nizk: update proof of linear relationship
This commit is contained in:
parent
b0fa32f533
commit
db71866b2c
123
src/nizk.rs
123
src/nizk.rs
|
@ -16,7 +16,6 @@ use ccs08::{RPPublicParams, RangeProof};
|
||||||
pub struct Proof<E: Engine> {
|
pub struct Proof<E: Engine> {
|
||||||
pub sig: Signature<E>,
|
pub sig: Signature<E>,
|
||||||
pub sigProof: SignatureProof<E>,
|
pub sigProof: SignatureProof<E>,
|
||||||
pub T: E::G1,
|
|
||||||
pub D: E::G1,
|
pub D: E::G1,
|
||||||
pub z: Vec<E::Fr>,
|
pub z: Vec<E::Fr>,
|
||||||
pub rpBC: RangeProof<E>,
|
pub rpBC: RangeProof<E>,
|
||||||
|
@ -44,20 +43,11 @@ impl<E: Engine> NIZKPublicParams<E> {
|
||||||
}
|
}
|
||||||
|
|
||||||
pub fn prove<R: Rng>(&self, rng: &mut R, r: E::Fr, oldWallet: Wallet<E>, newWallet: Wallet<E>,
|
pub fn prove<R: Rng>(&self, rng: &mut R, r: E::Fr, oldWallet: Wallet<E>, newWallet: Wallet<E>,
|
||||||
newWalletCom: Commitment<E>, rPrime: E::Fr, paymentToken: &Signature<E>, ) -> Proof<E> {
|
newWalletCom: Commitment<E>, rPrime: E::Fr, paymentToken: &Signature<E>) -> Proof<E> {
|
||||||
//Commitment phase
|
//Commitment phase
|
||||||
//Commit linear relationship
|
|
||||||
let mut T = self.comParams.pub_bases[2].clone();
|
|
||||||
let t1 = E::Fr::rand(rng);
|
|
||||||
T.mul_assign(t1);
|
|
||||||
let mut h = self.comParams.pub_bases[0].clone();
|
|
||||||
let t2 = E::Fr::rand(rng);
|
|
||||||
h.mul_assign(t2);
|
|
||||||
T.add_assign(&h);
|
|
||||||
|
|
||||||
//commit commitment
|
//commit commitment
|
||||||
let mut D = E::G1::zero();
|
let mut D = E::G1::zero();
|
||||||
let mut t = Vec::<E::Fr>::with_capacity(self.comParams.pub_bases.len() - 1);
|
let mut t = Vec::<E::Fr>::with_capacity(self.comParams.pub_bases.len());
|
||||||
for g in self.comParams.pub_bases.clone() {
|
for g in self.comParams.pub_bases.clone() {
|
||||||
let ti = E::Fr::rand(rng);
|
let ti = E::Fr::rand(rng);
|
||||||
t.push(ti);
|
t.push(ti);
|
||||||
|
@ -67,34 +57,23 @@ impl<E: Engine> NIZKPublicParams<E> {
|
||||||
}
|
}
|
||||||
|
|
||||||
//commit signature
|
//commit signature
|
||||||
let proofState = self.keypair.prove_commitment(rng, &self.mpk, &paymentToken, Some(vec!(t[1])), None);
|
let fr1 = E::Fr::rand(rng);
|
||||||
|
let proofState = self.keypair.prove_commitment(rng, &self.mpk, &paymentToken, Some(vec!(t[1], fr1, t[3].clone(), t[4].clone())), None);
|
||||||
|
|
||||||
//commit range proof
|
//commit range proof
|
||||||
let rpStateBC = self.rpParamsBC.prove_commitment(rng, newWallet.bc.clone(), newWalletCom.clone(), 3, Some(t[1..].to_vec()), Some(t[0].clone()));
|
let rpStateBC = self.rpParamsBC.prove_commitment(rng, newWallet.bc.clone(), newWalletCom.clone(), 3, Some(t[1..].to_vec()), Some(t[0].clone()));
|
||||||
let rpStateBM = self.rpParamsBM.prove_commitment(rng, newWallet.bm.clone(), newWalletCom.clone(), 4, Some(t[1..].to_vec()), Some(t[0].clone()));
|
let rpStateBM = self.rpParamsBM.prove_commitment(rng, newWallet.bm.clone(), newWalletCom.clone(), 4, Some(t[1..].to_vec()), Some(t[0].clone()));
|
||||||
|
|
||||||
//Compute challenge
|
//Compute challenge
|
||||||
let challenge = NIZKPublicParams::<E>::hash(proofState.a, vec! {T, D, rpStateBC.ps1.D, rpStateBC.ps2.D, rpStateBM.ps1.D, rpStateBM.ps2.D});
|
let challenge = NIZKPublicParams::<E>::hash(proofState.a, vec! {D, rpStateBC.ps1.D, rpStateBC.ps2.D, rpStateBM.ps1.D, rpStateBM.ps2.D});
|
||||||
|
|
||||||
//Response phase
|
//Response phase
|
||||||
//response for signature
|
//response for signature
|
||||||
let oldWalletVec = oldWallet.as_fr_vec();
|
let oldWalletVec = oldWallet.as_fr_vec();
|
||||||
let sigProof = self.keypair.prove_response(&proofState, challenge, &mut oldWalletVec.clone());
|
let sigProof = self.keypair.prove_response(&proofState, challenge, &mut oldWalletVec.clone());
|
||||||
|
|
||||||
//response linear relationship
|
|
||||||
let mut z = Vec::<E::Fr>::with_capacity(t.len() + 2);
|
|
||||||
let mut z1 = newWallet.wpk.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);
|
|
||||||
z.push(z2);
|
|
||||||
|
|
||||||
//response commitment
|
//response commitment
|
||||||
|
let mut z = Vec::<E::Fr>::with_capacity(t.len());
|
||||||
let mut z0 = rPrime.clone();
|
let mut z0 = rPrime.clone();
|
||||||
z0.mul_assign(&challenge);
|
z0.mul_assign(&challenge);
|
||||||
z0.add_assign(&t[0]);
|
z0.add_assign(&t[0]);
|
||||||
|
@ -111,39 +90,12 @@ impl<E: Engine> NIZKPublicParams<E> {
|
||||||
let rpBC = self.rpParamsBC.prove_response(rPrime.clone(), &rpStateBC, challenge.clone(), 3, vec! {newWalletVec[0], newWalletVec[1], newWalletVec[3]});
|
let rpBC = self.rpParamsBC.prove_response(rPrime.clone(), &rpStateBC, challenge.clone(), 3, vec! {newWalletVec[0], newWalletVec[1], newWalletVec[3]});
|
||||||
let rpBM = self.rpParamsBM.prove_response(rPrime.clone(), &rpStateBM, challenge.clone(), 4, vec! {newWalletVec[0], newWalletVec[1], newWalletVec[2]});
|
let rpBM = self.rpParamsBM.prove_response(rPrime.clone(), &rpStateBM, challenge.clone(), 4, vec! {newWalletVec[0], newWalletVec[1], newWalletVec[2]});
|
||||||
|
|
||||||
Proof { sig: proofState.blindSig, sigProof, T, D, z, rpBC, rpBM }
|
Proof { sig: proofState.blindSig, sigProof, D, z, rpBC, rpBM }
|
||||||
}
|
}
|
||||||
|
|
||||||
pub fn verify(&self, proof: Proof<E>, epsilon: E::Fr, com1: &Commitment<E>, com2: &Commitment<E>, wpk: E::Fr) -> bool {
|
pub fn verify(&self, proof: Proof<E>, epsilon: E::Fr, com2: &Commitment<E>, wpk: E::Fr) -> bool {
|
||||||
//compute challenge
|
//compute challenge
|
||||||
let challenge = NIZKPublicParams::<E>::hash(proof.sigProof.a, vec! {proof.T, proof.D, proof.rpBC.p1.D, proof.rpBC.p2.D, proof.rpBM.p1.D, proof.rpBM.p2.D});
|
let challenge = NIZKPublicParams::<E>::hash(proof.sigProof.a, vec! {proof.D, proof.rpBC.p1.D, proof.rpBC.p2.D, proof.rpBM.p1.D, proof.rpBM.p2.D});
|
||||||
|
|
||||||
//verify linear relationship
|
|
||||||
let mut gWpk = self.comParams.pub_bases[2].clone();
|
|
||||||
let mut minWpk = wpk.clone();
|
|
||||||
minWpk.negate();
|
|
||||||
gWpk.mul_assign(minWpk.into_repr());
|
|
||||||
let mut gEps = self.comParams.pub_bases[4].clone();
|
|
||||||
gEps.mul_assign(epsilon.into_repr());
|
|
||||||
let mut gMinEps = self.comParams.pub_bases[3].clone();
|
|
||||||
let mut mineps = epsilon.clone();
|
|
||||||
mineps.negate();
|
|
||||||
gMinEps.mul_assign(mineps.into_repr());
|
|
||||||
|
|
||||||
let mut commitment = com1.c.clone();
|
|
||||||
commitment.sub_assign(&com2.c.clone());
|
|
||||||
commitment.add_assign(&gWpk);
|
|
||||||
commitment.add_assign(&gEps);
|
|
||||||
commitment.add_assign(&gMinEps);
|
|
||||||
commitment.mul_assign(challenge.into_repr());
|
|
||||||
commitment.add_assign(&proof.T);
|
|
||||||
|
|
||||||
let mut g2 = self.comParams.pub_bases[2].clone();
|
|
||||||
g2.mul_assign(proof.z[0].into_repr());
|
|
||||||
let mut h = self.comParams.pub_bases[0].clone();
|
|
||||||
h.mul_assign(proof.z[1].into_repr());
|
|
||||||
g2.add_assign(&h);
|
|
||||||
let r = commitment == g2;
|
|
||||||
|
|
||||||
//verify knowledge of signature
|
//verify knowledge of signature
|
||||||
let r1 = self.keypair.public.verify_proof(&self.mpk, proof.sig, proof.sigProof.clone(), challenge);
|
let r1 = self.keypair.public.verify_proof(&self.mpk, proof.sig, proof.sigProof.clone(), challenge);
|
||||||
|
@ -153,8 +105,8 @@ impl<E: Engine> NIZKPublicParams<E> {
|
||||||
comc.mul_assign(challenge.into_repr());
|
comc.mul_assign(challenge.into_repr());
|
||||||
comc.add_assign(&proof.D.clone());
|
comc.add_assign(&proof.D.clone());
|
||||||
let mut x = E::G1::zero();
|
let mut x = E::G1::zero();
|
||||||
for i in 2..proof.z.len() {
|
for i in 0..proof.z.len() {
|
||||||
let mut base = self.comParams.pub_bases[i - 2].clone();
|
let mut base = self.comParams.pub_bases[i].clone();
|
||||||
base.mul_assign(proof.z[i].into_repr());
|
base.mul_assign(proof.z[i].into_repr());
|
||||||
x.add_assign(&base);
|
x.add_assign(&base);
|
||||||
}
|
}
|
||||||
|
@ -164,27 +116,37 @@ impl<E: Engine> NIZKPublicParams<E> {
|
||||||
let r3 = self.rpParamsBC.verify(proof.rpBC.clone(), challenge.clone(), 3);
|
let r3 = self.rpParamsBC.verify(proof.rpBC.clone(), challenge.clone(), 3);
|
||||||
let r4 = self.rpParamsBM.verify(proof.rpBM.clone(), challenge.clone(), 4);
|
let r4 = self.rpParamsBM.verify(proof.rpBM.clone(), challenge.clone(), 4);
|
||||||
|
|
||||||
let mut r5 = proof.z[3] == proof.sigProof.zsig[0];
|
//verify linear relationship
|
||||||
r5 = r5 && proof.z[2] == proof.rpBC.p1.zr;
|
let mut r5 = proof.z[1] == proof.sigProof.zsig[0];
|
||||||
r5 = r5 && proof.z[2] == proof.rpBC.p2.zr;
|
let mut zsig2 = proof.sigProof.zsig[2].clone();
|
||||||
r5 = r5 && proof.z[2] == proof.rpBM.p1.zr;
|
let mut epsC = epsilon.clone();
|
||||||
r5 = r5 && proof.z[2] == proof.rpBM.p2.zr;
|
epsC.mul_assign(&challenge.clone());
|
||||||
for i in 3..proof.z.len() {
|
zsig2.sub_assign(&epsC.clone());
|
||||||
if i == 5 {
|
r5 = r5 && proof.z[3] == zsig2;
|
||||||
r5 = r5 && proof.z[i] == proof.rpBM.p1.zs[i-3];
|
let mut zsig3 = proof.sigProof.zsig[3].clone();
|
||||||
r5 = r5 && proof.z[i] == proof.rpBM.p2.zs[i-3].clone();
|
zsig3.add_assign(&epsC.clone());
|
||||||
} else if i == 6 {
|
r5 = r5 && proof.z[4] == zsig3;
|
||||||
r5 = r5 && proof.z[i] == proof.rpBC.p1.zs[i-4].clone();
|
|
||||||
r5 = r5 && proof.z[i] == proof.rpBC.p2.zs[i-4].clone();
|
r5 = r5 && proof.z[0] == proof.rpBC.p1.zr;
|
||||||
|
r5 = r5 && proof.z[0] == proof.rpBC.p2.zr;
|
||||||
|
r5 = r5 && proof.z[0] == proof.rpBM.p1.zr;
|
||||||
|
r5 = r5 && proof.z[0] == proof.rpBM.p2.zr;
|
||||||
|
for i in 1..proof.z.len() {
|
||||||
|
if i == 3 {
|
||||||
|
r5 = r5 && proof.z[i] == proof.rpBM.p1.zs[i-1];
|
||||||
|
r5 = r5 && proof.z[i] == proof.rpBM.p2.zs[i-1].clone();
|
||||||
|
} else if i == 4 {
|
||||||
|
r5 = r5 && proof.z[i] == proof.rpBC.p1.zs[i-2].clone();
|
||||||
|
r5 = r5 && proof.z[i] == proof.rpBC.p2.zs[i-2].clone();
|
||||||
} else {
|
} else {
|
||||||
r5 = r5 && proof.z[i] == proof.rpBC.p1.zs[i-3].clone();
|
r5 = r5 && proof.z[i] == proof.rpBC.p1.zs[i-1].clone();
|
||||||
r5 = r5 && proof.z[i] == proof.rpBC.p2.zs[i-3].clone();
|
r5 = r5 && proof.z[i] == proof.rpBC.p2.zs[i-1].clone();
|
||||||
r5 = r5 && proof.z[i] == proof.rpBM.p1.zs[i-3].clone();
|
r5 = r5 && proof.z[i] == proof.rpBM.p1.zs[i-1].clone();
|
||||||
r5 = r5 && proof.z[i] == proof.rpBM.p2.zs[i-3].clone();
|
r5 = r5 && proof.z[i] == proof.rpBM.p2.zs[i-1].clone();
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
r && r1 && r2 && r3 && r4 && r5
|
r1 && r2 && r3 && r4 && r5
|
||||||
}
|
}
|
||||||
|
|
||||||
fn hash(a: E::Fqk, T: Vec<E::G1>) -> E::Fr {
|
fn hash(a: E::Fqk, T: Vec<E::G1>) -> E::Fr {
|
||||||
|
@ -230,8 +192,7 @@ mod tests {
|
||||||
let proof = pubParams.prove(rng, r, wallet1, wallet2,
|
let proof = pubParams.prove(rng, r, wallet1, wallet2,
|
||||||
commitment2.clone(), rprime, &paymentToken);
|
commitment2.clone(), rprime, &paymentToken);
|
||||||
|
|
||||||
assert_eq!(pubParams.verify(proof, Fr::from_str(&epsilon.to_string()).unwrap(), &commitment1,
|
assert_eq!(pubParams.verify(proof, Fr::from_str(&epsilon.to_string()).unwrap(), &commitment2, wpk), true);
|
||||||
&commitment2, wpk), true);
|
|
||||||
}
|
}
|
||||||
|
|
||||||
#[test]
|
#[test]
|
||||||
|
@ -261,17 +222,17 @@ mod tests {
|
||||||
let blindPaymentToken = pubParams.keypair.sign_blind(rng, &pubParams.mpk, commitment1.clone());
|
let blindPaymentToken = pubParams.keypair.sign_blind(rng, &pubParams.mpk, commitment1.clone());
|
||||||
let paymentToken = pubParams.keypair.unblind(&r, &blindPaymentToken);
|
let paymentToken = pubParams.keypair.unblind(&r, &blindPaymentToken);
|
||||||
let proof = pubParams.prove(rng, r, wallet1.clone(), wallet3, commitment2.clone(), rprime, &paymentToken);
|
let proof = pubParams.prove(rng, r, wallet1.clone(), wallet3, commitment2.clone(), rprime, &paymentToken);
|
||||||
assert_eq!(pubParams.verify(proof, Fr::from_str(&epsilon.to_string()).unwrap(), &commitment1, &commitment2, wpk), false);
|
assert_eq!(pubParams.verify(proof, Fr::from_str(&epsilon.to_string()).unwrap(), &commitment2, wpk), false);
|
||||||
|
|
||||||
let bm2Prime = bm.clone();
|
let bm2Prime = bm.clone();
|
||||||
let wallet4 = Wallet { pkc, wpk: wpkprime, bc: bc2, bm: bm2Prime };
|
let wallet4 = Wallet { pkc, wpk: wpkprime, bc: bc2, bm: bm2Prime };
|
||||||
let commitment2 = pubParams.comParams.commit(&wallet4.as_fr_vec(), &rprime);
|
let commitment2 = pubParams.comParams.commit(&wallet4.as_fr_vec(), &rprime);
|
||||||
let proof = pubParams.prove(rng, r, wallet1.clone(), wallet4, commitment2.clone(), rprime, &paymentToken);
|
let proof = pubParams.prove(rng, r, wallet1.clone(), wallet4, commitment2.clone(), rprime, &paymentToken);
|
||||||
assert_eq!(pubParams.verify(proof, Fr::from_str(&epsilon.to_string()).unwrap(), &commitment1, &commitment2, wpk), false);
|
assert_eq!(pubParams.verify(proof, Fr::from_str(&epsilon.to_string()).unwrap(), &commitment2, wpk), false);
|
||||||
|
|
||||||
let wallet5 = Wallet { pkc: Fr::rand(rng), wpk: wpkprime, bc: bc2, bm: bm2 };
|
let wallet5 = Wallet { pkc: Fr::rand(rng), wpk: wpkprime, bc: bc2, bm: bm2 };
|
||||||
let commitment2 = pubParams.comParams.commit(&wallet5.as_fr_vec(), &rprime);
|
let commitment2 = pubParams.comParams.commit(&wallet5.as_fr_vec(), &rprime);
|
||||||
let proof = pubParams.prove(rng, r, wallet1.clone(), wallet5, commitment2.clone(), rprime, &paymentToken);
|
let proof = pubParams.prove(rng, r, wallet1.clone(), wallet5, commitment2.clone(), rprime, &paymentToken);
|
||||||
assert_eq!(pubParams.verify(proof, Fr::from_str(&epsilon.to_string()).unwrap(), &commitment1, &commitment2, wpk), false);
|
assert_eq!(pubParams.verify(proof, Fr::from_str(&epsilon.to_string()).unwrap(), &commitment2, wpk), false);
|
||||||
}
|
}
|
||||||
}
|
}
|
Loading…
Reference in New Issue