adding circuit test: binary range proof

Author: olegfomenko

circuit_test.go

@@ -185,7 +185,7 @@ func TestArithmeticCircuit2(t *testing.T) {
 		Fm: false,
 
 		F: func(typ PartitionType, index int) *int {
-			if typ == PartitionLL { // map all to no
+			if typ == PartitionLL { // map all to ll
 				return &index
 			}
 
@@ -217,6 +217,153 @@ func TestArithmeticCircuit2(t *testing.T) {
 	}
 }
 
+func TestArithmeticCircuitBinaryRangeProof(t *testing.T) {
+	value := []*big.Int{bint(0), bint(1), bint(1), bint(0)} // bin(0110) = dec(6)
+	// We have prove that value < 2^n - 1
+	// Proving of the bits count is automatic (public parameters dimension will not allow to verify prove for bigger value)
+	// Then we should prove that every value is a bit
+	// To do that have to prove that every value[i] * (value[i] - 1) = 0
+
+	// For the 4-bit value we will have te following constraints:
+	// value0*value0 = a0
+	// a0 - value0 = 0
+
+	// value1*value1 = a1
+	// a1 - value1 = 0
+
+	// value2*value2 = a2
+	// a2 - x2 = 0
+
+	// value3*value3 = a3
+	// a3 - value3 = 0
+
+	Nm := 4
+	No := 4
+	Nv := 2
+	K := 4
+
+	Nl := Nv * K       // 8
+	Nw := Nm + Nm + No // 12
+
+	a := hadamardMul(value, value) // a[i] = value[i] * value[i]
+
+	v := [][]*big.Int{
+		{value[0], a[0]},
+		{value[1], a[1]},
+		{value[2], a[2]},
+		{value[3], a[3]},
+	}
+
+	wl := value
+	wr := value
+	wo := a
+
+	w := append(wl, wr...)
+	w = append(w, wo...) // w = wl||wl||wo
+
+	wv := make([]*big.Int, 0, Nw)
+	for i := range v {
+		wv = append(wv, v[i]...)
+	}
+
+	Wm := [][]*big.Int{
+		{bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(1), bint(0), bint(0), bint(0)},
+		{bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(1), bint(0), bint(0)},
+		{bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(1), bint(0)},
+		{bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(1)},
+	} // Nm*Nw = 4 * 12
+
+	Am := zeroVector(Nm) // Nm
+
+	Wl := [][]*big.Int{
+		{bint(-1), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0)},
+		{bint(-1), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0)},
+		{bint(0), bint(-1), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0)},
+		{bint(0), bint(-1), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0)},
+		{bint(0), bint(0), bint(-1), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0)},
+		{bint(0), bint(0), bint(-1), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0)},
+		{bint(0), bint(0), bint(0), bint(-1), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0)},
+		{bint(0), bint(0), bint(0), bint(-1), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0), bint(0)},
+	} // Nl*Nw  = 8 * 12
+
+	Al := zeroVector(Nl)
+
+	fmt.Println("Circuit check:", matrixMulOnVector(w, Wm), "=", hadamardMul(wl, wr))
+	fmt.Println("Circuit check:", vectorAdd(vectorAdd(matrixMulOnVector(w, Wl), wv), Al), "= 0")
+
+	wnla := NewWeightNormLinearPublic(16, Nm)
+
+	public := &ArithmeticCircuitPublic{
+		Nm: Nm,
+		Nl: Nl,
+		Nv: Nv,
+		Nw: Nw,
+		No: No,
+		K:  K,
+
+		G:    wnla.G,
+		GVec: wnla.GVec[:Nm],
+		HVec: wnla.HVec[:9+Nv],
+
+		Wm: Wm,
+		Wl: Wl,
+		Am: Am,
+		Al: Al,
+		Fl: true,
+		Fm: false,
+
+		F: func(typ PartitionType, index int) *int {
+			if typ == PartitionNO { // map all to no
+				return &index
+			}
+
+			return nil
+		},
+
+		GVec_: wnla.GVec[Nm:],
+		HVec_: wnla.HVec[9+Nv:],
+	}
+
+	private := &ArithmeticCircuitPrivate{
+		V:  v,
+		Sv: []*big.Int{MustRandScalar(), MustRandScalar(), MustRandScalar(), MustRandScalar()},
+		Wl: wl,
+		Wr: wr,
+		Wo: wo,
+	}
+
+	V := make([]*bn256.G1, public.K)
+	for i := range V {
+		V[i] = public.CommitCircuit(private.V[i], private.Sv[i])
+	}
+
+	proof := ProveCircuit(public, NewKeccakFS(), private)
+	spew.Dump(proof)
+
+	if err := VerifyCircuit(public, V, NewKeccakFS(), proof); err != nil {
+		panic(err)
+	}
+}
+
+func matrixMulOnVector(a []*big.Int, m [][]*big.Int) []*big.Int {
+	var res []*big.Int
+
+	for i := 0; i < len(m); i++ {
+		res = append(res, vectorMul(a, m[i]))
+	}
+
+	return res
+}
+
+func hadamardMul(a, b []*big.Int) []*big.Int {
+	res := make([]*big.Int, len(a))
+	for i := range res {
+		res[i] = mul(a[i], b[i])
+	}
+
+	return res
+}
+
 func frac(a, b int) *big.Int {
 	return mul(bint(a), inv(bint(b)))
 }