add folding verifier impl, add last steps of folding prover (except G(X) & K(X))

README.md

@@ -1,6 +1,6 @@
 # protogalaxy-poc
 
-Proof of concept implementation of ProtoGalaxy (https://eprint.iacr.org/2023/1106.pdf).
+Proof of concept implementation of ProtoGalaxy (https://eprint.iacr.org/2023/1106.pdf) using [arkworks](https://github.com/arkworks-rs).
 
 > Do not use in production.
 

src/protogalaxy.rs

@@ -2,11 +2,15 @@ use ark_crypto_primitives::sponge::Absorb;
 use ark_ec::{CurveGroup, Group};
 use ark_ff::fields::PrimeField;
 use ark_std::log2;
-use ark_std::{One, Zero};
+use ark_std::{cfg_into_iter, One, Zero};
 use std::marker::PhantomData;
-use std::ops::Add;
+use std::ops::{Add, Mul};
 
-use ark_poly::{univariate::SparsePolynomial, Polynomial};
+use ark_ff::{batch_inversion, FftField};
+use ark_poly::{
+    univariate::{DensePolynomial, SparsePolynomial},
+    DenseUVPolynomial, EvaluationDomain, Evaluations, GeneralEvaluationDomain, Polynomial,
+};
 
 use crate::pedersen::{Commitment, Params as PedersenParams, Pedersen, Proof as PedersenProof};
 use crate::transcript::Transcript;
@@ -38,25 +42,28 @@ where
     pub fn prover(
         tr: &mut Transcript<C::ScalarField, C>,
         pedersen_params: &PedersenParams<C>,
-        r1cs: R1CS<C::ScalarField>,
+        r1cs: &R1CS<C::ScalarField>,
         // running instance
         instance: CommittedInstance<C>,
         w: Witness<C>,
         // incomming instances
         vec_instances: Vec<CommittedInstance<C>>,
         vec_w: Vec<Witness<C>>,
+    ) -> (
+        Vec<C::ScalarField>,
+        Vec<C::ScalarField>,
+        CommittedInstance<C>,
+        Witness<C>,
     ) {
         let t = instance.betas.len();
         let n = r1cs.A[0].len();
 
+        // TODO initialize transcript
         let delta = tr.get_challenge();
-
         let deltas = powers_of_beta(delta, t);
 
         let f_w = eval_f(&r1cs, &w.w);
-        dbg!(w.w.len());
-        dbg!(f_w.len());
-        dbg!(n);
+        // println!("is f(w) {:?}", f_w);
 
         // F(X)
         let mut F_X: SparsePolynomial<C::ScalarField> = SparsePolynomial::zero();
@@ -65,9 +72,12 @@ where
             let curr = &lhs * f_w[i];
             F_X = F_X.add(curr);
         }
-        // TODO return F(X)
+
+        let F_X_dense = DensePolynomial::from(F_X.clone());
+        tr.add_vec(&F_X_dense.coeffs);
 
         let alpha = tr.get_challenge();
+
         // eval F(alpha)
         let F_alpha = F_X.evaluate(&alpha);
 
@@ -89,12 +99,122 @@ where
         assert!(check_instance(
             r1cs,
             CommittedInstance {
-                phi: instance.phi,
-                betas: betas_star,
+                phi: instance.phi.clone(),
+                betas: betas_star.clone(),
                 e: F_alpha,
             },
             w.clone(),
         ));
+
+        let gamma = tr.get_challenge();
+
+        // TODO WIP compute G(X) & K(X)
+        let G_evals: Vec<C::ScalarField> = vec![C::ScalarField::zero(); n];
+        let G_X: DensePolynomial<C::ScalarField> =
+            Evaluations::<C::ScalarField>::from_vec_and_domain(G_evals.clone(), H).interpolate();
+        // dbg!(&G_X);
+        let (K_X, remainder) = G_X.divide_by_vanishing_poly(H).unwrap();
+        // dbg!(&K_X);
+        assert!(remainder.is_zero());
+
+        let Z_X: DensePolynomial<C::ScalarField> = H.vanishing_polynomial().into();
+
+        let e_star =
+            F_alpha * L_X[0].evaluate(&gamma) + Z_X.evaluate(&gamma) * K_X.evaluate(&gamma);
+
+        let mut phi_star: C = instance.phi.0 * L_X[0].evaluate(&gamma);
+        for i in 0..k {
+            phi_star += vec_instances[i].phi.0 * L_X[i].evaluate(&gamma);
+        }
+        let mut w_star: Vec<C::ScalarField> = vec_scalar_mul(&w.w, &L_X[0].evaluate(&gamma));
+        for i in 0..k {
+            w_star = vec_add(
+                &w_star,
+                &vec_scalar_mul(&vec_w[i].w, &L_X[i].evaluate(&gamma)),
+            );
+        }
+
+        (
+            F_X_dense.coeffs,
+            K_X.coeffs,
+            CommittedInstance {
+                betas: betas_star,
+                phi: Commitment(phi_star),
+                e: e_star,
+            },
+            Witness {
+                w: w_star,
+                r_w: w.r_w,
+            },
+        )
+    }
+
+    pub fn verifier(
+        tr: &mut Transcript<C::ScalarField, C>,
+        pedersen_params: &PedersenParams<C>,
+        r1cs: R1CS<C::ScalarField>,
+        // running instance
+        instance: CommittedInstance<C>,
+        // incomming instances
+        vec_instances: Vec<CommittedInstance<C>>,
+        // polys from P
+        F_coeffs: Vec<C::ScalarField>,
+        K_coeffs: Vec<C::ScalarField>,
+    ) -> CommittedInstance<C> {
+        let t = instance.betas.len();
+        let n = r1cs.A[0].len();
+
+        let delta = tr.get_challenge();
+        let deltas = powers_of_beta(delta, t);
+
+        tr.add_vec(&F_coeffs);
+
+        let alpha = tr.get_challenge();
+        let alphas = all_powers(alpha, n);
+
+        // dbg!(instance.e);
+        // dbg!(F_coeffs[0]);
+
+        // F(alpha) = e + \sum_t F_i * alpha^i
+        let mut F_alpha = instance.e;
+        for (i, F_i) in F_coeffs.iter().enumerate() {
+            F_alpha += *F_i * alphas[i];
+        }
+
+        let betas_star: Vec<C::ScalarField> = instance
+            .betas
+            .iter()
+            .zip(
+                deltas
+                    .iter()
+                    .map(|delta_i| alpha * delta_i)
+                    .collect::<Vec<C::ScalarField>>(),
+            )
+            .map(|(beta_i, delta_i_alpha)| *beta_i + delta_i_alpha)
+            .collect();
+
+        let gamma = tr.get_challenge();
+
+        let k = vec_instances.len();
+        let domain_k = GeneralEvaluationDomain::<C::ScalarField>::new(k).unwrap();
+        let L_X: Vec<DensePolynomial<C::ScalarField>> = lagrange_polys(domain_k);
+        let Z_X: DensePolynomial<C::ScalarField> = domain_k.vanishing_polynomial().into();
+        let K_X: DensePolynomial<C::ScalarField> =
+            DensePolynomial::<C::ScalarField>::from_coefficients_vec(K_coeffs);
+        let e_star =
+            F_alpha * L_X[0].evaluate(&gamma) + Z_X.evaluate(&gamma) * K_X.evaluate(&gamma);
+
+        let mut phi_star: C = instance.phi.0 * L_X[0].evaluate(&gamma);
+        for i in 0..k {
+            phi_star += vec_instances[i].phi.0 * L_X[i].evaluate(&gamma);
+        }
+
+        // return the folded instance
+        CommittedInstance {
+            betas: betas_star,
+            phi: Commitment(phi_star),
+            e: e_star,
+        }
     }
 }
 
@@ -134,6 +254,19 @@ fn pow_i_over_x(i: usize, betas: &Vec, deltas: &Vec) -> Spa
     r
 }
 
+// method from caulk: https://github.com/caulk-crypto/caulk/tree/8210b51fb8a9eef4335505d1695c44ddc7bf8170/src/multi/setup.rs#L300
+fn lagrange_polys<F: PrimeField>(domain_n: GeneralEvaluationDomain<F>) -> Vec<DensePolynomial<F>> {
+    let mut lagrange_polynomials: Vec<DensePolynomial<F>> = Vec::new();
+
+    for i in 0..domain_n.size() {
+        let evals: Vec<F> = cfg_into_iter!(0..domain_n.size())
+            .map(|k| if k == i { F::one() } else { F::zero() })
+            .collect();
+        lagrange_polynomials.push(Evaluations::from_vec_and_domain(evals, domain_n).interpolate());
+    }
+    lagrange_polynomials
+}
+
 #[derive(Clone, Debug)]
 pub struct R1CS<F: PrimeField> {
     pub A: Vec<Vec<F>>,
@@ -150,7 +283,7 @@ fn eval_f(r1cs: &R1CS, w: &Vec) -> Vec {
 }
 
 fn check_instance<C: CurveGroup>(
-    r1cs: R1CS<C::ScalarField>,
+    r1cs: &R1CS<C::ScalarField>,
     instance: CommittedInstance<C>,
     w: Witness<C>,
 ) -> bool {
@@ -298,16 +431,24 @@ mod tests {
     }
 
     #[test]
-    fn test_fold_prover() {
+    fn test_fold() {
         let mut rng = ark_std::test_rng();
         let pedersen_params = Pedersen::<G1Projective>::new_params(&mut rng, 100); // 100 is wip, will get it from actual vec
         let poseidon_config = poseidon_test_config::<Fr>();
 
+        let k = 5;
+
         let r1cs = get_test_r1cs::<Fr>();
         let mut z = get_test_z::<Fr>(3);
+        let mut zs: Vec<Vec<Fr>> = Vec::new();
+        for i in 0..k {
+            let z_i = get_test_z::<Fr>(i + 4);
+            zs.push(z_i);
+        }
 
-        // init Prover's transcript
+        // init Prover & Verifier's transcript
         let mut transcript_p = Transcript::<Fr, G1Projective>::new(&poseidon_config);
+        let mut transcript_v = Transcript::<Fr, G1Projective>::new(&poseidon_config);
 
         let n = z.len();
         let t = log2(n) as usize;
@@ -318,24 +459,60 @@ mod tests {
         let betas = powers_of_beta(beta, t);
 
         let witness = Witness::<G1Projective> {
-            w: z, // WIP
+            w: z.clone(), // WIP
             r_w: Fr::rand(&mut rng),
         };
         let phi = Pedersen::<G1Projective>::commit(&pedersen_params, &witness.w, &witness.r_w);
         let instance = CommittedInstance::<G1Projective> {
             phi,
-            betas,
+            betas: betas.clone(),
             e: Fr::zero(),
         };
+        // same for the other instances
+        let mut witnesses: Vec<Witness<G1Projective>> = Vec::new();
+        let mut instances: Vec<CommittedInstance<G1Projective>> = Vec::new();
+        for i in 0..k {
+            let witness_i = Witness::<G1Projective> {
+                w: zs[i].clone(), // WIP
+                r_w: Fr::rand(&mut rng),
+            };
+            let phi_i =
+                Pedersen::<G1Projective>::commit(&pedersen_params, &witness_i.w, &witness_i.r_w);
+            let instance_i = CommittedInstance::<G1Projective> {
+                phi: phi_i,
+                betas: betas.clone(),
+                e: Fr::zero(),
+            };
+            witnesses.push(witness_i);
+            instances.push(instance_i);
+        }
 
-        Folding::<G1Projective>::prover(
+        let (F_coeffs, K_coeffs, folded_instance, folded_witness) = Folding::<G1Projective>::prover(
             &mut transcript_p,
             &pedersen_params,
-            r1cs,
-            instance,
+            &r1cs,
+            instance.clone(),
             witness,
-            Vec::new(),
-            Vec::new(),
+            instances.clone(),
+            witnesses,
         );
+        dbg!(&F_coeffs);
+
+        // veriier
+        let folded_instance_v = Folding::<G1Projective>::verifier(
+            &mut transcript_v,
+            &pedersen_params,
+            r1cs.clone(), // TODO rm clone do borrow
+            instance,
+            instances,
+            F_coeffs,
+            K_coeffs,
+        );
+
+        assert_eq!(folded_instance.phi.0, folded_instance_v.phi.0);
+        assert_eq!(folded_instance.betas, folded_instance_v.betas);
+        assert_eq!(folded_instance.e, folded_instance_v.e);
+
+        // assert!(check_instance(&r1cs, folded_instance, folded_witness));
     }
 }