(p.R[0]).Mul(c.C.Exp(p.Ch[0]))
+	e[1][0] = G.Exp(p.R[1]).Mul(c.A.Exp(p.Ch[1]))
+	e[1][1] = c.B.Exp(p.R[1]).Mul(c.C.Div(G).Exp(p.Ch[1]))
+	ch := Challenge(G, c.C, c.A, c.B, e[0][0], e[0][1], e[1][0], e[1][1])
 	return p.Ch[0].Add(p.Ch[1]).Equal(ch)
 }