zhenfei
2 years ago
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13 changed files with 1872 additions and 950 deletions
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Diff Options
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+18 -11pcs/benches/bench.rs
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+0 -620pcs/src/commit.rs
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+76 -36pcs/src/lib.rs
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+433 -0pcs/src/multilinear_kzg/batching.rs
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+441 -0pcs/src/multilinear_kzg/mod.rs
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+258 -0pcs/src/multilinear_kzg/srs.rs
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+101 -32pcs/src/multilinear_kzg/util.rs
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+2 -251pcs/src/param.rs
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+13 -0pcs/src/prelude.rs
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+9 -0pcs/src/structs.rs
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+384 -0pcs/src/univariate_kzg/mod.rs
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+127 -0pcs/src/univariate_kzg/srs.rs
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+10 -0poly-iop/src/transcript.rs
@ -1,620 +0,0 @@ |
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use crate::{
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util::{build_l, compute_w_circ_l, merge_polynomials},
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KZGMultilinearPC, MultilinearCommitmentScheme, PCSErrors, ProverParam, UniversalParams,
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VerifierParam,
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};
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use ark_ec::{
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msm::{FixedBaseMSM, VariableBaseMSM},
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AffineCurve, PairingEngine, ProjectiveCurve,
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};
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use ark_ff::PrimeField;
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use ark_poly::{univariate::DensePolynomial, MultilinearExtension, Polynomial, UVPolynomial};
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use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read, SerializationError, Write};
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use ark_std::{end_timer, log2, rand::RngCore, start_timer, vec::Vec, One, Zero};
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use poly_iop::IOPTranscript;
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#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
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/// commitment
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pub struct Commitment<E: PairingEngine> {
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/// number of variables
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pub nv: usize,
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/// product of g as described by the vRAM paper
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pub g_product: E::G1Affine,
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}
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#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
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/// proof of opening
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pub struct Proof<E: PairingEngine> {
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/// Evaluation of quotients
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pub proofs: Vec<E::G1Affine>,
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}
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#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
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/// proof of batch opening
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pub struct BatchProof<E: PairingEngine> {
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/// The actual proof
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pub proof: Proof<E>,
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/// The value which is `w` evaluated at `p:= l(r)`, where
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/// - `w` is the merged MLE
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/// - `l` is the list of univariate polys that goes through all points
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/// - `r` is sampled from the transcript.
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pub value: E::Fr,
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/// Commitment to q(x)
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// This is currently set to the entire coefficient list of q(x)
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// TODO: replace me with a KZG commit
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pub q_x_com: Vec<E::Fr>,
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}
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impl<E: PairingEngine> MultilinearCommitmentScheme<E> for KZGMultilinearPC<E> {
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type ProverParam = ProverParam<E>;
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type VerifierParam = VerifierParam<E>;
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type SRS = UniversalParams<E>;
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type Commitment = Commitment<E>;
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type Proof = Proof<E>;
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type Transcript = IOPTranscript<E::Fr>;
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type BatchProof = BatchProof<E>;
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/// Generate SRS from RNG.
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/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
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/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
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fn setup<R: RngCore>(rng: &mut R, num_vars: usize) -> Result<Self::SRS, PCSErrors> {
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let setup_timer = start_timer!(|| format!("SRS setup for dim {}", num_vars));
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let res = Self::SRS::gen_srs_for_testing(rng, num_vars);
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end_timer!(setup_timer);
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res
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}
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/// Generate a commitment for a polynomial.
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///
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/// This function takes `2^num_vars` number of scalar multiplications over
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/// G1.
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fn commit(
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prover_param: &Self::ProverParam,
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poly: &impl MultilinearExtension<E::Fr>,
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) -> Result<Self::Commitment, PCSErrors> {
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let commit_timer = start_timer!(|| "commit");
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let nv = poly.num_vars();
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let scalars: Vec<_> = poly
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.to_evaluations()
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.into_iter()
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.map(|x| x.into_repr())
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.collect();
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let g_product = VariableBaseMSM::multi_scalar_mul(
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&prover_param.powers_of_g[0].evals,
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scalars.as_slice(),
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)
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.into_affine();
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end_timer!(commit_timer);
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Ok(Commitment { nv, g_product })
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}
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/// Generate a commitment for a list of polynomials.
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///
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/// This function takes `2^(num_vars + log(polys.len())` number of scalar
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/// multiplications over G1.
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fn multi_commit(
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prover_param: &Self::ProverParam,
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polys: &[impl MultilinearExtension<E::Fr>],
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) -> Result<Self::Commitment, PCSErrors> {
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let commit_timer = start_timer!(|| "multi commit");
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let poly = merge_polynomials(polys)?;
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let scalars: Vec<_> = poly
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.to_evaluations()
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.iter()
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.map(|x| x.into_repr())
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.collect();
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let g_product = VariableBaseMSM::multi_scalar_mul(
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&prover_param.powers_of_g[0].evals,
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scalars.as_slice(),
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)
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.into_affine();
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end_timer!(commit_timer);
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Ok(Commitment {
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nv: poly.num_vars,
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g_product,
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})
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}
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/// On input a polynomial `p` and a point `point`, outputs a proof for the
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/// same. This function does not need to take the evaluation value as an
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/// input.
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///
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/// This function takes 2^{num_var +1} number of scalar multiplications over
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/// G1:
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/// - it proceeds with `num_var` number of rounds,
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/// - at round i, we compute an MSM for `2^{num_var - i + 1}` number of G2
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/// elements.
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fn open(
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prover_param: &Self::ProverParam,
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polynomial: &impl MultilinearExtension<E::Fr>,
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point: &[E::Fr],
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) -> Result<Self::Proof, PCSErrors> {
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let open_timer = start_timer!(|| "open");
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assert_eq!(
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polynomial.num_vars(),
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prover_param.num_vars,
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"Invalid size of polynomial"
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);
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let nv = polynomial.num_vars();
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let mut r: Vec<Vec<E::Fr>> = (0..nv + 1).map(|_| Vec::new()).collect();
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let mut q: Vec<Vec<E::Fr>> = (0..nv + 1).map(|_| Vec::new()).collect();
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r[nv] = polynomial.to_evaluations();
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let mut proofs = Vec::new();
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for (i, (&point_at_k, gi)) in point
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.iter()
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.zip(prover_param.powers_of_g.iter())
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.take(nv)
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.enumerate()
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{
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let ith_round = start_timer!(|| format!("{}-th round", i));
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let k = nv - i;
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let cur_dim = 1 << (k - 1);
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let mut cur_q = vec![E::Fr::zero(); cur_dim];
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let mut cur_r = vec![E::Fr::zero(); cur_dim];
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for b in 0..(1 << (k - 1)) {
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// q_b = pre_r [2^b + 1] - pre_r [2^b]
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cur_q[b] = r[k][(b << 1) + 1] - r[k][b << 1];
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// r_b = pre_r [2^b]*(1-p) + pre_r [2^b + 1] * p
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cur_r[b] =
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r[k][b << 1] * (E::Fr::one() - point_at_k) + (r[k][(b << 1) + 1] * point_at_k);
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}
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let scalars: Vec<_> = (0..(1 << k)).map(|x| cur_q[x >> 1].into_repr()).collect();
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q[k] = cur_q;
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r[k - 1] = cur_r;
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// this is a MSM over G1 and is likely to be the bottleneck
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proofs.push(VariableBaseMSM::multi_scalar_mul(&gi.evals, &scalars).into_affine());
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end_timer!(ith_round);
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}
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end_timer!(open_timer);
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Ok(Proof { proofs })
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}
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/// Input
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/// - the prover parameters,
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/// - a list of MLEs,
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/// - and a same number of points,
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/// - and a transcript,
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/// compute a multi-opening for all the polynomials.
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///
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/// For simplicity, this API requires each MLE to have only one point. If
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/// the caller wish to use more than one points per MLE, it should be
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/// handled at the caller layer.
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///
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/// Returns an error if the lengths do not match.
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///
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/// Returns:
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/// - the proof,
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/// - q(x), which is a univariate polynomial `w circ l` where `w` is the
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/// merged MLE, and `l` is a list of polynomials that go through all the
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/// points. TODO: change this field to a commitment to `q(x)`
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/// - and a value which is `w` evaluated at `p:= l(r)` from some `r` from
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/// the transcript.
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///
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/// Steps:
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/// 1. build `l(points)` which is a list of univariate polynomials that goes
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/// through the points
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/// 2. build MLE `w` which is the merge of all MLEs.
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/// 3. build `q(x)` which is a univariate polynomial `W circ l`
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/// 4. output `q(x)`' and put it into transcript
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/// 5. sample `r` from transcript
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/// 6. get a point `p := l(r)`
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/// 7. output an opening of `w` over point `p`
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/// 8. output `w(p)`
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fn multi_open(
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prover_param: &Self::ProverParam,
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polynomials: &[impl MultilinearExtension<E::Fr>],
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points: &[&[E::Fr]],
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transcript: &mut IOPTranscript<E::Fr>,
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) -> Result<Self::BatchProof, PCSErrors> {
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let open_timer = start_timer!(|| "multi open");
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if points.len() != polynomials.len() {
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return Err(PCSErrors::InvalidParameters(
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"polynomial length does not match point length".to_string(),
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));
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}
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let num_var = polynomials[0].num_vars();
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for poly in polynomials.iter().skip(1) {
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if poly.num_vars() != num_var {
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return Err(PCSErrors::InvalidParameters(
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"polynomials do not have same num_vars".to_string(),
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));
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}
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}
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for &point in points.iter() {
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if point.len() != num_var {
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return Err(PCSErrors::InvalidParameters(
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"points do not have same num_vars".to_string(),
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));
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}
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}
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// 1. build `l(points)` which is a list of univariate polynomials that goes
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// through the points
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let uni_polys = build_l(num_var, points)?;
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// 2. build MLE `w` which is the merge of all MLEs.
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let merge_poly = merge_polynomials(polynomials)?;
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// 3. build `q(x)` which is a univariate polynomial `W circ l`
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let q_x = compute_w_circ_l(&merge_poly, &uni_polys)?;
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// 4. output `q(x)`' and put it into transcript
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//
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// TODO: use KZG commit for q(x)
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// TODO: unwrap
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q_x.coeffs
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.iter()
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.for_each(|x| transcript.append_field_element(b"q(x)", x).unwrap());
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// 5. sample `r` from transcript
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let r = transcript.get_and_append_challenge(b"r")?;
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// 6. get a point `p := l(r)`
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let point: Vec<E::Fr> = uni_polys
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.iter()
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.rev()
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.map(|poly| poly.evaluate(&r))
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.collect();
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// 7. output an opening of `w` over point `p`
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let opening = Self::open(prover_param, &merge_poly, &point)?;
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// 8. output value that is `w` evaluated at `p` (which should match `q(r)`)
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let value = merge_poly.evaluate(&point).unwrap();
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let value2 = q_x.evaluate(&r);
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if value != value2 {
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return Err(PCSErrors::InvalidProver(
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"Q(r) does not match W(l(r))".to_string(),
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));
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}
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end_timer!(open_timer);
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Ok(Self::BatchProof {
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proof: opening,
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q_x_com: q_x.coeffs,
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value,
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})
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}
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/// Verifies that `value` is the evaluation at `x` of the polynomial
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/// committed inside `comm`.
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///
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/// This function takes
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/// - num_var number of pairing product.
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/// - num_var number of MSM
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fn verify(
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verifier_param: &Self::VerifierParam,
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commitment: &Self::Commitment,
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point: &[E::Fr],
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value: &E::Fr,
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proof: &Self::Proof,
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) -> Result<bool, PCSErrors> {
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let verify_timer = start_timer!(|| "verify");
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let prepare_inputs_timer = start_timer!(|| "prepare pairing inputs");
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let scalar_size = E::Fr::size_in_bits();
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let window_size = FixedBaseMSM::get_mul_window_size(verifier_param.num_vars);
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let h_table = FixedBaseMSM::get_window_table(
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scalar_size,
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window_size,
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verifier_param.h.into_projective(),
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);
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let h_mul: Vec<E::G2Projective> =
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FixedBaseMSM::multi_scalar_mul(scalar_size, window_size, &h_table, point);
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let h_vec: Vec<_> = (0..verifier_param.num_vars)
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.map(|i| verifier_param.h_mask[i].into_projective() - h_mul[i])
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.collect();
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let h_vec: Vec<E::G2Affine> = E::G2Projective::batch_normalization_into_affine(&h_vec);
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end_timer!(prepare_inputs_timer);
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let pairing_product_timer = start_timer!(|| "pairing product");
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|
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let mut pairings: Vec<_> = proof
|
|
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.proofs
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.iter()
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.map(|&x| E::G1Prepared::from(x))
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.zip(
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h_vec
|
|
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.into_iter()
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.take(verifier_param.num_vars)
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.map(E::G2Prepared::from),
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)
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.collect();
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|
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pairings.push((
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E::G1Prepared::from(
|
|
||||
(verifier_param.g.mul(*value) - commitment.g_product.into_projective())
|
|
||||
.into_affine(),
|
|
||||
),
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E::G2Prepared::from(verifier_param.h),
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|
||||
));
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|
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|
|
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let res = E::product_of_pairings(pairings.iter()) == E::Fqk::one();
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|
||||
|
|
||||
end_timer!(pairing_product_timer);
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|
||||
end_timer!(verify_timer);
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|
||||
Ok(res)
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|
||||
}
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|
||||
|
|
||||
/// Verifies that `value` is the evaluation at `x_i` of the polynomial
|
|
||||
/// `poly_i` committed inside `comm`.
|
|
||||
/// steps:
|
|
||||
///
|
|
||||
/// 1. put `q(x)`'s evaluations over `(1, omega,...)` into transcript
|
|
||||
/// 2. sample `r` from transcript
|
|
||||
/// 3. check `q(r) == value`
|
|
||||
/// 4. build `l(points)` which is a list of univariate polynomials that goes
|
|
||||
/// through the points
|
|
||||
/// 5. get a point `p := l(r)`
|
|
||||
/// 6. verifies `p` is verifies against proof
|
|
||||
fn batch_verify(
|
|
||||
verifier_param: &Self::VerifierParam,
|
|
||||
multi_commitment: &Self::Commitment,
|
|
||||
points: &[&[E::Fr]],
|
|
||||
batch_proof: &Self::BatchProof,
|
|
||||
transcript: &mut IOPTranscript<E::Fr>,
|
|
||||
) -> Result<bool, PCSErrors> {
|
|
||||
let verify_timer = start_timer!(|| "batch verify");
|
|
||||
let num_var = points[0].len();
|
|
||||
|
|
||||
for &point in points.iter().skip(1) {
|
|
||||
if point.len() != num_var {
|
|
||||
return Err(PCSErrors::InvalidParameters(format!(
|
|
||||
"points do not have same num_vars ({} vs {})",
|
|
||||
point.len(),
|
|
||||
num_var,
|
|
||||
)));
|
|
||||
}
|
|
||||
}
|
|
||||
if num_var + log2(points.len()) as usize != multi_commitment.nv {
|
|
||||
return Err(PCSErrors::InvalidParameters(format!(
|
|
||||
"points and multi_commitment do not have same num_vars ({} vs {})",
|
|
||||
num_var + log2(points.len()) as usize,
|
|
||||
num_var,
|
|
||||
)));
|
|
||||
}
|
|
||||
|
|
||||
// TODO: verify commitment of `q(x)` instead of receiving full `q(x)`
|
|
||||
|
|
||||
// 1. put `q(x)`'s evaluations over `(1, omega,...)` into transcript
|
|
||||
// TODO: unwrap
|
|
||||
batch_proof
|
|
||||
.q_x_com
|
|
||||
.iter()
|
|
||||
.for_each(|x| transcript.append_field_element(b"q(x)", x).unwrap());
|
|
||||
|
|
||||
// 2. sample `r` from transcript
|
|
||||
let r = transcript.get_and_append_challenge(b"r")?;
|
|
||||
|
|
||||
// 3. check `q(r) == value`
|
|
||||
let q_x = DensePolynomial::from_coefficients_slice(&batch_proof.q_x_com);
|
|
||||
let q_r = q_x.evaluate(&r);
|
|
||||
if q_r != batch_proof.value {
|
|
||||
return Ok(false);
|
|
||||
}
|
|
||||
|
|
||||
// 4. build `l(points)` which is a list of univariate polynomials that goes
|
|
||||
// through the points
|
|
||||
let uni_polys = build_l(num_var, points)?;
|
|
||||
|
|
||||
// 5. get a point `p := l(r)`
|
|
||||
let point: Vec<E::Fr> = uni_polys.iter().rev().map(|x| x.evaluate(&r)).collect();
|
|
||||
|
|
||||
// 6. verifies `p` is verifies against proof
|
|
||||
let res = Self::verify(
|
|
||||
verifier_param,
|
|
||||
multi_commitment,
|
|
||||
&point,
|
|
||||
&batch_proof.value,
|
|
||||
&batch_proof.proof,
|
|
||||
);
|
|
||||
end_timer!(verify_timer);
|
|
||||
|
|
||||
res
|
|
||||
}
|
|
||||
}
|
|
||||
|
|
||||
#[cfg(test)]
|
|
||||
mod tests {
|
|
||||
use crate::util::get_batched_nv;
|
|
||||
|
|
||||
use super::*;
|
|
||||
use ark_bls12_381::Bls12_381;
|
|
||||
use ark_ec::PairingEngine;
|
|
||||
use ark_poly::{DenseMultilinearExtension, MultilinearExtension};
|
|
||||
use ark_std::{rand::RngCore, test_rng, vec::Vec, UniformRand};
|
|
||||
type E = Bls12_381;
|
|
||||
type Fr = <E as PairingEngine>::Fr;
|
|
||||
|
|
||||
fn test_single_helper<R: RngCore>(
|
|
||||
uni_params: &UniversalParams<E>,
|
|
||||
poly: &impl MultilinearExtension<Fr>,
|
|
||||
rng: &mut R,
|
|
||||
) -> Result<(), PCSErrors> {
|
|
||||
let nv = poly.num_vars();
|
|
||||
assert_ne!(nv, 0);
|
|
||||
let (ck, vk) = uni_params.trim(nv)?;
|
|
||||
let point: Vec<_> = (0..nv).map(|_| Fr::rand(rng)).collect();
|
|
||||
let com = KZGMultilinearPC::commit(&ck, poly)?;
|
|
||||
let proof = KZGMultilinearPC::open(&ck, poly, &point)?;
|
|
||||
|
|
||||
let value = poly.evaluate(&point).unwrap();
|
|
||||
assert!(KZGMultilinearPC::verify(&vk, &com, &point, &value, &proof)?);
|
|
||||
|
|
||||
let value = Fr::rand(rng);
|
|
||||
assert!(!KZGMultilinearPC::verify(
|
|
||||
&vk, &com, &point, &value, &proof
|
|
||||
)?);
|
|
||||
|
|
||||
Ok(())
|
|
||||
}
|
|
||||
|
|
||||
#[test]
|
|
||||
fn test_single_commit() -> Result<(), PCSErrors> {
|
|
||||
let mut rng = test_rng();
|
|
||||
|
|
||||
let uni_params = KZGMultilinearPC::<E>::setup(&mut rng, 10)?;
|
|
||||
|
|
||||
// normal polynomials
|
|
||||
let poly1 = DenseMultilinearExtension::rand(8, &mut rng);
|
|
||||
test_single_helper(&uni_params, &poly1, &mut rng)?;
|
|
||||
|
|
||||
// single-variate polynomials
|
|
||||
let poly2 = DenseMultilinearExtension::rand(1, &mut rng);
|
|
||||
test_single_helper(&uni_params, &poly2, &mut rng)?;
|
|
||||
|
|
||||
Ok(())
|
|
||||
}
|
|
||||
|
|
||||
fn test_multi_commit_helper<R: RngCore>(
|
|
||||
uni_params: &UniversalParams<E>,
|
|
||||
polys: &[impl MultilinearExtension<Fr>],
|
|
||||
rng: &mut R,
|
|
||||
) -> Result<(), PCSErrors> {
|
|
||||
let mut transcript = IOPTranscript::new(b"test");
|
|
||||
|
|
||||
let nv = get_batched_nv(polys[0].num_vars(), polys.len());
|
|
||||
let (ck, vk) = uni_params.trim(nv)?;
|
|
||||
let mut points = Vec::new();
|
|
||||
|
|
||||
for poly in polys.iter() {
|
|
||||
let point = (0..poly.num_vars())
|
|
||||
.map(|_| Fr::rand(rng))
|
|
||||
.collect::<Vec<Fr>>();
|
|
||||
points.push(point);
|
|
||||
}
|
|
||||
let points_ref: Vec<&[Fr]> = points.iter().map(|x| x.as_ref()).collect();
|
|
||||
|
|
||||
let com = KZGMultilinearPC::multi_commit(&ck, polys)?;
|
|
||||
let batch_proof = KZGMultilinearPC::multi_open(&ck, polys, &points_ref, &mut transcript)?;
|
|
||||
|
|
||||
// good path
|
|
||||
let mut transcript = IOPTranscript::new(b"test");
|
|
||||
assert!(KZGMultilinearPC::batch_verify(
|
|
||||
&vk,
|
|
||||
&com,
|
|
||||
&points_ref,
|
|
||||
&batch_proof,
|
|
||||
&mut transcript
|
|
||||
)?);
|
|
||||
|
|
||||
// bad commitment
|
|
||||
assert!(KZGMultilinearPC::batch_verify(
|
|
||||
&vk,
|
|
||||
&Commitment {
|
|
||||
nv: 0,
|
|
||||
g_product: <E as PairingEngine>::G1Affine::default()
|
|
||||
},
|
|
||||
&points_ref,
|
|
||||
&batch_proof,
|
|
||||
&mut transcript
|
|
||||
)
|
|
||||
.is_err());
|
|
||||
|
|
||||
// bad points
|
|
||||
let points_ref: Vec<&[Fr]> = points.iter().skip(1).map(|x| x.as_ref()).collect();
|
|
||||
assert!(KZGMultilinearPC::batch_verify(
|
|
||||
&vk,
|
|
||||
&com,
|
|
||||
&points_ref,
|
|
||||
&batch_proof,
|
|
||||
&mut transcript
|
|
||||
)
|
|
||||
.is_err());
|
|
||||
|
|
||||
// bad proof
|
|
||||
assert!(KZGMultilinearPC::batch_verify(
|
|
||||
&vk,
|
|
||||
&com,
|
|
||||
&points_ref,
|
|
||||
&BatchProof {
|
|
||||
proof: Proof { proofs: Vec::new() },
|
|
||||
value: batch_proof.value,
|
|
||||
q_x_com: batch_proof.q_x_com.clone()
|
|
||||
},
|
|
||||
&mut transcript
|
|
||||
)
|
|
||||
.is_err());
|
|
||||
|
|
||||
// bad value
|
|
||||
assert!(KZGMultilinearPC::batch_verify(
|
|
||||
&vk,
|
|
||||
&com,
|
|
||||
&points_ref,
|
|
||||
&BatchProof {
|
|
||||
proof: batch_proof.proof.clone(),
|
|
||||
value: Fr::one(),
|
|
||||
q_x_com: batch_proof.q_x_com
|
|
||||
},
|
|
||||
&mut transcript
|
|
||||
)
|
|
||||
.is_err());
|
|
||||
|
|
||||
// bad q(x) commit
|
|
||||
assert!(KZGMultilinearPC::batch_verify(
|
|
||||
&vk,
|
|
||||
&com,
|
|
||||
&points_ref,
|
|
||||
&BatchProof {
|
|
||||
proof: batch_proof.proof,
|
|
||||
value: batch_proof.value,
|
|
||||
q_x_com: Vec::new()
|
|
||||
},
|
|
||||
&mut transcript
|
|
||||
)
|
|
||||
.is_err());
|
|
||||
|
|
||||
Ok(())
|
|
||||
}
|
|
||||
|
|
||||
#[test]
|
|
||||
fn test_multi_commit() -> Result<(), PCSErrors> {
|
|
||||
let mut rng = test_rng();
|
|
||||
|
|
||||
let uni_params = KZGMultilinearPC::<E>::setup(&mut rng, 15)?;
|
|
||||
|
|
||||
// normal polynomials
|
|
||||
let polys1: Vec<_> = (0..2)
|
|
||||
.map(|_| DenseMultilinearExtension::rand(4, &mut rng))
|
|
||||
.collect();
|
|
||||
test_multi_commit_helper(&uni_params, &polys1, &mut rng)?;
|
|
||||
|
|
||||
// single-variate polynomials
|
|
||||
let polys1: Vec<_> = (0..5)
|
|
||||
.map(|_| DenseMultilinearExtension::rand(1, &mut rng))
|
|
||||
.collect();
|
|
||||
test_multi_commit_helper(&uni_params, &polys1, &mut rng)?;
|
|
||||
|
|
||||
Ok(())
|
|
||||
}
|
|
||||
|
|
||||
#[test]
|
|
||||
fn setup_commit_verify_constant_polynomial() {
|
|
||||
let mut rng = test_rng();
|
|
||||
|
|
||||
// normal polynomials
|
|
||||
assert!(KZGMultilinearPC::<E>::setup(&mut rng, 0).is_err());
|
|
||||
}
|
|
||||
}
|
|
||||
@ -1,85 +1,125 @@ |
|||||
mod commit;
|
|
||||
mod errors;
|
mod errors;
|
||||
mod param;
|
|
||||
mod util;
|
|
||||
|
mod multilinear_kzg;
|
||||
|
mod structs;
|
||||
|
mod univariate_kzg;
|
||||
|
|
||||
|
pub mod prelude;
|
||||
|
|
||||
use ark_ec::PairingEngine;
|
use ark_ec::PairingEngine;
|
||||
use ark_poly::MultilinearExtension;
|
|
||||
use ark_std::rand::RngCore;
|
use ark_std::rand::RngCore;
|
||||
use poly_iop::IOPTranscript;
|
|
||||
use std::marker::PhantomData;
|
|
||||
|
|
||||
pub use errors::PCSErrors;
|
|
||||
pub use param::{ProverParam, UniversalParams, VerifierParam};
|
|
||||
|
|
||||
/// KZG Polynomial Commitment Scheme on multilinear extensions.
|
|
||||
pub struct KZGMultilinearPC<E: PairingEngine> {
|
|
||||
#[doc(hidden)]
|
|
||||
phantom: PhantomData<E>,
|
|
||||
}
|
|
||||
|
use errors::PCSErrors;
|
||||
|
|
||||
pub trait MultilinearCommitmentScheme<E: PairingEngine> {
|
|
||||
|
/// This trait defines APIs for polynomial commitment schemes.
|
||||
|
/// Note that for our usage of PCS, we do not require the hiding property.
|
||||
|
pub trait PolynomialCommitmentScheme<E: PairingEngine> {
|
||||
|
// Parameters
|
||||
type ProverParam;
|
type ProverParam;
|
||||
type VerifierParam;
|
type VerifierParam;
|
||||
type SRS;
|
type SRS;
|
||||
|
// Polynomial and its associated types
|
||||
|
type Polynomial;
|
||||
|
type Point;
|
||||
|
type Evaluation;
|
||||
|
// Commitments and proofs
|
||||
type Commitment;
|
type Commitment;
|
||||
type Proof;
|
type Proof;
|
||||
type BatchProof;
|
type BatchProof;
|
||||
type Transcript;
|
|
||||
|
type BatchCommitment;
|
||||
|
|
||||
/// Generate SRS from RNG.
|
|
||||
|
/// Build SRS for testing.
|
||||
|
///
|
||||
|
/// - For univariate polynomials, `log_size` is the log of maximum degree.
|
||||
|
/// - For multilinear polynomials, `log_size` is the number of variables.
|
||||
|
///
|
||||
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
||||
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
||||
fn setup<R: RngCore>(rng: &mut R, num_vars: usize) -> Result<Self::SRS, PCSErrors>;
|
|
||||
|
fn gen_srs_for_testing<R: RngCore>(
|
||||
|
rng: &mut R,
|
||||
|
log_size: usize,
|
||||
|
) -> Result<Self::SRS, PCSErrors>;
|
||||
|
|
||||
/// Generate a commitment for a polynomial
|
/// Generate a commitment for a polynomial
|
||||
fn commit(
|
fn commit(
|
||||
prover_param: &Self::ProverParam,
|
prover_param: &Self::ProverParam,
|
||||
poly: &impl MultilinearExtension<E::Fr>,
|
|
||||
|
poly: &Self::Polynomial,
|
||||
) -> Result<Self::Commitment, PCSErrors>;
|
) -> Result<Self::Commitment, PCSErrors>;
|
||||
|
|
||||
/// Generate a commitment for a list of polynomials
|
/// Generate a commitment for a list of polynomials
|
||||
fn multi_commit(
|
fn multi_commit(
|
||||
prover_param: &Self::ProverParam,
|
prover_param: &Self::ProverParam,
|
||||
polys: &[impl MultilinearExtension<E::Fr>],
|
|
||||
) -> Result<Self::Commitment, PCSErrors>;
|
|
||||
|
polys: &[Self::Polynomial],
|
||||
|
) -> Result<Self::BatchCommitment, PCSErrors>;
|
||||
|
|
||||
/// On input a polynomial `p` and a point `point`, outputs a proof for the
|
/// On input a polynomial `p` and a point `point`, outputs a proof for the
|
||||
/// same.
|
/// same.
|
||||
fn open(
|
fn open(
|
||||
prover_param: &Self::ProverParam,
|
prover_param: &Self::ProverParam,
|
||||
polynomial: &impl MultilinearExtension<E::Fr>,
|
|
||||
point: &[E::Fr],
|
|
||||
) -> Result<Self::Proof, PCSErrors>;
|
|
||||
|
polynomial: &Self::Polynomial,
|
||||
|
point: &Self::Point,
|
||||
|
) -> Result<(Self::Proof, Self::Evaluation), PCSErrors>;
|
||||
|
|
||||
/// Input a list of MLEs, and a same number of points, and a transcript,
|
/// Input a list of MLEs, and a same number of points, and a transcript,
|
||||
/// compute a multi-opening for all the polynomials.
|
/// compute a multi-opening for all the polynomials.
|
||||
#[allow(clippy::type_complexity)]
|
|
||||
// TODO: remove after we KZG-commit q(x)
|
|
||||
fn multi_open(
|
fn multi_open(
|
||||
prover_param: &Self::ProverParam,
|
prover_param: &Self::ProverParam,
|
||||
polynomials: &[impl MultilinearExtension<E::Fr>],
|
|
||||
point: &[&[E::Fr]],
|
|
||||
transcript: &mut Self::Transcript,
|
|
||||
) -> Result<Self::BatchProof, PCSErrors>;
|
|
||||
|
multi_commitment: &Self::Commitment,
|
||||
|
polynomials: &[Self::Polynomial],
|
||||
|
points: &[Self::Point],
|
||||
|
) -> Result<(Self::BatchProof, Vec<Self::Evaluation>), PCSErrors>;
|
||||
|
|
||||
/// Verifies that `value` is the evaluation at `x` of the polynomial
|
/// Verifies that `value` is the evaluation at `x` of the polynomial
|
||||
/// committed inside `comm`.
|
/// committed inside `comm`.
|
||||
fn verify(
|
fn verify(
|
||||
verifier_param: &Self::VerifierParam,
|
verifier_param: &Self::VerifierParam,
|
||||
commitment: &Self::Commitment,
|
commitment: &Self::Commitment,
|
||||
point: &[E::Fr],
|
|
||||
|
point: &Self::Point,
|
||||
value: &E::Fr,
|
value: &E::Fr,
|
||||
proof: &Self::Proof,
|
proof: &Self::Proof,
|
||||
) -> Result<bool, PCSErrors>;
|
) -> Result<bool, PCSErrors>;
|
||||
|
|
||||
/// Verifies that `value_i` is the evaluation at `x_i` of the polynomial
|
/// Verifies that `value_i` is the evaluation at `x_i` of the polynomial
|
||||
/// `poly_i` committed inside `comm`.
|
/// `poly_i` committed inside `comm`.
|
||||
fn batch_verify(
|
|
||||
|
fn batch_verify<R: RngCore>(
|
||||
verifier_param: &Self::VerifierParam,
|
verifier_param: &Self::VerifierParam,
|
||||
multi_commitment: &Self::Commitment,
|
|
||||
points: &[&[E::Fr]],
|
|
||||
|
multi_commitment: &Self::BatchCommitment,
|
||||
|
points: &[Self::Point],
|
||||
|
values: &[E::Fr],
|
||||
batch_proof: &Self::BatchProof,
|
batch_proof: &Self::BatchProof,
|
||||
transcript: &mut IOPTranscript<E::Fr>,
|
|
||||
|
rng: &mut R,
|
||||
) -> Result<bool, PCSErrors>;
|
) -> Result<bool, PCSErrors>;
|
||||
}
|
}
|
||||
|
|
||||
|
/// API definitions for structured reference string
|
||||
|
pub trait StructuredReferenceString<E: PairingEngine>: Sized {
|
||||
|
type ProverParam;
|
||||
|
type VerifierParam;
|
||||
|
|
||||
|
/// Extract the prover parameters from the public parameters.
|
||||
|
fn extract_prover_param(&self, supported_log_size: usize) -> Self::ProverParam;
|
||||
|
/// Extract the verifier parameters from the public parameters.
|
||||
|
fn extract_verifier_param(&self, supported_log_size: usize) -> Self::VerifierParam;
|
||||
|
|
||||
|
/// Trim the universal parameters to specialize the public parameters
|
||||
|
/// for polynomials to the given `supported_log_size`, and
|
||||
|
/// returns committer key and verifier key.
|
||||
|
///
|
||||
|
/// - For univariate polynomials, `supported_log_size` is the log of maximum
|
||||
|
/// degree.
|
||||
|
/// - For multilinear polynomials, `supported_log_size` is the number of
|
||||
|
/// variables.
|
||||
|
///
|
||||
|
/// `supported_log_size` should be in range `1..=params.log_size`
|
||||
|
fn trim(
|
||||
|
&self,
|
||||
|
supported_log_size: usize,
|
||||
|
) -> Result<(Self::ProverParam, Self::VerifierParam), PCSErrors>;
|
||||
|
|
||||
|
/// Build SRS for testing.
|
||||
|
///
|
||||
|
/// - For univariate polynomials, `log_size` is the log of maximum degree.
|
||||
|
/// - For multilinear polynomials, `log_size` is the number of variables.
|
||||
|
///
|
||||
|
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
||||
|
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
||||
|
fn gen_srs_for_testing<R: RngCore>(rng: &mut R, log_size: usize) -> Result<Self, PCSErrors>;
|
||||
|
}
|
||||
@ -0,0 +1,433 @@ |
|||||
|
use super::{
|
||||
|
open_internal,
|
||||
|
srs::{MultilinearProverParam, MultilinearVerifierParam},
|
||||
|
util::{build_l, compute_w_circ_l, merge_polynomials},
|
||||
|
verify_internal, BatchProof,
|
||||
|
};
|
||||
|
use crate::{
|
||||
|
multilinear_kzg::util::get_uni_domain,
|
||||
|
prelude::{Commitment, UnivariateProverParam, UnivariateVerifierParam},
|
||||
|
univariate_kzg::KZGUnivariatePCS,
|
||||
|
PCSErrors, PolynomialCommitmentScheme,
|
||||
|
};
|
||||
|
use ark_ec::PairingEngine;
|
||||
|
use ark_poly::{DenseMultilinearExtension, EvaluationDomain, MultilinearExtension, Polynomial};
|
||||
|
use ark_std::{end_timer, start_timer, vec::Vec};
|
||||
|
use poly_iop::IOPTranscript;
|
||||
|
|
||||
|
/// Input
|
||||
|
/// - the prover parameters for univariate KZG,
|
||||
|
/// - the prover parameters for multilinear KZG,
|
||||
|
/// - a list of MLEs,
|
||||
|
/// - a commitment to all MLEs
|
||||
|
/// - and a same number of points,
|
||||
|
/// compute a multi-opening for all the polynomials.
|
||||
|
///
|
||||
|
/// For simplicity, this API requires each MLE to have only one point. If
|
||||
|
/// the caller wish to use more than one points per MLE, it should be
|
||||
|
/// handled at the caller layer.
|
||||
|
///
|
||||
|
/// Returns an error if the lengths do not match.
|
||||
|
///
|
||||
|
/// Returns the proof, consists of
|
||||
|
/// - the multilinear KZG opening
|
||||
|
/// - the univariate KZG commitment to q(x)
|
||||
|
/// - the openings and evaluations of q(x) at omega^i and r
|
||||
|
///
|
||||
|
/// Steps:
|
||||
|
/// 1. build `l(points)` which is a list of univariate polynomials that goes
|
||||
|
/// through the points
|
||||
|
/// 2. build MLE `w` which is the merge of all MLEs.
|
||||
|
/// 3. build `q(x)` which is a univariate polynomial `W circ l`
|
||||
|
/// 4. commit to q(x) and sample r from transcript
|
||||
|
/// transcript contains: w commitment, points, q(x)'s commitment
|
||||
|
/// 5. build q(omega^i) and their openings
|
||||
|
/// 6. build q(r) and its opening
|
||||
|
/// 7. get a point `p := l(r)`
|
||||
|
/// 8. output an opening of `w` over point `p`
|
||||
|
/// 9. output `w(p)`
|
||||
|
pub(super) fn multi_open_internal<E: PairingEngine>(
|
||||
|
uni_prover_param: &UnivariateProverParam<E::G1Affine>,
|
||||
|
ml_prover_param: &MultilinearProverParam<E>,
|
||||
|
polynomials: &[DenseMultilinearExtension<E::Fr>],
|
||||
|
multi_commitment: &Commitment<E>,
|
||||
|
points: &[Vec<E::Fr>],
|
||||
|
) -> Result<(BatchProof<E>, Vec<E::Fr>), PCSErrors> {
|
||||
|
let open_timer = start_timer!(|| "multi open");
|
||||
|
|
||||
|
// ===================================
|
||||
|
// Sanity checks on inputs
|
||||
|
// ===================================
|
||||
|
let points_len = points.len();
|
||||
|
if points_len == 0 {
|
||||
|
return Err(PCSErrors::InvalidParameters("points is empty".to_string()));
|
||||
|
}
|
||||
|
|
||||
|
if points_len != polynomials.len() {
|
||||
|
return Err(PCSErrors::InvalidParameters(
|
||||
|
"polynomial length does not match point length".to_string(),
|
||||
|
));
|
||||
|
}
|
||||
|
|
||||
|
let num_var = polynomials[0].num_vars();
|
||||
|
for poly in polynomials.iter().skip(1) {
|
||||
|
if poly.num_vars() != num_var {
|
||||
|
return Err(PCSErrors::InvalidParameters(
|
||||
|
"polynomials do not have same num_vars".to_string(),
|
||||
|
));
|
||||
|
}
|
||||
|
}
|
||||
|
for point in points.iter() {
|
||||
|
if point.len() != num_var {
|
||||
|
return Err(PCSErrors::InvalidParameters(
|
||||
|
"points do not have same num_vars".to_string(),
|
||||
|
));
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
let domain = get_uni_domain::<E::Fr>(points_len)?;
|
||||
|
|
||||
|
// 1. build `l(points)` which is a list of univariate polynomials that goes
|
||||
|
// through the points
|
||||
|
let uni_polys = build_l(num_var, points, &domain)?;
|
||||
|
|
||||
|
// 2. build MLE `w` which is the merge of all MLEs.
|
||||
|
let merge_poly = merge_polynomials(polynomials)?;
|
||||
|
|
||||
|
// 3. build `q(x)` which is a univariate polynomial `W circ l`
|
||||
|
let q_x = compute_w_circ_l(&merge_poly, &uni_polys)?;
|
||||
|
|
||||
|
// 4. commit to q(x) and sample r from transcript
|
||||
|
// transcript contains: w commitment, points, q(x)'s commitment
|
||||
|
let mut transcript = IOPTranscript::new(b"ml kzg");
|
||||
|
transcript.append_serializable_element(b"w", multi_commitment)?;
|
||||
|
for point in points {
|
||||
|
transcript.append_serializable_element(b"w", point)?;
|
||||
|
}
|
||||
|
|
||||
|
let q_x_commit = KZGUnivariatePCS::<E>::commit(uni_prover_param, &q_x)?;
|
||||
|
transcript.append_serializable_element(b"q(x)", &q_x_commit)?;
|
||||
|
let r = transcript.get_and_append_challenge(b"r")?;
|
||||
|
|
||||
|
// 5. build q(omega^i) and their openings
|
||||
|
let mut q_x_opens = vec![];
|
||||
|
let mut q_x_evals = vec![];
|
||||
|
for i in 0..points_len {
|
||||
|
let (q_x_open, q_x_eval) =
|
||||
|
KZGUnivariatePCS::<E>::open(uni_prover_param, &q_x, &domain.element(i))?;
|
||||
|
q_x_opens.push(q_x_open);
|
||||
|
q_x_evals.push(q_x_eval);
|
||||
|
|
||||
|
// sanity check
|
||||
|
let point: Vec<E::Fr> = uni_polys
|
||||
|
.iter()
|
||||
|
.rev()
|
||||
|
.map(|poly| poly.evaluate(&domain.element(i)))
|
||||
|
.collect();
|
||||
|
let mle_eval = merge_poly.evaluate(&point).unwrap();
|
||||
|
if mle_eval != q_x_eval {
|
||||
|
return Err(PCSErrors::InvalidProver(
|
||||
|
"Q(omega) does not match W(l(omega))".to_string(),
|
||||
|
));
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
// 6. build q(r) and its opening
|
||||
|
let (q_x_open, q_r_value) = KZGUnivariatePCS::<E>::open(uni_prover_param, &q_x, &r)?;
|
||||
|
q_x_opens.push(q_x_open);
|
||||
|
q_x_evals.push(q_r_value);
|
||||
|
|
||||
|
// 7. get a point `p := l(r)`
|
||||
|
let point: Vec<E::Fr> = uni_polys
|
||||
|
.iter()
|
||||
|
.rev()
|
||||
|
.map(|poly| poly.evaluate(&r))
|
||||
|
.collect();
|
||||
|
|
||||
|
// 8. output an opening of `w` over point `p`
|
||||
|
let (mle_opening, mle_eval) = open_internal(ml_prover_param, &merge_poly, &point)?;
|
||||
|
|
||||
|
// 9. output value that is `w` evaluated at `p` (which should match `q(r)`)
|
||||
|
if mle_eval != q_r_value {
|
||||
|
return Err(PCSErrors::InvalidProver(
|
||||
|
"Q(r) does not match W(l(r))".to_string(),
|
||||
|
));
|
||||
|
}
|
||||
|
end_timer!(open_timer);
|
||||
|
|
||||
|
Ok((
|
||||
|
BatchProof {
|
||||
|
proof: mle_opening,
|
||||
|
q_x_commit,
|
||||
|
q_x_opens,
|
||||
|
},
|
||||
|
q_x_evals,
|
||||
|
))
|
||||
|
}
|
||||
|
|
||||
|
/// Verifies that the `multi_commitment` is a valid commitment
|
||||
|
/// to a list of MLEs for the given openings and evaluations in
|
||||
|
/// the batch_proof.
|
||||
|
///
|
||||
|
/// steps:
|
||||
|
///
|
||||
|
/// 1. push w, points and q_com into transcript
|
||||
|
/// 2. sample `r` from transcript
|
||||
|
/// 3. check `q(r) == batch_proof.q_x_value.last` and
|
||||
|
/// `q(omega^i) == batch_proof.q_x_value[i]`
|
||||
|
/// 4. build `l(points)` which is a list of univariate
|
||||
|
/// polynomials that goes through the points
|
||||
|
/// 5. get a point `p := l(r)`
|
||||
|
/// 6. verifies `p` is valid against multilinear KZG proof
|
||||
|
pub(super) fn batch_verify_internal<E: PairingEngine>(
|
||||
|
uni_verifier_param: &UnivariateVerifierParam<E>,
|
||||
|
ml_verifier_param: &MultilinearVerifierParam<E>,
|
||||
|
multi_commitment: &Commitment<E>,
|
||||
|
points: &[Vec<E::Fr>],
|
||||
|
values: &[E::Fr],
|
||||
|
batch_proof: &BatchProof<E>,
|
||||
|
) -> Result<bool, PCSErrors> {
|
||||
|
let verify_timer = start_timer!(|| "batch verify");
|
||||
|
|
||||
|
// ===================================
|
||||
|
// Sanity checks on inputs
|
||||
|
// ===================================
|
||||
|
let points_len = points.len();
|
||||
|
if points_len == 0 {
|
||||
|
return Err(PCSErrors::InvalidParameters("points is empty".to_string()));
|
||||
|
}
|
||||
|
|
||||
|
// add one here because we also have q(r) and its opening
|
||||
|
if points_len + 1 != batch_proof.q_x_opens.len() {
|
||||
|
return Err(PCSErrors::InvalidParameters(
|
||||
|
"openings length does not match point length".to_string(),
|
||||
|
));
|
||||
|
}
|
||||
|
|
||||
|
if points_len + 1 != values.len() {
|
||||
|
return Err(PCSErrors::InvalidParameters(
|
||||
|
"values length does not match point length".to_string(),
|
||||
|
));
|
||||
|
}
|
||||
|
|
||||
|
let num_var = points[0].len();
|
||||
|
for point in points.iter().skip(1) {
|
||||
|
if point.len() != num_var {
|
||||
|
return Err(PCSErrors::InvalidParameters(format!(
|
||||
|
"points do not have same num_vars ({} vs {})",
|
||||
|
point.len(),
|
||||
|
num_var,
|
||||
|
)));
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
let domain = get_uni_domain::<E::Fr>(points_len)?;
|
||||
|
|
||||
|
// 1. push w, points and q_com into transcript
|
||||
|
let mut transcript = IOPTranscript::new(b"ml kzg");
|
||||
|
transcript.append_serializable_element(b"w", multi_commitment)?;
|
||||
|
for point in points {
|
||||
|
transcript.append_serializable_element(b"w", point)?;
|
||||
|
}
|
||||
|
|
||||
|
transcript.append_serializable_element(b"q(x)", &batch_proof.q_x_commit)?;
|
||||
|
|
||||
|
// 2. sample `r` from transcript
|
||||
|
let r = transcript.get_and_append_challenge(b"r")?;
|
||||
|
|
||||
|
// 3. check `q(r) == batch_proof.q_x_value.last` and `q(omega^i) =
|
||||
|
// batch_proof.q_x_value[i]`
|
||||
|
for i in 0..points_len {
|
||||
|
if !KZGUnivariatePCS::verify(
|
||||
|
uni_verifier_param,
|
||||
|
&batch_proof.q_x_commit,
|
||||
|
&domain.element(i),
|
||||
|
&values[i],
|
||||
|
&batch_proof.q_x_opens[i],
|
||||
|
)? {
|
||||
|
#[cfg(debug_assertion)]
|
||||
|
println!("q(omega^{}) verification failed", i);
|
||||
|
return Ok(false);
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
if !KZGUnivariatePCS::verify(
|
||||
|
uni_verifier_param,
|
||||
|
&batch_proof.q_x_commit,
|
||||
|
&r,
|
||||
|
&values[points_len],
|
||||
|
&batch_proof.q_x_opens[points_len],
|
||||
|
)? {
|
||||
|
#[cfg(debug_assertion)]
|
||||
|
println!("q(r) verification failed");
|
||||
|
return Ok(false);
|
||||
|
}
|
||||
|
|
||||
|
// 4. build `l(points)` which is a list of univariate polynomials that goes
|
||||
|
// through the points
|
||||
|
let uni_polys = build_l(num_var, points, &domain)?;
|
||||
|
|
||||
|
// 5. get a point `p := l(r)`
|
||||
|
let point: Vec<E::Fr> = uni_polys.iter().rev().map(|x| x.evaluate(&r)).collect();
|
||||
|
|
||||
|
// 6. verifies `p` is valid against multilinear KZG proof
|
||||
|
let res = verify_internal(
|
||||
|
ml_verifier_param,
|
||||
|
multi_commitment,
|
||||
|
&point,
|
||||
|
&values[points_len],
|
||||
|
&batch_proof.proof,
|
||||
|
)?;
|
||||
|
|
||||
|
#[cfg(debug_assertion)]
|
||||
|
if !res {
|
||||
|
println!("multilinear KZG verification failed");
|
||||
|
}
|
||||
|
|
||||
|
end_timer!(verify_timer);
|
||||
|
|
||||
|
Ok(res)
|
||||
|
}
|
||||
|
|
||||
|
#[cfg(test)]
|
||||
|
mod tests {
|
||||
|
use super::{
|
||||
|
super::{util::get_batched_nv, *},
|
||||
|
*,
|
||||
|
};
|
||||
|
use crate::{
|
||||
|
multilinear_kzg::util::{compute_qx_degree, generate_evaluations},
|
||||
|
prelude::UnivariateUniversalParams,
|
||||
|
StructuredReferenceString,
|
||||
|
};
|
||||
|
use ark_bls12_381::Bls12_381 as E;
|
||||
|
use ark_ec::PairingEngine;
|
||||
|
use ark_poly::{DenseMultilinearExtension, MultilinearExtension};
|
||||
|
use ark_std::{log2, rand::RngCore, test_rng, vec::Vec, UniformRand};
|
||||
|
type Fr = <E as PairingEngine>::Fr;
|
||||
|
|
||||
|
fn test_multi_commit_helper<R: RngCore>(
|
||||
|
uni_params: &UnivariateUniversalParams<E>,
|
||||
|
ml_params: &MultilinearUniversalParams<E>,
|
||||
|
polys: &[DenseMultilinearExtension<Fr>],
|
||||
|
rng: &mut R,
|
||||
|
) -> Result<(), PCSErrors> {
|
||||
|
let merged_nv = get_batched_nv(polys[0].num_vars(), polys.len());
|
||||
|
let qx_degree = compute_qx_degree(merged_nv, polys.len());
|
||||
|
let log_qx_degree = log2(qx_degree) as usize;
|
||||
|
|
||||
|
let (uni_ck, uni_vk) = uni_params.trim(log_qx_degree)?;
|
||||
|
let (ml_ck, ml_vk) = ml_params.trim(merged_nv)?;
|
||||
|
|
||||
|
let mut points = Vec::new();
|
||||
|
for poly in polys.iter() {
|
||||
|
let point = (0..poly.num_vars())
|
||||
|
.map(|_| Fr::rand(rng))
|
||||
|
.collect::<Vec<Fr>>();
|
||||
|
points.push(point);
|
||||
|
}
|
||||
|
|
||||
|
let evals = generate_evaluations(polys, &points)?;
|
||||
|
|
||||
|
let com = KZGMultilinearPCS::multi_commit(&(ml_ck.clone(), uni_ck.clone()), polys)?;
|
||||
|
let (batch_proof, evaluations) =
|
||||
|
multi_open_internal(&uni_ck, &ml_ck, polys, &com, &points)?;
|
||||
|
|
||||
|
for (a, b) in evals.iter().zip(evaluations.iter()) {
|
||||
|
assert_eq!(a, b)
|
||||
|
}
|
||||
|
|
||||
|
// good path
|
||||
|
assert!(batch_verify_internal(
|
||||
|
&uni_vk,
|
||||
|
&ml_vk,
|
||||
|
&com,
|
||||
|
&points,
|
||||
|
&evaluations,
|
||||
|
&batch_proof,
|
||||
|
)?);
|
||||
|
|
||||
|
// bad commitment
|
||||
|
assert!(!batch_verify_internal(
|
||||
|
&uni_vk,
|
||||
|
&ml_vk,
|
||||
|
&Commitment {
|
||||
|
commitment: <E as PairingEngine>::G1Affine::default()
|
||||
|
},
|
||||
|
&points,
|
||||
|
&evaluations,
|
||||
|
&batch_proof,
|
||||
|
)?);
|
||||
|
|
||||
|
// bad points
|
||||
|
assert!(
|
||||
|
batch_verify_internal(&uni_vk, &ml_vk, &com, &points[1..], &[], &batch_proof,).is_err()
|
||||
|
);
|
||||
|
|
||||
|
// bad proof
|
||||
|
assert!(batch_verify_internal(
|
||||
|
&uni_vk,
|
||||
|
&ml_vk,
|
||||
|
&com,
|
||||
|
&points,
|
||||
|
&evaluations,
|
||||
|
&BatchProof {
|
||||
|
proof: Proof { proofs: Vec::new() },
|
||||
|
q_x_commit: Commitment {
|
||||
|
commitment: <E as PairingEngine>::G1Affine::default()
|
||||
|
},
|
||||
|
q_x_opens: vec![],
|
||||
|
},
|
||||
|
)
|
||||
|
.is_err());
|
||||
|
|
||||
|
// bad value
|
||||
|
let mut wrong_evals = evaluations.clone();
|
||||
|
wrong_evals[0] = Fr::default();
|
||||
|
assert!(!batch_verify_internal(
|
||||
|
&uni_vk,
|
||||
|
&ml_vk,
|
||||
|
&com,
|
||||
|
&points,
|
||||
|
&wrong_evals,
|
||||
|
&batch_proof
|
||||
|
)?);
|
||||
|
|
||||
|
// bad q(x) commit
|
||||
|
let mut wrong_proof = batch_proof.clone();
|
||||
|
wrong_proof.q_x_commit = Commitment {
|
||||
|
commitment: <E as PairingEngine>::G1Affine::default(),
|
||||
|
};
|
||||
|
assert!(!batch_verify_internal(
|
||||
|
&uni_vk,
|
||||
|
&ml_vk,
|
||||
|
&com,
|
||||
|
&points,
|
||||
|
&evaluations,
|
||||
|
&wrong_proof,
|
||||
|
)?);
|
||||
|
Ok(())
|
||||
|
}
|
||||
|
|
||||
|
#[test]
|
||||
|
fn test_multi_commit_internal() -> Result<(), PCSErrors> {
|
||||
|
let mut rng = test_rng();
|
||||
|
|
||||
|
let uni_params = UnivariateUniversalParams::<E>::gen_srs_for_testing(&mut rng, 15)?;
|
||||
|
let ml_params = MultilinearUniversalParams::<E>::gen_srs_for_testing(&mut rng, 15)?;
|
||||
|
|
||||
|
// normal polynomials
|
||||
|
let polys1: Vec<_> = (0..5)
|
||||
|
.map(|_| DenseMultilinearExtension::rand(4, &mut rng))
|
||||
|
.collect();
|
||||
|
test_multi_commit_helper(&uni_params, &ml_params, &polys1, &mut rng)?;
|
||||
|
|
||||
|
// single-variate polynomials
|
||||
|
let polys1: Vec<_> = (0..5)
|
||||
|
.map(|_| DenseMultilinearExtension::rand(1, &mut rng))
|
||||
|
.collect();
|
||||
|
test_multi_commit_helper(&uni_params, &ml_params, &polys1, &mut rng)?;
|
||||
|
|
||||
|
Ok(())
|
||||
|
}
|
||||
|
}
|
||||
@ -0,0 +1,441 @@ |
|||||
|
//! Main module for multilinear KZG commitment scheme
|
||||
|
|
||||
|
mod batching;
|
||||
|
pub(crate) mod srs;
|
||||
|
pub(crate) mod util;
|
||||
|
|
||||
|
use crate::{
|
||||
|
prelude::{
|
||||
|
Commitment, UnivariateProverParam, UnivariateUniversalParams, UnivariateVerifierParam,
|
||||
|
},
|
||||
|
univariate_kzg::KZGUnivariateOpening,
|
||||
|
PCSErrors, PolynomialCommitmentScheme, StructuredReferenceString,
|
||||
|
};
|
||||
|
use ark_ec::{
|
||||
|
msm::{FixedBaseMSM, VariableBaseMSM},
|
||||
|
AffineCurve, PairingEngine, ProjectiveCurve,
|
||||
|
};
|
||||
|
use ark_ff::PrimeField;
|
||||
|
use ark_poly::{DenseMultilinearExtension, MultilinearExtension};
|
||||
|
use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read, SerializationError, Write};
|
||||
|
use ark_std::{end_timer, rand::RngCore, start_timer, vec::Vec, One, Zero};
|
||||
|
use batching::{batch_verify_internal, multi_open_internal};
|
||||
|
use srs::{MultilinearProverParam, MultilinearUniversalParams, MultilinearVerifierParam};
|
||||
|
use std::marker::PhantomData;
|
||||
|
use util::merge_polynomials;
|
||||
|
|
||||
|
/// KZG Polynomial Commitment Scheme on multilinear polynomials.
|
||||
|
pub struct KZGMultilinearPCS<E: PairingEngine> {
|
||||
|
#[doc(hidden)]
|
||||
|
phantom: PhantomData<E>,
|
||||
|
}
|
||||
|
|
||||
|
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
||||
|
/// proof of opening
|
||||
|
pub struct Proof<E: PairingEngine> {
|
||||
|
/// Evaluation of quotients
|
||||
|
pub proofs: Vec<E::G1Affine>,
|
||||
|
}
|
||||
|
|
||||
|
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
||||
|
/// proof of batch opening
|
||||
|
pub struct BatchProof<E: PairingEngine> {
|
||||
|
/// The actual proof
|
||||
|
pub proof: Proof<E>,
|
||||
|
/// Commitment to q(x):= w(l(x)) where
|
||||
|
/// - `w` is the merged MLE
|
||||
|
/// - `l` is the list of univariate polys that goes through all points
|
||||
|
pub q_x_commit: Commitment<E>,
|
||||
|
/// openings of q(x) at 1, omega, ..., and r
|
||||
|
pub q_x_opens: Vec<KZGUnivariateOpening<E>>,
|
||||
|
}
|
||||
|
|
||||
|
impl<E: PairingEngine> PolynomialCommitmentScheme<E> for KZGMultilinearPCS<E> {
|
||||
|
// Parameters
|
||||
|
type ProverParam = (
|
||||
|
MultilinearProverParam<E>,
|
||||
|
UnivariateProverParam<E::G1Affine>,
|
||||
|
);
|
||||
|
type VerifierParam = (MultilinearVerifierParam<E>, UnivariateVerifierParam<E>);
|
||||
|
type SRS = (MultilinearUniversalParams<E>, UnivariateUniversalParams<E>);
|
||||
|
// Polynomial and its associated types
|
||||
|
type Polynomial = DenseMultilinearExtension<E::Fr>;
|
||||
|
type Point = Vec<E::Fr>;
|
||||
|
type Evaluation = E::Fr;
|
||||
|
// Commitments and proofs
|
||||
|
type Commitment = Commitment<E>;
|
||||
|
type Proof = Proof<E>;
|
||||
|
type BatchProof = BatchProof<E>;
|
||||
|
type BatchCommitment = Commitment<E>;
|
||||
|
|
||||
|
/// Build SRS for testing.
|
||||
|
///
|
||||
|
/// - For univariate polynomials, `log_size` is the log of maximum degree.
|
||||
|
/// - For multilinear polynomials, `log_size` is the number of variables.
|
||||
|
///
|
||||
|
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
||||
|
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
||||
|
fn gen_srs_for_testing<R: RngCore>(
|
||||
|
rng: &mut R,
|
||||
|
log_size: usize,
|
||||
|
) -> Result<Self::SRS, PCSErrors> {
|
||||
|
Ok((
|
||||
|
MultilinearUniversalParams::<E>::gen_srs_for_testing(rng, log_size)?,
|
||||
|
UnivariateUniversalParams::<E>::gen_srs_for_testing(rng, log_size)?,
|
||||
|
))
|
||||
|
}
|
||||
|
|
||||
|
/// Generate a commitment for a polynomial.
|
||||
|
///
|
||||
|
/// This function takes `2^num_vars` number of scalar multiplications over
|
||||
|
/// G1.
|
||||
|
fn commit(
|
||||
|
prover_param: &Self::ProverParam,
|
||||
|
poly: &Self::Polynomial,
|
||||
|
) -> Result<Self::Commitment, PCSErrors> {
|
||||
|
let commit_timer = start_timer!(|| "commit");
|
||||
|
|
||||
|
let scalars: Vec<_> = poly
|
||||
|
.to_evaluations()
|
||||
|
.into_iter()
|
||||
|
.map(|x| x.into_repr())
|
||||
|
.collect();
|
||||
|
let commitment = VariableBaseMSM::multi_scalar_mul(
|
||||
|
&prover_param.0.powers_of_g[0].evals,
|
||||
|
scalars.as_slice(),
|
||||
|
)
|
||||
|
.into_affine();
|
||||
|
|
||||
|
end_timer!(commit_timer);
|
||||
|
Ok(Commitment { commitment })
|
||||
|
}
|
||||
|
|
||||
|
/// Generate a commitment for a list of polynomials.
|
||||
|
///
|
||||
|
/// This function takes `2^(num_vars + log(polys.len())` number of scalar
|
||||
|
/// multiplications over G1.
|
||||
|
fn multi_commit(
|
||||
|
prover_param: &Self::ProverParam,
|
||||
|
polys: &[Self::Polynomial],
|
||||
|
) -> Result<Self::Commitment, PCSErrors> {
|
||||
|
let commit_timer = start_timer!(|| "multi commit");
|
||||
|
let poly = merge_polynomials(polys)?;
|
||||
|
|
||||
|
let scalars: Vec<_> = poly
|
||||
|
.to_evaluations()
|
||||
|
.iter()
|
||||
|
.map(|x| x.into_repr())
|
||||
|
.collect();
|
||||
|
|
||||
|
let commitment = VariableBaseMSM::multi_scalar_mul(
|
||||
|
&prover_param.0.powers_of_g[0].evals,
|
||||
|
scalars.as_slice(),
|
||||
|
)
|
||||
|
.into_affine();
|
||||
|
|
||||
|
end_timer!(commit_timer);
|
||||
|
Ok(Commitment { commitment })
|
||||
|
}
|
||||
|
|
||||
|
/// On input a polynomial `p` and a point `point`, outputs a proof for the
|
||||
|
/// same. This function does not need to take the evaluation value as an
|
||||
|
/// input.
|
||||
|
///
|
||||
|
/// This function takes 2^{num_var +1} number of scalar multiplications over
|
||||
|
/// G1:
|
||||
|
/// - it prodceeds with `num_var` number of rounds,
|
||||
|
/// - at round i, we compute an MSM for `2^{num_var - i + 1}` number of G2
|
||||
|
/// elements.
|
||||
|
fn open(
|
||||
|
prover_param: &Self::ProverParam,
|
||||
|
polynomial: &Self::Polynomial,
|
||||
|
point: &Self::Point,
|
||||
|
) -> Result<(Self::Proof, Self::Evaluation), PCSErrors> {
|
||||
|
open_internal(&prover_param.0, polynomial, point)
|
||||
|
}
|
||||
|
|
||||
|
/// Input
|
||||
|
/// - the prover parameters for univariate KZG,
|
||||
|
/// - the prover parameters for multilinear KZG,
|
||||
|
/// - a list of MLEs,
|
||||
|
/// - a commitment to all MLEs
|
||||
|
/// - and a same number of points,
|
||||
|
/// compute a multi-opening for all the polynomials.
|
||||
|
///
|
||||
|
/// For simplicity, this API requires each MLE to have only one point. If
|
||||
|
/// the caller wish to use more than one points per MLE, it should be
|
||||
|
/// handled at the caller layer.
|
||||
|
///
|
||||
|
/// Returns an error if the lengths do not match.
|
||||
|
///
|
||||
|
/// Returns the proof, consists of
|
||||
|
/// - the multilinear KZG opening
|
||||
|
/// - the univariate KZG commitment to q(x)
|
||||
|
/// - the openings and evaluations of q(x) at omega^i and r
|
||||
|
///
|
||||
|
/// Steps:
|
||||
|
/// 1. build `l(points)` which is a list of univariate polynomials that goes
|
||||
|
/// through the points
|
||||
|
/// 2. build MLE `w` which is the merge of all MLEs.
|
||||
|
/// 3. build `q(x)` which is a univariate polynomial `W circ l`
|
||||
|
/// 4. commit to q(x) and sample r from transcript
|
||||
|
/// transcript contains: w commitment, points, q(x)'s commitment
|
||||
|
/// 5. build q(omega^i) and their openings
|
||||
|
/// 6. build q(r) and its opening
|
||||
|
/// 7. get a point `p := l(r)`
|
||||
|
/// 8. output an opening of `w` over point `p`
|
||||
|
/// 9. output `w(p)`
|
||||
|
fn multi_open(
|
||||
|
prover_param: &Self::ProverParam,
|
||||
|
multi_commitment: &Self::Commitment,
|
||||
|
polynomials: &[Self::Polynomial],
|
||||
|
points: &[Self::Point],
|
||||
|
) -> Result<(Self::BatchProof, Vec<Self::Evaluation>), PCSErrors> {
|
||||
|
multi_open_internal::<E>(
|
||||
|
&prover_param.1,
|
||||
|
&prover_param.0,
|
||||
|
polynomials,
|
||||
|
multi_commitment,
|
||||
|
points,
|
||||
|
)
|
||||
|
}
|
||||
|
|
||||
|
/// Verifies that `value` is the evaluation at `x` of the polynomial
|
||||
|
/// committed inside `comm`.
|
||||
|
///
|
||||
|
/// This function takes
|
||||
|
/// - num_var number of pairing product.
|
||||
|
/// - num_var number of MSM
|
||||
|
fn verify(
|
||||
|
verifier_param: &Self::VerifierParam,
|
||||
|
commitment: &Self::Commitment,
|
||||
|
point: &Self::Point,
|
||||
|
value: &E::Fr,
|
||||
|
proof: &Self::Proof,
|
||||
|
) -> Result<bool, PCSErrors> {
|
||||
|
verify_internal(&verifier_param.0, commitment, point, value, proof)
|
||||
|
}
|
||||
|
|
||||
|
/// Verifies that `value` is the evaluation at `x_i` of the polynomial
|
||||
|
/// `poly_i` committed inside `comm`.
|
||||
|
/// steps:
|
||||
|
///
|
||||
|
/// 1. put `q(x)`'s evaluations over `(1, omega,...)` into transcript
|
||||
|
/// 2. sample `r` from transcript
|
||||
|
/// 3. check `q(r) == value`
|
||||
|
/// 4. build `l(points)` which is a list of univariate polynomials that goes
|
||||
|
/// through the points
|
||||
|
/// 5. get a point `p := l(r)`
|
||||
|
/// 6. verifies `p` is verifies against proof
|
||||
|
fn batch_verify<R: RngCore>(
|
||||
|
verifier_param: &Self::VerifierParam,
|
||||
|
multi_commitment: &Self::BatchCommitment,
|
||||
|
points: &[Self::Point],
|
||||
|
values: &[E::Fr],
|
||||
|
batch_proof: &Self::BatchProof,
|
||||
|
_rng: &mut R,
|
||||
|
) -> Result<bool, PCSErrors> {
|
||||
|
batch_verify_internal(
|
||||
|
&verifier_param.1,
|
||||
|
&verifier_param.0,
|
||||
|
multi_commitment,
|
||||
|
points,
|
||||
|
values,
|
||||
|
batch_proof,
|
||||
|
)
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
/// On input a polynomial `p` and a point `point`, outputs a proof for the
|
||||
|
/// same. This function does not need to take the evaluation value as an
|
||||
|
/// input.
|
||||
|
///
|
||||
|
/// This function takes 2^{num_var +1} number of scalar multiplications over
|
||||
|
/// G1:
|
||||
|
/// - it proceeds with `num_var` number of rounds,
|
||||
|
/// - at round i, we compute an MSM for `2^{num_var - i + 1}` number of G2
|
||||
|
/// elements.
|
||||
|
fn open_internal<E: PairingEngine>(
|
||||
|
prover_param: &MultilinearProverParam<E>,
|
||||
|
polynomial: &DenseMultilinearExtension<E::Fr>,
|
||||
|
point: &[E::Fr],
|
||||
|
) -> Result<(Proof<E>, E::Fr), PCSErrors> {
|
||||
|
let open_timer = start_timer!(|| format!("open mle with {} variable", polynomial.num_vars));
|
||||
|
|
||||
|
assert_eq!(
|
||||
|
polynomial.num_vars(),
|
||||
|
prover_param.num_vars,
|
||||
|
"Invalid size of polynomial"
|
||||
|
);
|
||||
|
let nv = polynomial.num_vars();
|
||||
|
let mut r: Vec<Vec<E::Fr>> = (0..nv + 1).map(|_| Vec::new()).collect();
|
||||
|
let mut q: Vec<Vec<E::Fr>> = (0..nv + 1).map(|_| Vec::new()).collect();
|
||||
|
|
||||
|
r[nv] = polynomial.to_evaluations();
|
||||
|
|
||||
|
let mut proofs = Vec::new();
|
||||
|
|
||||
|
for (i, (&point_at_k, gi)) in point
|
||||
|
.iter()
|
||||
|
.zip(prover_param.powers_of_g.iter())
|
||||
|
.take(nv)
|
||||
|
.enumerate()
|
||||
|
{
|
||||
|
let ith_round = start_timer!(|| format!("{}-th round", i));
|
||||
|
|
||||
|
let k = nv - i;
|
||||
|
let cur_dim = 1 << (k - 1);
|
||||
|
let mut cur_q = vec![E::Fr::zero(); cur_dim];
|
||||
|
let mut cur_r = vec![E::Fr::zero(); cur_dim];
|
||||
|
|
||||
|
for b in 0..(1 << (k - 1)) {
|
||||
|
// q_b = pre_r [2^b + 1] - pre_r [2^b]
|
||||
|
cur_q[b] = r[k][(b << 1) + 1] - r[k][b << 1];
|
||||
|
|
||||
|
// r_b = pre_r [2^b]*(1-p) + pre_r [2^b + 1] * p
|
||||
|
cur_r[b] =
|
||||
|
r[k][b << 1] * (E::Fr::one() - point_at_k) + (r[k][(b << 1) + 1] * point_at_k);
|
||||
|
}
|
||||
|
|
||||
|
let scalars: Vec<_> = (0..(1 << k)).map(|x| cur_q[x >> 1].into_repr()).collect();
|
||||
|
|
||||
|
q[k] = cur_q;
|
||||
|
r[k - 1] = cur_r;
|
||||
|
|
||||
|
// this is a MSM over G1 and is likely to be the bottleneck
|
||||
|
proofs.push(VariableBaseMSM::multi_scalar_mul(&gi.evals, &scalars).into_affine());
|
||||
|
end_timer!(ith_round);
|
||||
|
}
|
||||
|
let eval = polynomial.evaluate(point).ok_or_else(|| {
|
||||
|
PCSErrors::InvalidParameters("fail to evaluate the polynomial".to_string())
|
||||
|
})?;
|
||||
|
end_timer!(open_timer);
|
||||
|
Ok((Proof { proofs }, eval))
|
||||
|
}
|
||||
|
|
||||
|
/// Verifies that `value` is the evaluation at `x` of the polynomial
|
||||
|
/// committed inside `comm`.
|
||||
|
///
|
||||
|
/// This function takes
|
||||
|
/// - num_var number of pairing product.
|
||||
|
/// - num_var number of MSM
|
||||
|
fn verify_internal<E: PairingEngine>(
|
||||
|
verifier_param: &MultilinearVerifierParam<E>,
|
||||
|
commitment: &Commitment<E>,
|
||||
|
point: &[E::Fr],
|
||||
|
value: &E::Fr,
|
||||
|
proof: &Proof<E>,
|
||||
|
) -> Result<bool, PCSErrors> {
|
||||
|
let verify_timer = start_timer!(|| "verify");
|
||||
|
let prepare_inputs_timer = start_timer!(|| "prepare pairing inputs");
|
||||
|
|
||||
|
let scalar_size = E::Fr::size_in_bits();
|
||||
|
let window_size = FixedBaseMSM::get_mul_window_size(verifier_param.num_vars);
|
||||
|
|
||||
|
let h_table = FixedBaseMSM::get_window_table(
|
||||
|
scalar_size,
|
||||
|
window_size,
|
||||
|
verifier_param.h.into_projective(),
|
||||
|
);
|
||||
|
let h_mul: Vec<E::G2Projective> =
|
||||
|
FixedBaseMSM::multi_scalar_mul(scalar_size, window_size, &h_table, point);
|
||||
|
|
||||
|
let h_vec: Vec<_> = (0..verifier_param.num_vars)
|
||||
|
.map(|i| verifier_param.h_mask[i].into_projective() - h_mul[i])
|
||||
|
.collect();
|
||||
|
let h_vec: Vec<E::G2Affine> = E::G2Projective::batch_normalization_into_affine(&h_vec);
|
||||
|
end_timer!(prepare_inputs_timer);
|
||||
|
|
||||
|
let pairing_product_timer = start_timer!(|| "pairing product");
|
||||
|
|
||||
|
let mut pairings: Vec<_> = proof
|
||||
|
.proofs
|
||||
|
.iter()
|
||||
|
.map(|&x| E::G1Prepared::from(x))
|
||||
|
.zip(
|
||||
|
h_vec
|
||||
|
.into_iter()
|
||||
|
.take(verifier_param.num_vars)
|
||||
|
.map(E::G2Prepared::from),
|
||||
|
)
|
||||
|
.collect();
|
||||
|
|
||||
|
pairings.push((
|
||||
|
E::G1Prepared::from(
|
||||
|
(verifier_param.g.mul(*value) - commitment.commitment.into_projective()).into_affine(),
|
||||
|
),
|
||||
|
E::G2Prepared::from(verifier_param.h),
|
||||
|
));
|
||||
|
|
||||
|
let res = E::product_of_pairings(pairings.iter()) == E::Fqk::one();
|
||||
|
|
||||
|
end_timer!(pairing_product_timer);
|
||||
|
end_timer!(verify_timer);
|
||||
|
Ok(res)
|
||||
|
}
|
||||
|
|
||||
|
#[cfg(test)]
|
||||
|
mod tests {
|
||||
|
use super::*;
|
||||
|
use crate::StructuredReferenceString;
|
||||
|
use ark_bls12_381::Bls12_381;
|
||||
|
use ark_ec::PairingEngine;
|
||||
|
use ark_poly::{DenseMultilinearExtension, MultilinearExtension};
|
||||
|
use ark_std::{rand::RngCore, test_rng, vec::Vec, UniformRand};
|
||||
|
type E = Bls12_381;
|
||||
|
type Fr = <E as PairingEngine>::Fr;
|
||||
|
|
||||
|
fn test_single_helper<R: RngCore>(
|
||||
|
params: &(MultilinearUniversalParams<E>, UnivariateUniversalParams<E>),
|
||||
|
poly: &DenseMultilinearExtension<Fr>,
|
||||
|
rng: &mut R,
|
||||
|
) -> Result<(), PCSErrors> {
|
||||
|
let nv = poly.num_vars();
|
||||
|
assert_ne!(nv, 0);
|
||||
|
let uni_degree = 1;
|
||||
|
let (uni_ck, uni_vk) = params.1.trim(uni_degree)?;
|
||||
|
let (ml_ck, ml_vk) = params.0.trim(nv)?;
|
||||
|
let ck = (ml_ck, uni_ck);
|
||||
|
let vk = (ml_vk, uni_vk);
|
||||
|
|
||||
|
let point: Vec<_> = (0..nv).map(|_| Fr::rand(rng)).collect();
|
||||
|
let com = KZGMultilinearPCS::commit(&ck, poly)?;
|
||||
|
let (proof, value) = KZGMultilinearPCS::open(&ck, poly, &point)?;
|
||||
|
|
||||
|
assert!(KZGMultilinearPCS::verify(
|
||||
|
&vk, &com, &point, &value, &proof
|
||||
|
)?);
|
||||
|
|
||||
|
let value = Fr::rand(rng);
|
||||
|
assert!(!KZGMultilinearPCS::verify(
|
||||
|
&vk, &com, &point, &value, &proof
|
||||
|
)?);
|
||||
|
|
||||
|
Ok(())
|
||||
|
}
|
||||
|
|
||||
|
#[test]
|
||||
|
fn test_single_commit() -> Result<(), PCSErrors> {
|
||||
|
let mut rng = test_rng();
|
||||
|
|
||||
|
let params = KZGMultilinearPCS::<E>::gen_srs_for_testing(&mut rng, 10)?;
|
||||
|
|
||||
|
// normal polynomials
|
||||
|
let poly1 = DenseMultilinearExtension::rand(8, &mut rng);
|
||||
|
test_single_helper(¶ms, &poly1, &mut rng)?;
|
||||
|
|
||||
|
// single-variate polynomials
|
||||
|
let poly2 = DenseMultilinearExtension::rand(1, &mut rng);
|
||||
|
test_single_helper(¶ms, &poly2, &mut rng)?;
|
||||
|
|
||||
|
Ok(())
|
||||
|
}
|
||||
|
|
||||
|
#[test]
|
||||
|
fn setup_commit_verify_constant_polynomial() {
|
||||
|
let mut rng = test_rng();
|
||||
|
|
||||
|
// normal polynomials
|
||||
|
assert!(KZGMultilinearPCS::<E>::gen_srs_for_testing(&mut rng, 0).is_err());
|
||||
|
}
|
||||
|
}
|
||||
@ -0,0 +1,258 @@ |
|||||
|
//! Implementing Structured Reference Strings for multilinear polynomial KZG
|
||||
|
|
||||
|
use crate::{prelude::PCSErrors, StructuredReferenceString};
|
||||
|
use ark_ec::{msm::FixedBaseMSM, AffineCurve, PairingEngine, ProjectiveCurve};
|
||||
|
use ark_ff::{Field, PrimeField};
|
||||
|
use ark_poly::DenseMultilinearExtension;
|
||||
|
use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read, SerializationError, Write};
|
||||
|
use ark_std::{end_timer, rand::RngCore, start_timer, vec::Vec, UniformRand};
|
||||
|
use std::collections::LinkedList;
|
||||
|
|
||||
|
/// Evaluations over {0,1}^n for G1 or G2
|
||||
|
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
||||
|
pub struct Evaluations<C: AffineCurve> {
|
||||
|
/// The evaluations.
|
||||
|
pub evals: Vec<C>,
|
||||
|
}
|
||||
|
|
||||
|
/// Universal Parameter
|
||||
|
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
||||
|
pub struct MultilinearUniversalParams<E: PairingEngine> {
|
||||
|
/// prover parameters
|
||||
|
pub prover_param: MultilinearProverParam<E>,
|
||||
|
/// h^randomness: h^t1, h^t2, ..., **h^{t_nv}**
|
||||
|
pub h_mask: Vec<E::G2Affine>,
|
||||
|
}
|
||||
|
|
||||
|
/// Prover Parameters
|
||||
|
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
||||
|
pub struct MultilinearProverParam<E: PairingEngine> {
|
||||
|
/// number of variables
|
||||
|
pub num_vars: usize,
|
||||
|
/// `pp_{num_vars}`, `pp_{num_vars - 1}`, `pp_{num_vars - 2}`, ..., defined
|
||||
|
/// by XZZPD19
|
||||
|
pub powers_of_g: Vec<Evaluations<E::G1Affine>>,
|
||||
|
/// generator for G1
|
||||
|
pub g: E::G1Affine,
|
||||
|
/// generator for G2
|
||||
|
pub h: E::G2Affine,
|
||||
|
}
|
||||
|
|
||||
|
/// Verifier Parameters
|
||||
|
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
||||
|
pub struct MultilinearVerifierParam<E: PairingEngine> {
|
||||
|
/// number of variables
|
||||
|
pub num_vars: usize,
|
||||
|
/// generator of G1
|
||||
|
pub g: E::G1Affine,
|
||||
|
/// generator of G2
|
||||
|
pub h: E::G2Affine,
|
||||
|
/// h^randomness: h^t1, h^t2, ..., **h^{t_nv}**
|
||||
|
pub h_mask: Vec<E::G2Affine>,
|
||||
|
}
|
||||
|
|
||||
|
impl<E: PairingEngine> StructuredReferenceString<E> for MultilinearUniversalParams<E> {
|
||||
|
type ProverParam = MultilinearProverParam<E>;
|
||||
|
type VerifierParam = MultilinearVerifierParam<E>;
|
||||
|
|
||||
|
/// Extract the prover parameters from the public parameters.
|
||||
|
fn extract_prover_param(&self, supported_num_vars: usize) -> Self::ProverParam {
|
||||
|
let to_reduce = self.prover_param.num_vars - supported_num_vars;
|
||||
|
|
||||
|
Self::ProverParam {
|
||||
|
powers_of_g: self.prover_param.powers_of_g[to_reduce..].to_vec(),
|
||||
|
g: self.prover_param.g,
|
||||
|
h: self.prover_param.h,
|
||||
|
num_vars: supported_num_vars,
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
/// Extract the verifier parameters from the public parameters.
|
||||
|
fn extract_verifier_param(&self, supported_num_vars: usize) -> Self::VerifierParam {
|
||||
|
let to_reduce = self.prover_param.num_vars - supported_num_vars;
|
||||
|
Self::VerifierParam {
|
||||
|
num_vars: supported_num_vars,
|
||||
|
g: self.prover_param.g,
|
||||
|
h: self.prover_param.h,
|
||||
|
h_mask: self.h_mask[to_reduce..].to_vec(),
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
/// Trim the universal parameters to specialize the public parameters
|
||||
|
/// for multilinear polynomials to the given `supported_num_vars`, and
|
||||
|
/// returns committer key and verifier key. `supported_num_vars` should
|
||||
|
/// be in range `1..=params.num_vars`
|
||||
|
fn trim(
|
||||
|
&self,
|
||||
|
supported_num_vars: usize,
|
||||
|
) -> Result<(Self::ProverParam, Self::VerifierParam), PCSErrors> {
|
||||
|
if supported_num_vars > self.prover_param.num_vars {
|
||||
|
return Err(PCSErrors::InvalidParameters(format!(
|
||||
|
"SRS does not support target number of vars {}",
|
||||
|
supported_num_vars
|
||||
|
)));
|
||||
|
}
|
||||
|
|
||||
|
let to_reduce = self.prover_param.num_vars - supported_num_vars;
|
||||
|
let ck = Self::ProverParam {
|
||||
|
powers_of_g: self.prover_param.powers_of_g[to_reduce..].to_vec(),
|
||||
|
g: self.prover_param.g,
|
||||
|
h: self.prover_param.h,
|
||||
|
num_vars: supported_num_vars,
|
||||
|
};
|
||||
|
let vk = Self::VerifierParam {
|
||||
|
num_vars: supported_num_vars,
|
||||
|
g: self.prover_param.g,
|
||||
|
h: self.prover_param.h,
|
||||
|
h_mask: self.h_mask[to_reduce..].to_vec(),
|
||||
|
};
|
||||
|
Ok((ck, vk))
|
||||
|
}
|
||||
|
|
||||
|
/// Build SRS for testing.
|
||||
|
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
||||
|
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
||||
|
fn gen_srs_for_testing<R: RngCore>(rng: &mut R, num_vars: usize) -> Result<Self, PCSErrors> {
|
||||
|
if num_vars == 0 {
|
||||
|
return Err(PCSErrors::InvalidParameters(
|
||||
|
"constant polynomial not supported".to_string(),
|
||||
|
));
|
||||
|
}
|
||||
|
|
||||
|
let total_timer = start_timer!(|| "SRS generation");
|
||||
|
|
||||
|
let pp_generation_timer = start_timer!(|| "Prover Param generation");
|
||||
|
|
||||
|
let g = E::G1Projective::rand(rng);
|
||||
|
let h = E::G2Projective::rand(rng);
|
||||
|
|
||||
|
let mut powers_of_g = Vec::new();
|
||||
|
|
||||
|
let t: Vec<_> = (0..num_vars).map(|_| E::Fr::rand(rng)).collect();
|
||||
|
let scalar_bits = E::Fr::size_in_bits();
|
||||
|
|
||||
|
let mut eq: LinkedList<DenseMultilinearExtension<E::Fr>> =
|
||||
|
LinkedList::from_iter(eq_extension(&t).into_iter());
|
||||
|
let mut eq_arr = LinkedList::new();
|
||||
|
let mut base = eq.pop_back().unwrap().evaluations;
|
||||
|
|
||||
|
for i in (0..num_vars).rev() {
|
||||
|
eq_arr.push_front(remove_dummy_variable(&base, i)?);
|
||||
|
if i != 0 {
|
||||
|
let mul = eq.pop_back().unwrap().evaluations;
|
||||
|
base = base
|
||||
|
.into_iter()
|
||||
|
.zip(mul.into_iter())
|
||||
|
.map(|(a, b)| a * b)
|
||||
|
.collect();
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
let mut pp_powers = Vec::new();
|
||||
|
let mut total_scalars = 0;
|
||||
|
for i in 0..num_vars {
|
||||
|
let eq = eq_arr.pop_front().unwrap();
|
||||
|
let pp_k_powers = (0..(1 << (num_vars - i))).map(|x| eq[x]);
|
||||
|
pp_powers.extend(pp_k_powers);
|
||||
|
total_scalars += 1 << (num_vars - i);
|
||||
|
}
|
||||
|
let window_size = FixedBaseMSM::get_mul_window_size(total_scalars);
|
||||
|
let g_table = FixedBaseMSM::get_window_table(scalar_bits, window_size, g);
|
||||
|
|
||||
|
let pp_g = E::G1Projective::batch_normalization_into_affine(
|
||||
|
&FixedBaseMSM::multi_scalar_mul(scalar_bits, window_size, &g_table, &pp_powers),
|
||||
|
);
|
||||
|
|
||||
|
let mut start = 0;
|
||||
|
for i in 0..num_vars {
|
||||
|
let size = 1 << (num_vars - i);
|
||||
|
let pp_k_g = Evaluations {
|
||||
|
evals: pp_g[start..(start + size)].to_vec(),
|
||||
|
};
|
||||
|
powers_of_g.push(pp_k_g);
|
||||
|
start += size;
|
||||
|
}
|
||||
|
|
||||
|
let pp = Self::ProverParam {
|
||||
|
num_vars,
|
||||
|
g: g.into_affine(),
|
||||
|
h: h.into_affine(),
|
||||
|
powers_of_g,
|
||||
|
};
|
||||
|
|
||||
|
end_timer!(pp_generation_timer);
|
||||
|
|
||||
|
let vp_generation_timer = start_timer!(|| "VP generation");
|
||||
|
let h_mask = {
|
||||
|
let window_size = FixedBaseMSM::get_mul_window_size(num_vars);
|
||||
|
let h_table = FixedBaseMSM::get_window_table(scalar_bits, window_size, h);
|
||||
|
E::G2Projective::batch_normalization_into_affine(&FixedBaseMSM::multi_scalar_mul(
|
||||
|
scalar_bits,
|
||||
|
window_size,
|
||||
|
&h_table,
|
||||
|
&t,
|
||||
|
))
|
||||
|
};
|
||||
|
end_timer!(vp_generation_timer);
|
||||
|
end_timer!(total_timer);
|
||||
|
Ok(Self {
|
||||
|
prover_param: pp,
|
||||
|
h_mask,
|
||||
|
})
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
/// fix first `pad` variables of `poly` represented in evaluation form to zero
|
||||
|
fn remove_dummy_variable<F: Field>(poly: &[F], pad: usize) -> Result<Vec<F>, PCSErrors> {
|
||||
|
if pad == 0 {
|
||||
|
return Ok(poly.to_vec());
|
||||
|
}
|
||||
|
if !poly.len().is_power_of_two() {
|
||||
|
return Err(PCSErrors::InvalidParameters(
|
||||
|
"Size of polynomial should be power of two.".to_string(),
|
||||
|
));
|
||||
|
}
|
||||
|
let nv = ark_std::log2(poly.len()) as usize - pad;
|
||||
|
|
||||
|
Ok((0..(1 << nv)).map(|x| poly[x << pad]).collect())
|
||||
|
}
|
||||
|
|
||||
|
/// Generate eq(t,x), a product of multilinear polynomials with fixed t.
|
||||
|
/// eq(a,b) is takes extensions of a,b in {0,1}^num_vars such that if a and b in
|
||||
|
/// {0,1}^num_vars are equal then this polynomial evaluates to 1.
|
||||
|
fn eq_extension<F: PrimeField>(t: &[F]) -> Vec<DenseMultilinearExtension<F>> {
|
||||
|
let start = start_timer!(|| "eq extension");
|
||||
|
|
||||
|
let dim = t.len();
|
||||
|
let mut result = Vec::new();
|
||||
|
for (i, &ti) in t.iter().enumerate().take(dim) {
|
||||
|
let mut poly = Vec::with_capacity(1 << dim);
|
||||
|
for x in 0..(1 << dim) {
|
||||
|
let xi = if x >> i & 1 == 1 { F::one() } else { F::zero() };
|
||||
|
let ti_xi = ti * xi;
|
||||
|
poly.push(ti_xi + ti_xi - xi - ti + F::one());
|
||||
|
}
|
||||
|
result.push(DenseMultilinearExtension::from_evaluations_vec(dim, poly));
|
||||
|
}
|
||||
|
|
||||
|
end_timer!(start);
|
||||
|
result
|
||||
|
}
|
||||
|
|
||||
|
#[cfg(test)]
|
||||
|
mod tests {
|
||||
|
use super::*;
|
||||
|
use ark_bls12_381::Bls12_381;
|
||||
|
use ark_std::test_rng;
|
||||
|
type E = Bls12_381;
|
||||
|
|
||||
|
#[test]
|
||||
|
fn test_srs_gen() -> Result<(), PCSErrors> {
|
||||
|
let mut rng = test_rng();
|
||||
|
for nv in 4..10 {
|
||||
|
let _ = MultilinearUniversalParams::<E>::gen_srs_for_testing(&mut rng, nv)?;
|
||||
|
}
|
||||
|
|
||||
|
Ok(())
|
||||
|
}
|
||||
|
}
|
||||
@ -1,252 +1,3 @@ |
|||||
use std::collections::LinkedList;
|
|
||||
|
|
||||
use crate::PCSErrors;
|
|
||||
use ark_ec::{msm::FixedBaseMSM, AffineCurve, PairingEngine, ProjectiveCurve};
|
|
||||
use ark_ff::{Field, PrimeField};
|
|
||||
use ark_poly::DenseMultilinearExtension;
|
|
||||
|
use ark_ec::{AffineCurve, PairingEngine};
|
||||
use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read, SerializationError, Write};
|
use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read, SerializationError, Write};
|
||||
use ark_std::{end_timer, rand::RngCore, start_timer, vec::Vec, UniformRand};
|
|
||||
|
|
||||
/// Evaluations over {0,1}^n for G1 or G2
|
|
||||
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
|
||||
pub struct Evaluations<C: AffineCurve> {
|
|
||||
/// The evaluations.
|
|
||||
pub evals: Vec<C>,
|
|
||||
}
|
|
||||
|
|
||||
/// Universal Parameter
|
|
||||
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
|
||||
pub struct UniversalParams<E: PairingEngine> {
|
|
||||
/// prover parameters
|
|
||||
pub prover_param: ProverParam<E>,
|
|
||||
/// h^randomness: h^t1, h^t2, ..., **h^{t_nv}**
|
|
||||
pub h_mask: Vec<E::G2Affine>,
|
|
||||
}
|
|
||||
|
|
||||
/// Prover Parameters
|
|
||||
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
|
||||
pub struct ProverParam<E: PairingEngine> {
|
|
||||
/// number of variables
|
|
||||
pub num_vars: usize,
|
|
||||
/// `pp_{num_vars}`, `pp_{num_vars - 1}`, `pp_{num_vars - 2}`, ..., defined
|
|
||||
/// by XZZPD19
|
|
||||
pub powers_of_g: Vec<Evaluations<E::G1Affine>>,
|
|
||||
/// generator for G1
|
|
||||
pub g: E::G1Affine,
|
|
||||
/// generator for G2
|
|
||||
pub h: E::G2Affine,
|
|
||||
}
|
|
||||
|
|
||||
/// Verifier Parameters
|
|
||||
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
|
||||
pub struct VerifierParam<E: PairingEngine> {
|
|
||||
/// number of variables
|
|
||||
pub num_vars: usize,
|
|
||||
|
|
||||
/// generator of G1
|
|
||||
pub g: E::G1Affine,
|
|
||||
|
|
||||
/// generator of G2
|
|
||||
pub h: E::G2Affine,
|
|
||||
|
|
||||
/// h^randomness: h^t1, h^t2, ..., **h^{t_nv}**
|
|
||||
pub h_mask: Vec<E::G2Affine>,
|
|
||||
}
|
|
||||
|
|
||||
impl<E: PairingEngine> UniversalParams<E> {
|
|
||||
/// Extract the prover parameters from the public parameters.
|
|
||||
pub fn extract_prover_param(&self) -> ProverParam<E> {
|
|
||||
self.prover_param.clone()
|
|
||||
}
|
|
||||
|
|
||||
/// Extract the verifier parameters from the public parameters.
|
|
||||
pub fn extract_verifier_param(&self) -> VerifierParam<E> {
|
|
||||
VerifierParam {
|
|
||||
num_vars: self.prover_param.num_vars,
|
|
||||
g: self.prover_param.g,
|
|
||||
h: self.prover_param.h,
|
|
||||
h_mask: self.h_mask.clone(),
|
|
||||
}
|
|
||||
}
|
|
||||
|
|
||||
/// Trim the universal parameters to specialize the public parameters
|
|
||||
/// for multilinear polynomials to the given `supported_num_vars`, and
|
|
||||
/// returns committer key and verifier key. `supported_num_vars` should
|
|
||||
/// be in range `1..=params.num_vars`
|
|
||||
pub fn trim(
|
|
||||
&self,
|
|
||||
supported_num_vars: usize,
|
|
||||
) -> Result<(ProverParam<E>, VerifierParam<E>), PCSErrors> {
|
|
||||
if supported_num_vars > self.prover_param.num_vars {
|
|
||||
return Err(PCSErrors::InvalidParameters(format!(
|
|
||||
"SRS does not support target number of vars {}",
|
|
||||
supported_num_vars
|
|
||||
)));
|
|
||||
}
|
|
||||
|
|
||||
let to_reduce = self.prover_param.num_vars - supported_num_vars;
|
|
||||
let ck = ProverParam {
|
|
||||
powers_of_g: self.prover_param.powers_of_g[to_reduce..].to_vec(),
|
|
||||
g: self.prover_param.g,
|
|
||||
h: self.prover_param.h,
|
|
||||
num_vars: supported_num_vars,
|
|
||||
};
|
|
||||
let vk = VerifierParam {
|
|
||||
num_vars: supported_num_vars,
|
|
||||
g: self.prover_param.g,
|
|
||||
h: self.prover_param.h,
|
|
||||
h_mask: self.h_mask[to_reduce..].to_vec(),
|
|
||||
};
|
|
||||
Ok((ck, vk))
|
|
||||
}
|
|
||||
|
|
||||
/// Build SRS for testing.
|
|
||||
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
|
||||
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
|
||||
pub fn gen_srs_for_testing<R: RngCore>(
|
|
||||
rng: &mut R,
|
|
||||
num_vars: usize,
|
|
||||
) -> Result<Self, PCSErrors> {
|
|
||||
if num_vars == 0 {
|
|
||||
return Err(PCSErrors::InvalidParameters(
|
|
||||
"constant polynomial not supported".to_string(),
|
|
||||
));
|
|
||||
}
|
|
||||
|
|
||||
let total_timer = start_timer!(|| "SRS generation");
|
|
||||
|
|
||||
let pp_generation_timer = start_timer!(|| "Prover Param generation");
|
|
||||
|
|
||||
let g = E::G1Projective::rand(rng);
|
|
||||
let h = E::G2Projective::rand(rng);
|
|
||||
|
|
||||
let mut powers_of_g = Vec::new();
|
|
||||
|
|
||||
let t: Vec<_> = (0..num_vars).map(|_| E::Fr::rand(rng)).collect();
|
|
||||
let scalar_bits = E::Fr::size_in_bits();
|
|
||||
|
|
||||
let mut eq: LinkedList<DenseMultilinearExtension<E::Fr>> =
|
|
||||
LinkedList::from_iter(eq_extension(&t).into_iter());
|
|
||||
let mut eq_arr = LinkedList::new();
|
|
||||
let mut base = eq.pop_back().unwrap().evaluations;
|
|
||||
|
|
||||
for i in (0..num_vars).rev() {
|
|
||||
eq_arr.push_front(remove_dummy_variable(&base, i)?);
|
|
||||
if i != 0 {
|
|
||||
let mul = eq.pop_back().unwrap().evaluations;
|
|
||||
base = base
|
|
||||
.into_iter()
|
|
||||
.zip(mul.into_iter())
|
|
||||
.map(|(a, b)| a * b)
|
|
||||
.collect();
|
|
||||
}
|
|
||||
}
|
|
||||
|
|
||||
let mut pp_powers = Vec::new();
|
|
||||
let mut total_scalars = 0;
|
|
||||
for i in 0..num_vars {
|
|
||||
let eq = eq_arr.pop_front().unwrap();
|
|
||||
let pp_k_powers = (0..(1 << (num_vars - i))).map(|x| eq[x]);
|
|
||||
pp_powers.extend(pp_k_powers);
|
|
||||
total_scalars += 1 << (num_vars - i);
|
|
||||
}
|
|
||||
let window_size = FixedBaseMSM::get_mul_window_size(total_scalars);
|
|
||||
let g_table = FixedBaseMSM::get_window_table(scalar_bits, window_size, g);
|
|
||||
|
|
||||
let pp_g = E::G1Projective::batch_normalization_into_affine(
|
|
||||
&FixedBaseMSM::multi_scalar_mul(scalar_bits, window_size, &g_table, &pp_powers),
|
|
||||
);
|
|
||||
|
|
||||
let mut start = 0;
|
|
||||
for i in 0..num_vars {
|
|
||||
let size = 1 << (num_vars - i);
|
|
||||
let pp_k_g = Evaluations {
|
|
||||
evals: pp_g[start..(start + size)].to_vec(),
|
|
||||
};
|
|
||||
powers_of_g.push(pp_k_g);
|
|
||||
start += size;
|
|
||||
}
|
|
||||
|
|
||||
let pp = ProverParam {
|
|
||||
num_vars,
|
|
||||
g: g.into_affine(),
|
|
||||
h: h.into_affine(),
|
|
||||
powers_of_g,
|
|
||||
};
|
|
||||
|
|
||||
end_timer!(pp_generation_timer);
|
|
||||
|
|
||||
let vp_generation_timer = start_timer!(|| "VP generation");
|
|
||||
let h_mask = {
|
|
||||
let window_size = FixedBaseMSM::get_mul_window_size(num_vars);
|
|
||||
let h_table = FixedBaseMSM::get_window_table(scalar_bits, window_size, h);
|
|
||||
E::G2Projective::batch_normalization_into_affine(&FixedBaseMSM::multi_scalar_mul(
|
|
||||
scalar_bits,
|
|
||||
window_size,
|
|
||||
&h_table,
|
|
||||
&t,
|
|
||||
))
|
|
||||
};
|
|
||||
end_timer!(vp_generation_timer);
|
|
||||
end_timer!(total_timer);
|
|
||||
Ok(Self {
|
|
||||
prover_param: pp,
|
|
||||
h_mask,
|
|
||||
})
|
|
||||
}
|
|
||||
}
|
|
||||
|
|
||||
/// fix first `pad` variables of `poly` represented in evaluation form to zero
|
|
||||
fn remove_dummy_variable<F: Field>(poly: &[F], pad: usize) -> Result<Vec<F>, PCSErrors> {
|
|
||||
if pad == 0 {
|
|
||||
return Ok(poly.to_vec());
|
|
||||
}
|
|
||||
if !poly.len().is_power_of_two() {
|
|
||||
return Err(PCSErrors::InvalidParameters(
|
|
||||
"Size of polynomial should be power of two.".to_string(),
|
|
||||
));
|
|
||||
}
|
|
||||
let nv = ark_std::log2(poly.len()) as usize - pad;
|
|
||||
|
|
||||
Ok((0..(1 << nv)).map(|x| poly[x << pad]).collect())
|
|
||||
}
|
|
||||
|
|
||||
/// Generate eq(t,x), a product of multilinear polynomials with fixed t.
|
|
||||
/// eq(a,b) is takes extensions of a,b in {0,1}^num_vars such that if a and b in
|
|
||||
/// {0,1}^num_vars are equal then this polynomial evaluates to 1.
|
|
||||
fn eq_extension<F: PrimeField>(t: &[F]) -> Vec<DenseMultilinearExtension<F>> {
|
|
||||
let start = start_timer!(|| "eq extension");
|
|
||||
|
|
||||
let dim = t.len();
|
|
||||
let mut result = Vec::new();
|
|
||||
for (i, &ti) in t.iter().enumerate().take(dim) {
|
|
||||
let mut poly = Vec::with_capacity(1 << dim);
|
|
||||
for x in 0..(1 << dim) {
|
|
||||
let xi = if x >> i & 1 == 1 { F::one() } else { F::zero() };
|
|
||||
let ti_xi = ti * xi;
|
|
||||
poly.push(ti_xi + ti_xi - xi - ti + F::one());
|
|
||||
}
|
|
||||
result.push(DenseMultilinearExtension::from_evaluations_vec(dim, poly));
|
|
||||
}
|
|
||||
|
|
||||
end_timer!(start);
|
|
||||
result
|
|
||||
}
|
|
||||
|
|
||||
#[cfg(test)]
|
|
||||
mod tests {
|
|
||||
use super::*;
|
|
||||
use ark_bls12_381::Bls12_381;
|
|
||||
use ark_std::test_rng;
|
|
||||
type E = Bls12_381;
|
|
||||
|
|
||||
#[test]
|
|
||||
fn test_srs_gen() -> Result<(), PCSErrors> {
|
|
||||
let mut rng = test_rng();
|
|
||||
for nv in 4..10 {
|
|
||||
let _ = UniversalParams::<E>::gen_srs_for_testing(&mut rng, nv)?;
|
|
||||
}
|
|
||||
|
|
||||
Ok(())
|
|
||||
}
|
|
||||
}
|
|
||||
|
use ark_std::vec::Vec;
|
||||
@ -0,0 +1,13 @@ |
|||||
|
pub use crate::{
|
||||
|
errors::PCSErrors,
|
||||
|
multilinear_kzg::{
|
||||
|
srs::{MultilinearProverParam, MultilinearUniversalParams, MultilinearVerifierParam},
|
||||
|
util::merge_polynomials,
|
||||
|
BatchProof, KZGMultilinearPCS, Proof,
|
||||
|
},
|
||||
|
structs::Commitment,
|
||||
|
univariate_kzg::srs::{
|
||||
|
UnivariateProverParam, UnivariateUniversalParams, UnivariateVerifierParam,
|
||||
|
},
|
||||
|
PolynomialCommitmentScheme, StructuredReferenceString,
|
||||
|
};
|
||||
@ -0,0 +1,9 @@ |
|||||
|
use ark_ec::PairingEngine;
|
||||
|
use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read, SerializationError, Write};
|
||||
|
|
||||
|
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug, Default, PartialEq)]
|
||||
|
/// A commitment is an Affine point.
|
||||
|
pub struct Commitment<E: PairingEngine> {
|
||||
|
/// the actual commitment is an affine point.
|
||||
|
pub commitment: E::G1Affine,
|
||||
|
}
|
||||
@ -0,0 +1,384 @@ |
|||||
|
//! Main module for univariate KZG commitment scheme
|
||||
|
|
||||
|
use crate::{
|
||||
|
prelude::{Commitment, PCSErrors},
|
||||
|
PolynomialCommitmentScheme, StructuredReferenceString,
|
||||
|
};
|
||||
|
use ark_ec::{msm::VariableBaseMSM, AffineCurve, PairingEngine, ProjectiveCurve};
|
||||
|
use ark_ff::PrimeField;
|
||||
|
use ark_poly::{univariate::DensePolynomial, Polynomial, UVPolynomial};
|
||||
|
use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read, SerializationError, Write};
|
||||
|
use ark_std::{end_timer, rand::RngCore, start_timer, One, UniformRand, Zero};
|
||||
|
use srs::{UnivariateProverParam, UnivariateUniversalParams, UnivariateVerifierParam};
|
||||
|
use std::marker::PhantomData;
|
||||
|
|
||||
|
pub(crate) mod srs;
|
||||
|
|
||||
|
/// KZG Polynomial Commitment Scheme on univariate polynomial.
|
||||
|
pub struct KZGUnivariatePCS<E: PairingEngine> {
|
||||
|
#[doc(hidden)]
|
||||
|
phantom: PhantomData<E>,
|
||||
|
}
|
||||
|
|
||||
|
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
||||
|
/// proof of opening
|
||||
|
pub struct KZGUnivariateOpening<E: PairingEngine> {
|
||||
|
/// Evaluation of quotients
|
||||
|
pub proof: E::G1Affine,
|
||||
|
}
|
||||
|
|
||||
|
impl<E: PairingEngine> PolynomialCommitmentScheme<E> for KZGUnivariatePCS<E> {
|
||||
|
// Parameters
|
||||
|
type ProverParam = UnivariateProverParam<E::G1Affine>;
|
||||
|
type VerifierParam = UnivariateVerifierParam<E>;
|
||||
|
type SRS = UnivariateUniversalParams<E>;
|
||||
|
// Polynomial and its associated types
|
||||
|
type Polynomial = DensePolynomial<E::Fr>;
|
||||
|
type Point = E::Fr;
|
||||
|
type Evaluation = E::Fr;
|
||||
|
// Polynomial and its associated types
|
||||
|
type Commitment = Commitment<E>;
|
||||
|
type Proof = KZGUnivariateOpening<E>;
|
||||
|
type BatchProof = Vec<Self::Proof>;
|
||||
|
type BatchCommitment = Vec<Self::Commitment>;
|
||||
|
|
||||
|
/// Build SRS for testing.
|
||||
|
///
|
||||
|
/// - For univariate polynomials, `log_size` is the log of maximum degree.
|
||||
|
/// - For multilinear polynomials, `log_size` is the number of variables.
|
||||
|
///
|
||||
|
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
||||
|
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
||||
|
fn gen_srs_for_testing<R: RngCore>(
|
||||
|
rng: &mut R,
|
||||
|
log_size: usize,
|
||||
|
) -> Result<Self::SRS, PCSErrors> {
|
||||
|
Self::SRS::gen_srs_for_testing(rng, log_size)
|
||||
|
}
|
||||
|
|
||||
|
/// Generate a commitment for a polynomial
|
||||
|
/// Note that the scheme is not hidding
|
||||
|
fn commit(
|
||||
|
prover_param: &Self::ProverParam,
|
||||
|
poly: &Self::Polynomial,
|
||||
|
) -> Result<Self::Commitment, PCSErrors> {
|
||||
|
let commit_time =
|
||||
|
start_timer!(|| format!("Committing to polynomial of degree {} ", poly.degree()));
|
||||
|
|
||||
|
if poly.degree() > prover_param.powers_of_g.len() {
|
||||
|
return Err(PCSErrors::InvalidParameters(format!(
|
||||
|
"poly degree {} is larger than allowed {}",
|
||||
|
poly.degree(),
|
||||
|
prover_param.powers_of_g.len()
|
||||
|
)));
|
||||
|
}
|
||||
|
|
||||
|
let (num_leading_zeros, plain_coeffs) = skip_leading_zeros_and_convert_to_bigints(poly);
|
||||
|
|
||||
|
let msm_time = start_timer!(|| "MSM to compute commitment to plaintext poly");
|
||||
|
let commitment = VariableBaseMSM::multi_scalar_mul(
|
||||
|
&prover_param.powers_of_g[num_leading_zeros..],
|
||||
|
&plain_coeffs,
|
||||
|
)
|
||||
|
.into_affine();
|
||||
|
end_timer!(msm_time);
|
||||
|
|
||||
|
end_timer!(commit_time);
|
||||
|
Ok(Commitment { commitment })
|
||||
|
}
|
||||
|
|
||||
|
/// Generate a commitment for a list of polynomials
|
||||
|
fn multi_commit(
|
||||
|
prover_param: &Self::ProverParam,
|
||||
|
polys: &[Self::Polynomial],
|
||||
|
) -> Result<Self::BatchCommitment, PCSErrors> {
|
||||
|
let commit_time = start_timer!(|| format!("batch commit {} polynomials", polys.len()));
|
||||
|
let res = polys
|
||||
|
.iter()
|
||||
|
.map(|poly| Self::commit(prover_param, poly))
|
||||
|
.collect::<Result<Vec<Self::Commitment>, PCSErrors>>()?;
|
||||
|
|
||||
|
end_timer!(commit_time);
|
||||
|
Ok(res)
|
||||
|
}
|
||||
|
|
||||
|
/// On input a polynomial `p` and a point `point`, outputs a proof for the
|
||||
|
/// same.
|
||||
|
fn open(
|
||||
|
prover_param: &Self::ProverParam,
|
||||
|
polynomial: &Self::Polynomial,
|
||||
|
point: &Self::Point,
|
||||
|
) -> Result<(Self::Proof, Self::Evaluation), PCSErrors> {
|
||||
|
let open_time =
|
||||
|
start_timer!(|| format!("Opening polynomial of degree {}", polynomial.degree()));
|
||||
|
let divisor = Self::Polynomial::from_coefficients_vec(vec![-*point, E::Fr::one()]);
|
||||
|
|
||||
|
let witness_time = start_timer!(|| "Computing witness polynomial");
|
||||
|
let witness_polynomial = polynomial / &divisor;
|
||||
|
end_timer!(witness_time);
|
||||
|
|
||||
|
let (num_leading_zeros, witness_coeffs) =
|
||||
|
skip_leading_zeros_and_convert_to_bigints(&witness_polynomial);
|
||||
|
|
||||
|
let proof = VariableBaseMSM::multi_scalar_mul(
|
||||
|
&prover_param.powers_of_g[num_leading_zeros..],
|
||||
|
&witness_coeffs,
|
||||
|
)
|
||||
|
.into_affine();
|
||||
|
|
||||
|
let eval = polynomial.evaluate(point);
|
||||
|
|
||||
|
end_timer!(open_time);
|
||||
|
Ok((Self::Proof { proof }, eval))
|
||||
|
}
|
||||
|
|
||||
|
/// Input a list of polynomials, and a same number of points,
|
||||
|
/// compute a multi-opening for all the polynomials.
|
||||
|
// This is a naive approach
|
||||
|
// TODO: to implement the more efficient batch opening algorithm
|
||||
|
// (e.g., the appendix C.4 in https://eprint.iacr.org/2020/1536.pdf)
|
||||
|
fn multi_open(
|
||||
|
prover_param: &Self::ProverParam,
|
||||
|
_multi_commitment: &Self::Commitment,
|
||||
|
polynomials: &[Self::Polynomial],
|
||||
|
points: &[Self::Point],
|
||||
|
) -> Result<(Self::BatchProof, Vec<Self::Evaluation>), PCSErrors> {
|
||||
|
let open_time = start_timer!(|| format!("batch opening {} polynomials", polynomials.len()));
|
||||
|
if polynomials.len() != points.len() {
|
||||
|
return Err(PCSErrors::InvalidParameters(format!(
|
||||
|
"poly length {} is different from points length {}",
|
||||
|
polynomials.len(),
|
||||
|
points.len()
|
||||
|
)));
|
||||
|
}
|
||||
|
let mut batch_proof = vec![];
|
||||
|
let mut evals = vec![];
|
||||
|
for (poly, point) in polynomials.iter().zip(points.iter()) {
|
||||
|
let (proof, eval) = Self::open(prover_param, poly, point)?;
|
||||
|
batch_proof.push(proof);
|
||||
|
evals.push(eval);
|
||||
|
}
|
||||
|
|
||||
|
end_timer!(open_time);
|
||||
|
Ok((batch_proof, evals))
|
||||
|
}
|
||||
|
/// Verifies that `value` is the evaluation at `x` of the polynomial
|
||||
|
/// committed inside `comm`.
|
||||
|
fn verify(
|
||||
|
verifier_param: &Self::VerifierParam,
|
||||
|
commitment: &Self::Commitment,
|
||||
|
point: &Self::Point,
|
||||
|
value: &E::Fr,
|
||||
|
proof: &Self::Proof,
|
||||
|
) -> Result<bool, PCSErrors> {
|
||||
|
let check_time = start_timer!(|| "Checking evaluation");
|
||||
|
let pairing_inputs: Vec<(E::G1Prepared, E::G2Prepared)> = vec![
|
||||
|
(
|
||||
|
(verifier_param.g.mul(value.into_repr())
|
||||
|
- proof.proof.mul(point.into_repr())
|
||||
|
- commitment.commitment.into_projective())
|
||||
|
.into_affine()
|
||||
|
.into(),
|
||||
|
verifier_param.h.into(),
|
||||
|
),
|
||||
|
(proof.proof.into(), verifier_param.beta_h.into()),
|
||||
|
];
|
||||
|
|
||||
|
let res = E::product_of_pairings(pairing_inputs.iter()).is_one();
|
||||
|
|
||||
|
end_timer!(check_time, || format!("Result: {}", res));
|
||||
|
Ok(res)
|
||||
|
}
|
||||
|
|
||||
|
/// Verifies that `value_i` is the evaluation at `x_i` of the polynomial
|
||||
|
/// `poly_i` committed inside `comm`.
|
||||
|
// This is a naive approach
|
||||
|
// TODO: to implement the more efficient batch verification algorithm
|
||||
|
// (e.g., the appendix C.4 in https://eprint.iacr.org/2020/1536.pdf)
|
||||
|
fn batch_verify<R: RngCore>(
|
||||
|
verifier_param: &Self::VerifierParam,
|
||||
|
multi_commitment: &Self::BatchCommitment,
|
||||
|
points: &[Self::Point],
|
||||
|
values: &[E::Fr],
|
||||
|
batch_proof: &Self::BatchProof,
|
||||
|
rng: &mut R,
|
||||
|
) -> Result<bool, PCSErrors> {
|
||||
|
let check_time =
|
||||
|
start_timer!(|| format!("Checking {} evaluation proofs", multi_commitment.len()));
|
||||
|
|
||||
|
let mut total_c = <E::G1Projective>::zero();
|
||||
|
let mut total_w = <E::G1Projective>::zero();
|
||||
|
|
||||
|
let combination_time = start_timer!(|| "Combining commitments and proofs");
|
||||
|
let mut randomizer = E::Fr::one();
|
||||
|
// Instead of multiplying g and gamma_g in each turn, we simply accumulate
|
||||
|
// their coefficients and perform a final multiplication at the end.
|
||||
|
let mut g_multiplier = E::Fr::zero();
|
||||
|
for (((c, z), v), proof) in multi_commitment
|
||||
|
.iter()
|
||||
|
.zip(points)
|
||||
|
.zip(values)
|
||||
|
.zip(batch_proof)
|
||||
|
{
|
||||
|
let w = proof.proof;
|
||||
|
let mut temp = w.mul(*z);
|
||||
|
temp.add_assign_mixed(&c.commitment);
|
||||
|
let c = temp;
|
||||
|
g_multiplier += &(randomizer * v);
|
||||
|
total_c += &c.mul(randomizer.into_repr());
|
||||
|
total_w += &w.mul(randomizer.into_repr());
|
||||
|
// We don't need to sample randomizers from the full field,
|
||||
|
// only from 128-bit strings.
|
||||
|
randomizer = u128::rand(rng).into();
|
||||
|
}
|
||||
|
total_c -= &verifier_param.g.mul(g_multiplier);
|
||||
|
end_timer!(combination_time);
|
||||
|
|
||||
|
let to_affine_time = start_timer!(|| "Converting results to affine for pairing");
|
||||
|
let affine_points = E::G1Projective::batch_normalization_into_affine(&[-total_w, total_c]);
|
||||
|
let (total_w, total_c) = (affine_points[0], affine_points[1]);
|
||||
|
end_timer!(to_affine_time);
|
||||
|
|
||||
|
let pairing_time = start_timer!(|| "Performing product of pairings");
|
||||
|
let result = E::product_of_pairings(&[
|
||||
|
(total_w.into(), verifier_param.beta_h.into()),
|
||||
|
(total_c.into(), verifier_param.h.into()),
|
||||
|
])
|
||||
|
.is_one();
|
||||
|
end_timer!(pairing_time);
|
||||
|
end_timer!(check_time, || format!("Result: {}", result));
|
||||
|
Ok(result)
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
fn skip_leading_zeros_and_convert_to_bigints<F: PrimeField, P: UVPolynomial<F>>(
|
||||
|
p: &P,
|
||||
|
) -> (usize, Vec<F::BigInt>) {
|
||||
|
let mut num_leading_zeros = 0;
|
||||
|
while num_leading_zeros < p.coeffs().len() && p.coeffs()[num_leading_zeros].is_zero() {
|
||||
|
num_leading_zeros += 1;
|
||||
|
}
|
||||
|
let coeffs = convert_to_bigints(&p.coeffs()[num_leading_zeros..]);
|
||||
|
(num_leading_zeros, coeffs)
|
||||
|
}
|
||||
|
|
||||
|
fn convert_to_bigints<F: PrimeField>(p: &[F]) -> Vec<F::BigInt> {
|
||||
|
let to_bigint_time = start_timer!(|| "Converting polynomial coeffs to bigints");
|
||||
|
let coeffs = p.iter().map(|s| s.into_repr()).collect::<Vec<_>>();
|
||||
|
end_timer!(to_bigint_time);
|
||||
|
coeffs
|
||||
|
}
|
||||
|
|
||||
|
#[cfg(test)]
|
||||
|
mod tests {
|
||||
|
use super::*;
|
||||
|
use crate::StructuredReferenceString;
|
||||
|
use ark_bls12_381::Bls12_381;
|
||||
|
use ark_ec::PairingEngine;
|
||||
|
use ark_poly::univariate::DensePolynomial;
|
||||
|
use ark_std::{log2, test_rng, UniformRand};
|
||||
|
|
||||
|
fn end_to_end_test_template<E>() -> Result<(), PCSErrors>
|
||||
|
where
|
||||
|
E: PairingEngine,
|
||||
|
{
|
||||
|
let rng = &mut test_rng();
|
||||
|
for _ in 0..100 {
|
||||
|
let mut degree = 0;
|
||||
|
while degree <= 1 {
|
||||
|
degree = usize::rand(rng) % 20;
|
||||
|
}
|
||||
|
let log_degree = log2(degree) as usize;
|
||||
|
let pp = KZGUnivariatePCS::<E>::gen_srs_for_testing(rng, log_degree)?;
|
||||
|
let (ck, vk) = pp.trim(log_degree)?;
|
||||
|
let p = <DensePolynomial<E::Fr> as UVPolynomial<E::Fr>>::rand(degree, rng);
|
||||
|
let comm = KZGUnivariatePCS::<E>::commit(&ck, &p)?;
|
||||
|
let point = E::Fr::rand(rng);
|
||||
|
let (proof, value) = KZGUnivariatePCS::<E>::open(&ck, &p, &point)?;
|
||||
|
assert!(
|
||||
|
KZGUnivariatePCS::<E>::verify(&vk, &comm, &point, &value, &proof)?,
|
||||
|
"proof was incorrect for max_degree = {}, polynomial_degree = {}",
|
||||
|
degree,
|
||||
|
p.degree(),
|
||||
|
);
|
||||
|
}
|
||||
|
Ok(())
|
||||
|
}
|
||||
|
|
||||
|
fn linear_polynomial_test_template<E>() -> Result<(), PCSErrors>
|
||||
|
where
|
||||
|
E: PairingEngine,
|
||||
|
{
|
||||
|
let rng = &mut test_rng();
|
||||
|
for _ in 0..100 {
|
||||
|
let degree = 50;
|
||||
|
let log_degree = log2(degree) as usize;
|
||||
|
|
||||
|
let pp = KZGUnivariatePCS::<E>::gen_srs_for_testing(rng, log_degree)?;
|
||||
|
let (ck, vk) = pp.trim(log_degree)?;
|
||||
|
let p = <DensePolynomial<E::Fr> as UVPolynomial<E::Fr>>::rand(degree, rng);
|
||||
|
let comm = KZGUnivariatePCS::<E>::commit(&ck, &p)?;
|
||||
|
let point = E::Fr::rand(rng);
|
||||
|
let (proof, value) = KZGUnivariatePCS::<E>::open(&ck, &p, &point)?;
|
||||
|
assert!(
|
||||
|
KZGUnivariatePCS::<E>::verify(&vk, &comm, &point, &value, &proof)?,
|
||||
|
"proof was incorrect for max_degree = {}, polynomial_degree = {}",
|
||||
|
degree,
|
||||
|
p.degree(),
|
||||
|
);
|
||||
|
}
|
||||
|
Ok(())
|
||||
|
}
|
||||
|
|
||||
|
fn batch_check_test_template<E>() -> Result<(), PCSErrors>
|
||||
|
where
|
||||
|
E: PairingEngine,
|
||||
|
{
|
||||
|
let rng = &mut test_rng();
|
||||
|
for _ in 0..10 {
|
||||
|
let mut degree = 0;
|
||||
|
while degree <= 1 {
|
||||
|
degree = usize::rand(rng) % 20;
|
||||
|
}
|
||||
|
let log_degree = log2(degree) as usize;
|
||||
|
let pp = KZGUnivariatePCS::<E>::gen_srs_for_testing(rng, log_degree)?;
|
||||
|
let (ck, vk) = pp.trim(log_degree)?;
|
||||
|
let mut comms = Vec::new();
|
||||
|
let mut values = Vec::new();
|
||||
|
let mut points = Vec::new();
|
||||
|
let mut proofs = Vec::new();
|
||||
|
for _ in 0..10 {
|
||||
|
let p = <DensePolynomial<E::Fr> as UVPolynomial<E::Fr>>::rand(degree, rng);
|
||||
|
let comm = KZGUnivariatePCS::<E>::commit(&ck, &p)?;
|
||||
|
let point = E::Fr::rand(rng);
|
||||
|
let (proof, value) = KZGUnivariatePCS::<E>::open(&ck, &p, &point)?;
|
||||
|
|
||||
|
assert!(KZGUnivariatePCS::<E>::verify(
|
||||
|
&vk, &comm, &point, &value, &proof
|
||||
|
)?);
|
||||
|
comms.push(comm);
|
||||
|
values.push(value);
|
||||
|
points.push(point);
|
||||
|
proofs.push(proof);
|
||||
|
}
|
||||
|
assert!(KZGUnivariatePCS::<E>::batch_verify(
|
||||
|
&vk, &comms, &points, &values, &proofs, rng
|
||||
|
)?);
|
||||
|
}
|
||||
|
Ok(())
|
||||
|
}
|
||||
|
|
||||
|
#[test]
|
||||
|
fn end_to_end_test() {
|
||||
|
end_to_end_test_template::<Bls12_381>().expect("test failed for bls12-381");
|
||||
|
}
|
||||
|
|
||||
|
#[test]
|
||||
|
fn linear_polynomial_test() {
|
||||
|
linear_polynomial_test_template::<Bls12_381>().expect("test failed for bls12-381");
|
||||
|
}
|
||||
|
#[test]
|
||||
|
fn batch_check_test() {
|
||||
|
batch_check_test_template::<Bls12_381>().expect("test failed for bls12-381");
|
||||
|
}
|
||||
|
}
|
||||
@ -0,0 +1,127 @@ |
|||||
|
//! Implementing Structured Reference Strings for univariate polynomial KZG
|
||||
|
|
||||
|
use crate::{prelude::PCSErrors, StructuredReferenceString};
|
||||
|
use ark_ec::{msm::FixedBaseMSM, AffineCurve, PairingEngine, ProjectiveCurve};
|
||||
|
use ark_ff::PrimeField;
|
||||
|
use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read, SerializationError, Write};
|
||||
|
use ark_std::{end_timer, rand::RngCore, start_timer, One, UniformRand};
|
||||
|
|
||||
|
/// `UniversalParams` are the universal parameters for the KZG10 scheme.
|
||||
|
/// Adapted from
|
||||
|
/// https://github.com/arkworks-rs/poly-commit/blob/master/src/kzg10/data_structures.rs#L20
|
||||
|
#[derive(Clone, Debug)]
|
||||
|
pub struct UnivariateUniversalParams<E: PairingEngine> {
|
||||
|
/// Group elements of the form `{ \beta^i G }`, where `i` ranges from 0 to
|
||||
|
/// `degree`.
|
||||
|
pub powers_of_g: Vec<E::G1Affine>,
|
||||
|
/// The generator of G2.
|
||||
|
pub h: E::G2Affine,
|
||||
|
/// \beta times the above generator of G2.
|
||||
|
pub beta_h: E::G2Affine,
|
||||
|
}
|
||||
|
|
||||
|
/// Prover Parameters
|
||||
|
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
||||
|
pub struct UnivariateProverParam<C: AffineCurve> {
|
||||
|
pub powers_of_g: Vec<C>,
|
||||
|
}
|
||||
|
|
||||
|
/// `VerifierKey` is used to check evaluation proofs for a given commitment.
|
||||
|
/// https://github.com/arkworks-rs/poly-commit/blob/master/src/kzg10/data_structures.rs#L236
|
||||
|
#[derive(Clone, Debug)]
|
||||
|
pub struct UnivariateVerifierParam<E: PairingEngine> {
|
||||
|
/// The generator of G1.
|
||||
|
pub g: E::G1Affine,
|
||||
|
/// The generator of G2.
|
||||
|
pub h: E::G2Affine,
|
||||
|
/// \beta times the above generator of G2.
|
||||
|
pub beta_h: E::G2Affine,
|
||||
|
}
|
||||
|
|
||||
|
impl<E: PairingEngine> StructuredReferenceString<E> for UnivariateUniversalParams<E> {
|
||||
|
type ProverParam = UnivariateProverParam<E::G1Affine>;
|
||||
|
type VerifierParam = UnivariateVerifierParam<E>;
|
||||
|
|
||||
|
/// Extract the prover parameters from the public parameters.
|
||||
|
fn extract_prover_param(&self, supported_log_size: usize) -> Self::ProverParam {
|
||||
|
let support_size = 1usize << supported_log_size;
|
||||
|
let powers_of_g = self.powers_of_g[..=support_size].to_vec();
|
||||
|
|
||||
|
Self::ProverParam { powers_of_g }
|
||||
|
}
|
||||
|
|
||||
|
/// Extract the verifier parameters from the public parameters.
|
||||
|
fn extract_verifier_param(&self, _supported_log_size: usize) -> Self::VerifierParam {
|
||||
|
Self::VerifierParam {
|
||||
|
g: self.powers_of_g[0],
|
||||
|
h: self.h,
|
||||
|
beta_h: self.beta_h,
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
/// Trim the universal parameters to specialize the public parameters
|
||||
|
/// for univariate polynomials to the given `supported_log_size`, and
|
||||
|
/// returns committer key and verifier key. `supported_log_size` should
|
||||
|
/// be in range `1..log(params.len())`
|
||||
|
fn trim(
|
||||
|
&self,
|
||||
|
supported_log_size: usize,
|
||||
|
) -> Result<(Self::ProverParam, Self::VerifierParam), PCSErrors> {
|
||||
|
let support_size = 1usize << supported_log_size;
|
||||
|
let powers_of_g = self.powers_of_g[..=support_size].to_vec();
|
||||
|
|
||||
|
let pk = Self::ProverParam { powers_of_g };
|
||||
|
let vk = Self::VerifierParam {
|
||||
|
g: self.powers_of_g[0],
|
||||
|
h: self.h,
|
||||
|
beta_h: self.beta_h,
|
||||
|
};
|
||||
|
Ok((pk, vk))
|
||||
|
}
|
||||
|
|
||||
|
/// Build SRS for testing.
|
||||
|
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
||||
|
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
||||
|
fn gen_srs_for_testing<R: RngCore>(rng: &mut R, log_degree: usize) -> Result<Self, PCSErrors> {
|
||||
|
let max_degree = 1usize << log_degree;
|
||||
|
let setup_time = start_timer!(|| format!("KZG10::Setup with degree {}", max_degree));
|
||||
|
let beta = E::Fr::rand(rng);
|
||||
|
let g = E::G1Projective::rand(rng);
|
||||
|
let h = E::G2Projective::rand(rng);
|
||||
|
|
||||
|
let mut powers_of_beta = vec![E::Fr::one()];
|
||||
|
|
||||
|
let mut cur = beta;
|
||||
|
for _ in 0..max_degree {
|
||||
|
powers_of_beta.push(cur);
|
||||
|
cur *= β
|
||||
|
}
|
||||
|
|
||||
|
let window_size = FixedBaseMSM::get_mul_window_size(max_degree + 1);
|
||||
|
|
||||
|
let scalar_bits = E::Fr::size_in_bits();
|
||||
|
let g_time = start_timer!(|| "Generating powers of G");
|
||||
|
// TODO: parallelization
|
||||
|
let g_table = FixedBaseMSM::get_window_table(scalar_bits, window_size, g);
|
||||
|
let powers_of_g = FixedBaseMSM::multi_scalar_mul::<E::G1Projective>(
|
||||
|
scalar_bits,
|
||||
|
window_size,
|
||||
|
&g_table,
|
||||
|
&powers_of_beta,
|
||||
|
);
|
||||
|
end_timer!(g_time);
|
||||
|
|
||||
|
let powers_of_g = E::G1Projective::batch_normalization_into_affine(&powers_of_g);
|
||||
|
|
||||
|
let h = h.into_affine();
|
||||
|
let beta_h = h.mul(beta).into_affine();
|
||||
|
|
||||
|
let pp = Self {
|
||||
|
powers_of_g,
|
||||
|
h,
|
||||
|
beta_h,
|
||||
|
};
|
||||
|
end_timer!(setup_time);
|
||||
|
Ok(pp)
|
||||
|
}
|
||||
|
}
|
||||