nizk: add proof of knowledge of committed values

src/nizk.rs

@@ -15,12 +15,14 @@ struct Proof<E: Engine> {
     sig: Signature<E>,
     sigProof: SignatureProof<E>,
     T: E::G2,
+    D: E::G2,
     z: Vec<E::Fr>,
 }
 
 fn prove<R: Rng, E: Engine>(rng: &mut R, comParams: &CSMultiParams<E>, com1: &Commitment<E>, com2: &Commitment<E>, oldWallet: Vec<E::Fr>, r: E::Fr,
                             newWallet: Vec<E::Fr>, rPrime: E::Fr, paymentToken: &Signature<E>,
                             mpk: &PublicParams<E>, kp: &BlindKeyPair<E>) -> Proof<E> {
+    //Commitment phase
     let mut T = comParams.pub_bases[2].clone();
     let t1 = E::Fr::rand(rng);
     T.mul_assign(t1);
@@ -29,23 +31,48 @@ fn prove<R: Rng, E: Engine>(rng: &mut R, comParams: &CSMultiParams<E>, com1: &Co
     h.mul_assign(t2);
     T.add_assign(&h);
     let proofState = kp.prove_commitment(rng, &mpk, &paymentToken);
-    let challenge = hash::<E>(proofState.a, T);
+
+    let mut D = E::G2::zero();
+    let mut t = Vec::<E::Fr>::with_capacity(comParams.pub_bases.len() - 1);
+    for g in comParams.pub_bases.clone() {
+        let ti = E::Fr::rand(rng);
+        t.push(ti);
+        let mut gt = g.clone();
+        gt.mul_assign(ti.into_repr());
+        D.add_assign(&gt);
+    }
+
+    //Compute challenge
+    let challenge = hash::<E>(proofState.a, T, D);
+
+    //Response phase
     let sigProof = kp.prove_response(&proofState, challenge, &mut vec! {hash_g2_to_fr::<E>(&com1.c)});
 
+    let mut z = Vec::<E::Fr>::with_capacity(t.len() + 2);
     let mut z1 = newWallet[2].clone();
     z1.negate();
     z1.mul_assign(&challenge);
     z1.add_assign(&t1);
+    z.push(z1);
     let mut z2 = r.clone();
     z2.sub_assign(&rPrime.clone());
     z2.mul_assign(&challenge);
     z2.add_assign(&t2);
-    Proof { sig: proofState.blindSig, sigProof, T, z: vec! {z1, z2} }
+    z.push(z2);
+
+    for i in 0..t.len() {
+        let mut zi = newWallet[i].clone();
+        zi.mul_assign(&challenge);
+        zi.add_assign(&t[i]);
+        z.push(zi);
+    }
+
+    Proof { sig: proofState.blindSig, sigProof, T, D, z }
 }
 
 fn verify<E: Engine>(proof: Proof<E>, epsilon: E::Fr, com1: &Commitment<E>, com2: &Commitment<E>,
                      paymentToken: &Signature<E>, wpk: E::Fr, comParams: &CSMultiParams<E>, mpk: &PublicParams<E>, pk: &BlindPublicKey<E>) -> bool {
-    let challenge = hash::<E>(proof.sigProof.a, proof.T);
+    let challenge = hash::<E>(proof.sigProof.a, proof.T, proof.D);
 
     let mut gWpk = comParams.pub_bases[2].clone();
     let mut minWpk = wpk.clone();
@@ -75,13 +102,24 @@ fn verify<E: Engine>(proof: Proof<E>, epsilon: E::Fr, com1: &Commitment<E>, com2
 
     let r = pk.verify_proof(&mpk, proof.sig, proof.sigProof, challenge);
 
-    r && commitment == g2
+    let mut comc = com2.c.clone();
+    comc.mul_assign(challenge.into_repr());
+    comc.add_assign(&proof.D.clone());
+    let mut x = E::G2::zero();
+    for i in 2..proof.z.len() {
+        let mut base = comParams.pub_bases[i - 2].clone();
+        base.mul_assign(proof.z[i].into_repr());
+        x.add_assign(&base);
+    }
+
+    r && commitment == g2 && x == comc
 }
 
-fn hash<E: Engine>(a: E::Fqk, T: E::G2) -> E::Fr {
+fn hash<E: Engine>(a: E::Fqk, T: E::G2, D: E::G2) -> E::Fr {
     let mut x_vec: Vec<u8> = Vec::new();
     x_vec.extend(format!("{}", a).bytes());
     x_vec.extend(format!("{}", T).bytes());
+    x_vec.extend(format!("{}", D).bytes());
 
     util::hash_to_fr::<E>(x_vec)
 }