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protocol_1.rs
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use crate::modules::algebra::curve::bn128::{optimal_ate_pairing, FqOrder, G1Point, G2Point};
use crate::modules::algebra::field::Field;
use crate::modules::algebra::ring::Ring;
use crate::modules::arithmetization::qap::QAP;
use crate::modules::zksnark::utils::{
accumulate_curve_points, generate_alpha_challenge_vec, generate_challenge_vec,
generate_s_powers, get_h,
};
#[derive(Debug, Clone)]
pub struct ProofKey1 {
g1_ell_i_vec: Vec<G1Point>,
g2_r_i_vec: Vec<G2Point>,
g1_o_i_vec: Vec<G1Point>,
g1_alpha_ell_i_vec: Vec<G1Point>,
g2_alpha_r_i_vec: Vec<G2Point>,
g1_alpha_o_i_vec: Vec<G1Point>,
g1_sj_vec: Vec<G1Point>,
}
#[derive(Debug, Clone)]
pub struct VerificationKey1 {
g1_alpha: G1Point,
g2_alpha: G2Point,
g2_t_s: G2Point,
}
#[derive(Debug, Clone)]
pub struct Proof1 {
g1_ell: G1Point,
g2_r: G2Point,
g1_o: G1Point,
g1_ell_prime: G1Point,
g2_r_prime: G2Point,
g1_o_prime: G1Point,
g1_h: G1Point,
}
pub fn setup(g1: &G1Point, g2: &G2Point, qap: &QAP<FqOrder>) -> (ProofKey1, VerificationKey1) {
let s = FqOrder::random_element(&[]);
let alpha = FqOrder::random_element(&[]);
(
ProofKey1 {
g1_ell_i_vec: generate_challenge_vec(g1, &qap.ell_i_vec, &s),
g2_r_i_vec: generate_challenge_vec(g2, &qap.r_i_vec, &s),
g1_o_i_vec: generate_challenge_vec(g1, &qap.o_i_vec, &s),
g1_alpha_ell_i_vec: generate_alpha_challenge_vec(g1, &qap.ell_i_vec, &s, &alpha),
g2_alpha_r_i_vec: generate_alpha_challenge_vec(g2, &qap.r_i_vec, &s, &alpha),
g1_alpha_o_i_vec: generate_alpha_challenge_vec(g1, &qap.o_i_vec, &s, &alpha),
g1_sj_vec: generate_s_powers(g1, &s, qap.m),
},
VerificationKey1 {
g1_alpha: g1 * &alpha,
g2_alpha: g2 * &alpha,
g2_t_s: g2 * qap.t.eval(&s).sanitize(),
},
)
}
pub fn prove(assignment: &Vec<FqOrder>, proof_key: &ProofKey1, qap: &QAP<FqOrder>) -> Proof1 {
Proof1 {
g1_ell: accumulate_curve_points(&proof_key.g1_ell_i_vec, assignment),
g2_r: accumulate_curve_points(&proof_key.g2_r_i_vec, assignment),
g1_o: accumulate_curve_points(&proof_key.g1_o_i_vec, assignment),
g1_ell_prime: accumulate_curve_points(&proof_key.g1_alpha_ell_i_vec, assignment),
g2_r_prime: accumulate_curve_points(&proof_key.g2_alpha_r_i_vec, assignment),
g1_o_prime: accumulate_curve_points(&proof_key.g1_alpha_o_i_vec, assignment),
g1_h: get_h(qap, assignment).eval_with_powers_on_curve(&proof_key.g1_sj_vec),
}
}
pub fn verify(
g1: &G1Point,
g2: &G2Point,
proof: &Proof1,
verification_key: &VerificationKey1,
) -> bool {
let pairing1 = optimal_ate_pairing(&proof.g1_ell, &verification_key.g2_alpha);
let pairing2 = optimal_ate_pairing(&proof.g1_ell_prime, &g2);
if pairing1 != pairing2 {
return false;
}
let pairing3 = optimal_ate_pairing(&verification_key.g1_alpha, &proof.g2_r);
let pairing4 = optimal_ate_pairing(&g1, &proof.g2_r_prime);
if pairing3 != pairing4 {
return false;
}
let pairing5 = optimal_ate_pairing(&proof.g1_o, &verification_key.g2_alpha);
let pairing6 = optimal_ate_pairing(&proof.g1_o_prime, &g2);
if pairing5 != pairing6 {
return false;
}
let pairing7 = optimal_ate_pairing(&proof.g1_ell, &proof.g2_r);
let pairing8 = optimal_ate_pairing(&proof.g1_h, &verification_key.g2_t_s);
let pairing9 = optimal_ate_pairing(&proof.g1_o, &g2);
pairing7 == pairing8 * pairing9
}
pub fn interchange_attack(proof: &Proof1) -> Proof1 {
let mut new_proof = proof.clone();
new_proof.g1_ell = proof.g1_o.clone();
new_proof.g1_ell_prime = proof.g1_o_prime.clone();
new_proof
}
#[cfg(test)]
mod tests {
use super::*;
use num_traits::{One, Zero};
use crate::modules::algebra::curve::bn128::BN128;
use crate::modules::arithmetization::r1cs::R1CS;
#[test]
fn test_snark_naive_single_multiplication() {
let left = vec![
vec![
FqOrder::zero(),
FqOrder::zero(),
FqOrder::one(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
],
vec![
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::one(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
],
vec![
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::one(),
FqOrder::zero(),
],
];
let right = vec![
vec![
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::one(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
],
vec![
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::one(),
FqOrder::zero(),
FqOrder::zero(),
],
vec![
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::one(),
],
];
let out = vec![
vec![
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::one(),
FqOrder::zero(),
],
vec![
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::one(),
],
vec![
FqOrder::zero(),
FqOrder::one(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
FqOrder::zero(),
],
];
let v = vec![
FqOrder::one(),
FqOrder::from_value(210),
FqOrder::from_value(2),
FqOrder::from_value(3),
FqOrder::from_value(5),
FqOrder::from_value(7),
FqOrder::from_value(6),
FqOrder::from_value(35),
];
let v_prime = vec![
FqOrder::one(),
FqOrder::from_value(211),
FqOrder::from_value(2),
FqOrder::from_value(3),
FqOrder::from_value(5),
FqOrder::from_value(7),
FqOrder::from_value(6),
FqOrder::from_value(35),
];
let g1 = BN128::generator_g1();
let g2 = BN128::generator_g2();
let r1cs = R1CS::new(left, right, out);
let qap = QAP::from_r1cs(&r1cs);
let (proof_key, verification_key) = setup(&g1, &g2, &qap);
let proof = prove(&v, &proof_key, &qap);
assert!(verify(&g1, &g2, &proof, &verification_key));
let wrong_proof = prove(&v_prime, &proof_key, &qap);
assert!(!verify(&g1, &g2, &wrong_proof, &verification_key));
//let bogus_proof = interchange_attack(&proof);
//assert!(verify(&g1, &g2, &bogus_proof, &verification_key));
}
}