1/// Adaptation of the prover methods and structs from arkworks/poly-commit's KZG10 implementation
  2/// into the CommitmentProver trait.
  3///
  4/// The motivation to do so, is that we want to be able to use KZG / Pedersen for committing to
  5/// vectors indistinctly, and the arkworks KZG10 implementation contains all the methods under the
  6/// same trait, which requires the Pairing trait, where the prover does not need access to the
  7/// Pairing but only to G1.
  8/// For our case, we want the folding schemes prover to be agnostic to pairings, since in the
  9/// non-ethereum cases we may use non-pairing-friendly curves with Pedersen commitments, so the
 10/// trait & types that we use should not depend on the Pairing type for the prover. Therefore, we
 11/// separate the CommitmentSchemeProver from the setup and verify phases, so the prover can be
 12/// defined without depending on pairings.
 13use ark_ec::{pairing::Pairing, CurveGroup, VariableBaseMSM};
 14use ark_ff::PrimeField;
 15use ark_poly::{
 16    univariate::{DenseOrSparsePolynomial, DensePolynomial},
 17    DenseUVPolynomial, EvaluationDomain, Evaluations, GeneralEvaluationDomain, Polynomial,
 18};
 19use ark_poly_commit::kzg10::{VerifierKey, KZG10};
 20use ark_std::rand::Rng;
 21use ark_std::{borrow::Cow, fmt::Debug};
 22use ark_std::{One, Zero};
 23use core::marker::PhantomData;
 24use rayon::iter::{IntoParallelRefIterator, ParallelIterator};
 25
 26use super::CommitmentProver;
 27use crate::transcript::Transcript;
 28use crate::Error;
 29
 30/// ProverKey defines a similar struct as in ark_poly_commit::kzg10::Powers, but instead of
 31/// depending on the Pairing trait it depends on the CurveGroup trait.
 32#[derive(Debug, Clone, Default, Eq, PartialEq)]
 33pub struct ProverKey<'a, C: CurveGroup> {
 34    /// Group elements of the form `β^i G`, for different values of `i`.
 35    pub powers_of_g: Cow<'a, [C::Affine]>,
 36}
 37
 38pub struct KZGSetup<P: Pairing> {
 39    _p: PhantomData<P>,
 40}
 41impl<'a, P> KZGSetup<P>
 42where
 43    P: Pairing,
 44{
 45    /// setup returns the tuple (ProverKey, VerifierKey). For real world deployments the setup must
 46    /// be computed in the most trustless way possible, usually through a MPC ceremony.
 47    pub fn setup<R: Rng>(rng: &mut R, len: usize) -> (ProverKey<'a, P::G1>, VerifierKey<P>) {
 48        let len = len.next_power_of_two();
 49        let universal_params = KZG10::<P, DensePolynomial<P::ScalarField>>::setup(len, false, rng)
 50            .expect("Setup failed");
 51        let powers_of_g = universal_params.powers_of_g[..=len].to_vec();
 52        let powers = ProverKey::<P::G1> {
 53            powers_of_g: ark_std::borrow::Cow::Owned(powers_of_g),
 54        };
 55        let vk = VerifierKey {
 56            g: universal_params.powers_of_g[0],
 57            gamma_g: universal_params.powers_of_gamma_g[&0],
 58            h: universal_params.h,
 59            beta_h: universal_params.beta_h,
 60            prepared_h: universal_params.prepared_h.clone(),
 61            prepared_beta_h: universal_params.prepared_beta_h.clone(),
 62        };
 63        (powers, vk)
 64    }
 65}
 66
 67/// KZGProver implements the CommitmentProver trait for the KZG commitment scheme.
 68#[derive(Debug, Clone, Default, Eq, PartialEq)]
 69pub struct KZGProver<'a, C: CurveGroup> {
 70    _a: PhantomData<&'a ()>,
 71    _c: PhantomData<C>,
 72}
 73impl<'a, C> CommitmentProver<C> for KZGProver<'a, C>
 74where
 75    C: CurveGroup,
 76{
 77    type Params = ProverKey<'a, C>;
 78    /// Proof is a tuple containing (evaluation, proof)
 79    type Proof = (C::ScalarField, C);
 80
 81    /// commit implements the CommitmentProver commit interface, adapting the implementation from
 82    /// https://github.com/arkworks-rs/poly-commit/tree/c724fa666e935bbba8db5a1421603bab542e15ab/poly-commit/src/kzg10/mod.rs#L178
 83    /// with the main difference being the removal of the blinding factors and the no-dependancy to
 84    /// the Pairing trait.
 85    fn commit(
 86        params: &Self::Params,
 87        v: &[C::ScalarField],
 88        _blind: &C::ScalarField,
 89    ) -> Result<C, Error> {
 90        if !_blind.is_zero() {
 91            return Err(Error::NotSupportedYet("blinding factors".to_string()));
 92        }
 93
 94        let polynomial = poly_from_vec(v.to_vec())?;
 95        check_degree_is_too_large(polynomial.degree(), params.powers_of_g.len())?;
 96
 97        let (num_leading_zeros, plain_coeffs) =
 98            skip_first_zero_coeffs_and_convert_to_bigints(&polynomial);
 99        let commitment = <C as VariableBaseMSM>::msm_bigint(
100            &params.powers_of_g[num_leading_zeros..],
101            &plain_coeffs,
102        );
103        Ok(commitment)
104    }
105
106    /// prove implements the CommitmentProver prove interface, adapting the implementation from
107    /// https://github.com/arkworks-rs/poly-commit/tree/c724fa666e935bbba8db5a1421603bab542e15ab/poly-commit/src/kzg10/mod.rs#L307
108    /// with the main difference being the removal of the blinding factors and the no-dependancy to
109    /// the Pairing trait.
110    fn prove(
111        params: &Self::Params,
112        transcript: &mut impl Transcript<C>,
113        cm: &C,
114        v: &[C::ScalarField],
115        _blind: &C::ScalarField,
116    ) -> Result<Self::Proof, Error> {
117        if !_blind.is_zero() {
118            return Err(Error::NotSupportedYet("blinding factors".to_string()));
119        }
120
121        let polynomial = poly_from_vec(v.to_vec())?;
122        check_degree_is_too_large(polynomial.degree(), params.powers_of_g.len())?;
123
124        transcript.absorb_point(cm)?;
125        let challenge = transcript.get_challenge();
126
127        // Compute q(x) = (p(x) - p(z)) / (x-z). Observe that this quotient does not change with z
128        // because p(z) is the remainder term. We can therefore omit p(z) when computing the
129        // quotient.
130        let divisor = DensePolynomial::<C::ScalarField>::from_coefficients_vec(vec![
131            -challenge,
132            C::ScalarField::one(),
133        ]);
134        let (witness_poly, remainder_poly) = DenseOrSparsePolynomial::from(&polynomial)
135            .divide_with_q_and_r(&DenseOrSparsePolynomial::from(&divisor))
136            // the panic inside `divide_with_q_and_r` should never be reached, since the divisor
137            // polynomial is constructed right before and is set to not be zero. And the `.unwrap`
138            // should not give an error.
139            .unwrap();
140        let evaluation = remainder_poly[0];
141
142        check_degree_is_too_large(witness_poly.degree(), params.powers_of_g.len())?;
143        let (num_leading_zeros, witness_coeffs) =
144            skip_first_zero_coeffs_and_convert_to_bigints(&witness_poly);
145        let proof = <C as VariableBaseMSM>::msm_bigint(
146            &params.powers_of_g[num_leading_zeros..],
147            &witness_coeffs,
148        );
149
150        Ok((evaluation, proof))
151    }
152}
153
154/// returns the interpolated polynomial of degree=v.len().next_power_of_two(), which passes through all
155/// the given elements of v.
156fn poly_from_vec<F: PrimeField>(v: Vec<F>) -> Result<DensePolynomial<F>, Error> {
157    let D = GeneralEvaluationDomain::<F>::new(v.len()).ok_or(Error::NewDomainFail)?;
158    Ok(Evaluations::from_vec_and_domain(v, D).interpolate())
159}
160
161fn check_degree_is_too_large(
162    degree: usize,
163    num_powers: usize,
164) -> Result<(), ark_poly_commit::error::Error> {
165    let num_coefficients = degree + 1;
166    if num_coefficients > num_powers {
167        Err(ark_poly_commit::error::Error::TooManyCoefficients {
168            num_coefficients,
169            num_powers,
170        })
171    } else {
172        Ok(())
173    }
174}
175
176fn skip_first_zero_coeffs_and_convert_to_bigints<F: PrimeField, P: DenseUVPolynomial<F>>(
177    p: &P,
178) -> (usize, Vec<F::BigInt>) {
179    let mut num_leading_zeros = 0;
180    while num_leading_zeros < p.coeffs().len() && p.coeffs()[num_leading_zeros].is_zero() {
181        num_leading_zeros += 1;
182    }
183    let coeffs = convert_to_bigints(&p.coeffs()[num_leading_zeros..]);
184    (num_leading_zeros, coeffs)
185}
186
187fn convert_to_bigints<F: PrimeField>(p: &[F]) -> Vec<F::BigInt> {
188    ark_std::cfg_iter!(p)
189        .map(|s| s.into_bigint())
190        .collect::<Vec<_>>()
191}
192
193#[cfg(test)]
194mod tests {
195    use ark_bn254::{Bn254, Fr, G1Projective as G1};
196    use ark_poly_commit::kzg10::{Commitment as KZG10Commitment, Proof as KZG10Proof, KZG10};
197    use ark_std::{test_rng, UniformRand};
198
199    use super::*;
200    use crate::transcript::poseidon::{poseidon_test_config, PoseidonTranscript};
201
202    #[test]
203    fn test_kzg_commitment_scheme() {
204        let rng = &mut test_rng();
205        let poseidon_config = poseidon_test_config::<Fr>();
206        let transcript_p = &mut PoseidonTranscript::<G1>::new(&poseidon_config);
207        let transcript_v = &mut PoseidonTranscript::<G1>::new(&poseidon_config);
208
209        let n = 10;
210        let (pk, vk): (ProverKey<G1>, VerifierKey<Bn254>) = KZGSetup::<Bn254>::setup(rng, n);
211
212        let v: Vec<Fr> = std::iter::repeat_with(|| Fr::rand(rng)).take(n).collect();
213        let cm = KZGProver::<G1>::commit(&pk, &v, &Fr::zero()).unwrap();
214
215        let (eval, proof) =
216            KZGProver::<G1>::prove(&pk, transcript_p, &cm, &v, &Fr::zero()).unwrap();
217
218        // verify the proof:
219        // get evaluation challenge
220        transcript_v.absorb_point(&cm).unwrap();
221        let challenge = transcript_v.get_challenge();
222        // verify the KZG proof using arkworks method
223        assert!(KZG10::<Bn254, DensePolynomial<Fr>>::check(
224            &vk,
225            &KZG10Commitment(cm.into_affine()),
226            challenge,
227            eval,
228            &KZG10Proof::<Bn254> {
229                w: proof.into_affine(),
230                random_v: None,
231            },
232        )
233        .unwrap());
234    }
235}