1// Copyright (c) 2023 Espresso Systems (espressosys.com)
  2// This file is part of the HyperPlonk library.
  3
  4// You should have received a copy of the MIT License
  5// along with the HyperPlonk library. If not, see <https://mit-license.org/>.
  6
  7//! Main module for univariate KZG commitment scheme
  8
  9use crate::pcs::{
 10    prelude::Commitment, PCSError, PolynomialCommitmentScheme, StructuredReferenceString,
 11};
 12use ark_ec::{
 13    pairing::Pairing, scalar_mul::variable_base::VariableBaseMSM, AffineRepr, CurveGroup,
 14};
 15use ark_ff::PrimeField;
 16use ark_poly::{univariate::DensePolynomial, DenseUVPolynomial, Polynomial};
 17use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 18use ark_std::{
 19    borrow::Borrow, end_timer, format, marker::PhantomData, rand::Rng, start_timer,
 20    string::ToString, vec, vec::Vec, One,
 21};
 22use srs::{UnivariateProverParam, UnivariateUniversalParams, UnivariateVerifierParam};
 23use std::ops::Mul;
 24
 25pub(crate) mod srs;
 26
 27/// KZG Polynomial Commitment Scheme on univariate polynomial.
 28pub struct UnivariateKzgPCS<E: Pairing> {
 29    #[doc(hidden)]
 30    phantom: PhantomData<E>,
 31}
 32
 33#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug, PartialEq, Eq)]
 34/// proof of opening
 35pub struct UnivariateKzgProof<E: Pairing> {
 36    /// Evaluation of quotients
 37    pub proof: E::G1Affine,
 38}
 39/// batch proof
 40pub type UnivariateKzgBatchProof<E> = Vec<UnivariateKzgProof<E>>;
 41
 42impl<E: Pairing> PolynomialCommitmentScheme<E> for UnivariateKzgPCS<E> {
 43    // Parameters
 44    type ProverParam = UnivariateProverParam<E::G1Affine>;
 45    type VerifierParam = UnivariateVerifierParam<E>;
 46    type SRS = UnivariateUniversalParams<E>;
 47    // Polynomial and its associated types
 48    type Polynomial = DensePolynomial<E::ScalarField>;
 49    type Point = E::ScalarField;
 50    type Evaluation = E::ScalarField;
 51    // Polynomial and its associated types
 52    type Commitment = Commitment<E>;
 53    type Proof = UnivariateKzgProof<E>;
 54
 55    // We do not implement batch univariate KZG at the current version.
 56    type BatchProof = ();
 57
 58    /// Build SRS for testing.
 59    ///
 60    /// - For univariate polynomials, `supported_size` is the maximum degree.
 61    ///
 62    /// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
 63    /// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
 64    fn gen_srs_for_testing<R: Rng>(
 65        rng: &mut R,
 66        supported_size: usize,
 67    ) -> Result<Self::SRS, PCSError> {
 68        Self::SRS::gen_srs_for_testing(rng, supported_size)
 69    }
 70
 71    /// Trim the universal parameters to specialize the public parameters.
 72    /// Input `max_degree` for univariate.
 73    /// `supported_num_vars` must be None or an error is returned.
 74    fn trim(
 75        srs: impl Borrow<Self::SRS>,
 76        supported_degree: Option<usize>,
 77        supported_num_vars: Option<usize>,
 78    ) -> Result<(Self::ProverParam, Self::VerifierParam), PCSError> {
 79        assert!(supported_num_vars.is_none());
 80        if supported_num_vars.is_some() {
 81            return Err(PCSError::InvalidParameters(
 82                "univariate should not receive a num_var param".to_string(),
 83            ));
 84        }
 85        srs.borrow().trim(supported_degree.unwrap())
 86    }
 87
 88    /// Generate a commitment for a polynomial
 89    /// Note that the scheme is not hidding
 90    fn commit(
 91        prover_param: impl Borrow<Self::ProverParam>,
 92        poly: &Self::Polynomial,
 93    ) -> Result<Self::Commitment, PCSError> {
 94        let prover_param = prover_param.borrow();
 95        let commit_time =
 96            start_timer!(|| format!("Committing to polynomial of degree {} ", poly.degree()));
 97
 98        if poly.degree() >= prover_param.powers_of_g.len() {
 99            return Err(PCSError::InvalidParameters(format!(
100                "uni poly degree {} is larger than allowed {}",
101                poly.degree(),
102                prover_param.powers_of_g.len()
103            )));
104        }
105
106        let (num_leading_zeros, plain_coeffs) = skip_leading_zeros(poly);
107
108        let msm_time = start_timer!(|| "MSM to compute commitment to plaintext poly");
109        let commitment =
110            E::G1::msm_unchecked(&prover_param.powers_of_g[num_leading_zeros..], plain_coeffs)
111                .into_affine();
112        end_timer!(msm_time);
113
114        end_timer!(commit_time);
115        Ok(Commitment(commitment))
116    }
117
118    /// On input a polynomial `p` and a point `point`, outputs a proof for the
119    /// same.
120    fn open(
121        prover_param: impl Borrow<Self::ProverParam>,
122        polynomial: &Self::Polynomial,
123        point: &Self::Point,
124    ) -> Result<(Self::Proof, Self::Evaluation), PCSError> {
125        let open_time =
126            start_timer!(|| format!("Opening polynomial of degree {}", polynomial.degree()));
127        let divisor = Self::Polynomial::from_coefficients_vec(vec![-*point, E::ScalarField::one()]);
128
129        let witness_time = start_timer!(|| "Computing witness polynomial");
130        let witness_polynomial = polynomial / &divisor;
131        end_timer!(witness_time);
132
133        let (num_leading_zeros, witness_coeffs) = skip_leading_zeros(&witness_polynomial);
134
135        let proof = E::G1::msm_unchecked(
136            &prover_param.borrow().powers_of_g[num_leading_zeros..],
137            witness_coeffs,
138        )
139        .into_affine();
140
141        let eval = polynomial.evaluate(point);
142
143        end_timer!(open_time);
144        Ok((Self::Proof { proof }, eval))
145    }
146
147    /// Verifies that `value` is the evaluation at `x` of the polynomial
148    /// committed inside `comm`.
149    fn verify(
150        verifier_param: &Self::VerifierParam,
151        commitment: &Self::Commitment,
152        point: &Self::Point,
153        value: &E::ScalarField,
154        proof: &Self::Proof,
155    ) -> Result<bool, PCSError> {
156        let check_time = start_timer!(|| "Checking evaluation");
157        let pairing_inputs: Vec<(E::G1Prepared, E::G2Prepared)> = vec![
158            (
159                (verifier_param.g.mul(value) - proof.proof.mul(point) - commitment.0.into_group())
160                    .into_affine()
161                    .into(),
162                verifier_param.h.into(),
163            ),
164            (proof.proof.into(), verifier_param.beta_h.into()),
165        ];
166
167        let p1 = pairing_inputs.iter().map(|(a, _)| a.clone());
168        let p2 = pairing_inputs.iter().map(|(_, a)| a.clone());
169
170        let res = E::multi_pairing(p1, p2).0.is_one();
171
172        end_timer!(check_time, || format!("Result: {}", res));
173        Ok(res)
174    }
175}
176
177fn skip_leading_zeros<F: PrimeField, P: DenseUVPolynomial<F>>(p: &P) -> (usize, &[F]) {
178    let mut num_leading_zeros = 0;
179    while num_leading_zeros < p.coeffs().len() && p.coeffs()[num_leading_zeros].is_zero() {
180        num_leading_zeros += 1;
181    }
182    (num_leading_zeros, &p.coeffs()[num_leading_zeros..])
183}
184
185#[cfg(test)]
186mod tests {
187    use super::*;
188    use crate::StructuredReferenceString;
189    use ark_bls12_381::Bls12_381;
190    use ark_ec::pairing::Pairing;
191    use ark_poly::univariate::DensePolynomial;
192    use ark_std::{test_rng, UniformRand};
193
194    fn end_to_end_test_template<E>() -> Result<(), PCSError>
195    where
196        E: Pairing,
197    {
198        let rng = &mut test_rng();
199        for _ in 0..100 {
200            let mut degree = 0;
201            while degree <= 1 {
202                degree = usize::rand(rng) % 20;
203            }
204            let pp = UnivariateKzgPCS::<E>::gen_srs_for_testing(rng, degree)?;
205            let (ck, vk) = pp.trim(degree)?;
206            let p = <DensePolynomial<E::ScalarField> as DenseUVPolynomial<E::ScalarField>>::rand(
207                degree, rng,
208            );
209            let comm = UnivariateKzgPCS::<E>::commit(&ck, &p)?;
210            let point = E::ScalarField::rand(rng);
211            let (proof, value) = UnivariateKzgPCS::<E>::open(&ck, &p, &point)?;
212            assert!(
213                UnivariateKzgPCS::<E>::verify(&vk, &comm, &point, &value, &proof)?,
214                "proof was incorrect for max_degree = {}, polynomial_degree = {}",
215                degree,
216                p.degree(),
217            );
218        }
219        Ok(())
220    }
221
222    fn linear_polynomial_test_template<E>() -> Result<(), PCSError>
223    where
224        E: Pairing,
225    {
226        let rng = &mut test_rng();
227        for _ in 0..100 {
228            let degree = 50;
229
230            let pp = UnivariateKzgPCS::<E>::gen_srs_for_testing(rng, degree)?;
231            let (ck, vk) = pp.trim(degree)?;
232            let p = <DensePolynomial<E::ScalarField> as DenseUVPolynomial<E::ScalarField>>::rand(
233                degree, rng,
234            );
235            let comm = UnivariateKzgPCS::<E>::commit(&ck, &p)?;
236            let point = E::ScalarField::rand(rng);
237            let (proof, value) = UnivariateKzgPCS::<E>::open(&ck, &p, &point)?;
238            assert!(
239                UnivariateKzgPCS::<E>::verify(&vk, &comm, &point, &value, &proof)?,
240                "proof was incorrect for max_degree = {}, polynomial_degree = {}",
241                degree,
242                p.degree(),
243            );
244        }
245        Ok(())
246    }
247
248    #[test]
249    fn end_to_end_test() {
250        end_to_end_test_template::<Bls12_381>().expect("test failed for bls12-381");
251    }
252
253    #[test]
254    fn linear_polynomial_test() {
255        linear_polynomial_test_template::<Bls12_381>().expect("test failed for bls12-381");
256    }
257}