@ -0,0 +1,81 @@ |
|||
use ark_bls12_381::{Bls12_381, Fr};
|
|||
use ark_ff::UniformRand;
|
|||
use ark_poly::{DenseMultilinearExtension, MultilinearExtension};
|
|||
use ark_std::test_rng;
|
|||
use pcs::{KZGMultilinearPC, MultilinearCommitmentScheme, PCSErrors};
|
|||
use std::time::Instant;
|
|||
|
|||
fn main() -> Result<(), PCSErrors> {
|
|||
bench_pcs()
|
|||
}
|
|||
|
|||
fn bench_pcs() -> Result<(), PCSErrors> {
|
|||
let mut rng = test_rng();
|
|||
|
|||
// normal polynomials
|
|||
let uni_params = KZGMultilinearPC::<Bls12_381>::setup(&mut rng, 18)?;
|
|||
|
|||
for nv in 4..19 {
|
|||
let repetition = if nv < 10 {
|
|||
100
|
|||
} else if nv < 20 {
|
|||
50
|
|||
} else {
|
|||
10
|
|||
};
|
|||
|
|||
let poly = DenseMultilinearExtension::rand(nv, &mut rng);
|
|||
let (ck, vk) = uni_params.trim(nv)?;
|
|||
let point: Vec<_> = (0..nv).map(|_| Fr::rand(&mut rng)).collect();
|
|||
|
|||
// commit
|
|||
let com = {
|
|||
let start = Instant::now();
|
|||
for _ in 0..repetition {
|
|||
let _commit = KZGMultilinearPC::commit(&ck, &poly)?;
|
|||
}
|
|||
|
|||
println!(
|
|||
"KZG commit for {} variables: {} ns",
|
|||
nv,
|
|||
start.elapsed().as_nanos() / repetition as u128
|
|||
);
|
|||
|
|||
KZGMultilinearPC::commit(&ck, &poly)?
|
|||
};
|
|||
|
|||
// open
|
|||
let proof = {
|
|||
let start = Instant::now();
|
|||
for _ in 0..repetition {
|
|||
let _open = KZGMultilinearPC::open(&ck, &poly, &point)?;
|
|||
}
|
|||
|
|||
println!(
|
|||
"KZG open for {} variables: {} ns",
|
|||
nv,
|
|||
start.elapsed().as_nanos() / repetition as u128
|
|||
);
|
|||
KZGMultilinearPC::open(&ck, &poly, &point)?
|
|||
};
|
|||
let value = poly.evaluate(&point).unwrap();
|
|||
|
|||
// verify
|
|||
|
|||
{
|
|||
let start = Instant::now();
|
|||
for _ in 0..repetition {
|
|||
assert!(KZGMultilinearPC::verify(&vk, &com, &point, value, &proof)?);
|
|||
}
|
|||
println!(
|
|||
"KZG verify for {} variables: {} ns",
|
|||
nv,
|
|||
start.elapsed().as_nanos() / repetition as u128
|
|||
);
|
|||
}
|
|||
|
|||
println!("====================================");
|
|||
}
|
|||
|
|||
Ok(())
|
|||
}
|
@ -0,0 +1,257 @@ |
|||
use ark_ec::{
|
|||
msm::{FixedBaseMSM, VariableBaseMSM},
|
|||
AffineCurve, PairingEngine, ProjectiveCurve,
|
|||
};
|
|||
use ark_ff::PrimeField;
|
|||
use ark_poly::MultilinearExtension;
|
|||
use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read, SerializationError, Write};
|
|||
use ark_std::{end_timer, rand::RngCore, start_timer, vec::Vec, One, Zero};
|
|||
|
|||
use crate::{
|
|||
KZGMultilinearPC, MultilinearCommitmentScheme, PCSErrors, ProverParam, UniversalParams,
|
|||
VerifierParam,
|
|||
};
|
|||
|
|||
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
|||
/// commitment
|
|||
pub struct Commitment<E: PairingEngine> {
|
|||
/// number of variables
|
|||
pub nv: usize,
|
|||
/// product of g as described by the vRAM paper
|
|||
pub g_product: E::G1Affine,
|
|||
}
|
|||
|
|||
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
|||
/// proof of opening
|
|||
pub struct Proof<E: PairingEngine> {
|
|||
/// Evaluation of quotients
|
|||
pub proofs: Vec<E::G2Affine>,
|
|||
}
|
|||
|
|||
impl<E: PairingEngine> MultilinearCommitmentScheme<E> for KZGMultilinearPC<E> {
|
|||
type ProverParam = ProverParam<E>;
|
|||
type VerifierParam = VerifierParam<E>;
|
|||
type SRS = UniversalParams<E>;
|
|||
type Commitment = Commitment<E>;
|
|||
type Proof = Proof<E>;
|
|||
|
|||
/// Generate SRS from RNG.
|
|||
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
|||
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
|||
fn setup<R: RngCore>(rng: &mut R, num_vars: usize) -> Result<Self::SRS, PCSErrors> {
|
|||
let setup_timer = start_timer!(|| format!("SRS setup for dim {}", num_vars));
|
|||
let res = Self::SRS::gen_srs_for_testing(rng, num_vars);
|
|||
end_timer!(setup_timer);
|
|||
res
|
|||
}
|
|||
|
|||
/// 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: &impl MultilinearExtension<E::Fr>,
|
|||
) -> Result<Self::Commitment, PCSErrors> {
|
|||
let commit_timer = start_timer!(|| "commit");
|
|||
|
|||
let nv = poly.num_vars();
|
|||
let scalars: Vec<_> = poly
|
|||
.to_evaluations()
|
|||
.into_iter()
|
|||
.map(|x| x.into_repr())
|
|||
.collect();
|
|||
let g_product = VariableBaseMSM::multi_scalar_mul(
|
|||
&prover_param.powers_of_g[0].evals,
|
|||
scalars.as_slice(),
|
|||
)
|
|||
.into_affine();
|
|||
|
|||
end_timer!(commit_timer);
|
|||
Ok(Commitment { nv, g_product })
|
|||
}
|
|||
|
|||
/// 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
|
|||
/// G2:
|
|||
/// - 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(
|
|||
prover_param: &Self::ProverParam,
|
|||
polynomial: &impl MultilinearExtension<E::Fr>,
|
|||
point: &[E::Fr],
|
|||
) -> Result<Self::Proof, PCSErrors> {
|
|||
let open_timer = start_timer!(|| "open");
|
|||
|
|||
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, hi)) in point
|
|||
.iter()
|
|||
.zip(prover_param.powers_of_h.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 G2 and is likely to be the bottleneck
|
|||
proofs.push(VariableBaseMSM::multi_scalar_mul(&hi.evals, &scalars).into_affine());
|
|||
end_timer!(ith_round);
|
|||
}
|
|||
|
|||
end_timer!(open_timer);
|
|||
Ok(Proof { proofs })
|
|||
}
|
|||
|
|||
/// 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: &[E::Fr],
|
|||
value: E::Fr,
|
|||
proof: &Self::Proof,
|
|||
) -> 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 g_table = FixedBaseMSM::get_window_table(
|
|||
scalar_size,
|
|||
window_size,
|
|||
verifier_param.g.into_projective(),
|
|||
);
|
|||
let g_mul: Vec<E::G1Projective> =
|
|||
FixedBaseMSM::multi_scalar_mul(scalar_size, window_size, &g_table, point);
|
|||
|
|||
let mut g1_vec: Vec<_> = (0..verifier_param.num_vars)
|
|||
.map(|i| verifier_param.g_mask[i].into_projective() - g_mul[i])
|
|||
.collect();
|
|||
g1_vec.push(verifier_param.g.mul(value) - commitment.g_product.into_projective());
|
|||
|
|||
let g1_vec: Vec<E::G1Affine> = E::G1Projective::batch_normalization_into_affine(&g1_vec);
|
|||
let tmp = g1_vec[verifier_param.num_vars];
|
|||
end_timer!(prepare_inputs_timer);
|
|||
|
|||
let pairing_product_timer = start_timer!(|| "pairing product");
|
|||
|
|||
let mut pairings: Vec<_> = g1_vec
|
|||
.into_iter()
|
|||
.take(verifier_param.num_vars)
|
|||
.map(E::G1Prepared::from)
|
|||
.zip(proof.proofs.iter().map(|&x| E::G2Prepared::from(x)))
|
|||
.collect();
|
|||
|
|||
pairings.push((
|
|||
E::G1Prepared::from(tmp),
|
|||
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 ark_bls12_381::Bls12_381;
|
|||
use ark_ec::PairingEngine;
|
|||
use ark_poly::{DenseMultilinearExtension, MultilinearExtension, SparseMultilinearExtension};
|
|||
use ark_std::{rand::RngCore, test_rng, vec::Vec, UniformRand};
|
|||
type E = Bls12_381;
|
|||
type Fr = <E as PairingEngine>::Fr;
|
|||
|
|||
fn test_kzg_mlpc_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 setup_commit_verify_correct_polynomials() -> 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_kzg_mlpc_helper(&uni_params, &poly1, &mut rng)?;
|
|||
|
|||
let poly2 = SparseMultilinearExtension::rand_with_config(9, 1 << 5, &mut rng);
|
|||
test_kzg_mlpc_helper(&uni_params, &poly2, &mut rng)?;
|
|||
|
|||
// single-variate polynomials
|
|||
let poly3 = DenseMultilinearExtension::rand(1, &mut rng);
|
|||
test_kzg_mlpc_helper(&uni_params, &poly3, &mut rng)?;
|
|||
|
|||
let poly4 = SparseMultilinearExtension::rand_with_config(1, 1 << 1, &mut rng);
|
|||
test_kzg_mlpc_helper(&uni_params, &poly4, &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());
|
|||
}
|
|||
}
|
@ -0,0 +1,25 @@ |
|||
//! Error module.
|
|||
|
|||
use ark_std::string::String;
|
|||
use displaydoc::Display;
|
|||
|
|||
/// A `enum` specifying the possible failure modes of the PCS.
|
|||
#[derive(Display, Debug)]
|
|||
pub enum PCSErrors {
|
|||
/// Invalid Prover: {0}
|
|||
InvalidProver(String),
|
|||
/// Invalid Verifier: {0}
|
|||
InvalidVerifier(String),
|
|||
/// Invalid Proof: {0}
|
|||
InvalidProof(String),
|
|||
/// Invalid parameters: {0}
|
|||
InvalidParameters(String),
|
|||
/// An error during (de)serialization: {0}
|
|||
SerializationError(ark_serialize::SerializationError),
|
|||
}
|
|||
|
|||
impl From<ark_serialize::SerializationError> for PCSErrors {
|
|||
fn from(e: ark_serialize::SerializationError) -> Self {
|
|||
Self::SerializationError(e)
|
|||
}
|
|||
}
|
@ -1,8 +1,53 @@ |
|||
#[cfg(test)]
|
|||
mod tests {
|
|||
#[test]
|
|||
fn it_works() {
|
|||
let result = 2 + 2;
|
|||
assert_eq!(result, 4);
|
|||
}
|
|||
mod commit;
|
|||
mod errors;
|
|||
mod param;
|
|||
|
|||
use ark_ec::PairingEngine;
|
|||
use ark_poly::MultilinearExtension;
|
|||
use ark_std::rand::RngCore;
|
|||
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> {
|
|||
phantom: PhantomData<E>,
|
|||
}
|
|||
|
|||
pub trait MultilinearCommitmentScheme<E: PairingEngine> {
|
|||
type ProverParam;
|
|||
type VerifierParam;
|
|||
type SRS;
|
|||
type Commitment;
|
|||
type Proof;
|
|||
|
|||
/// Generate SRS from RNG.
|
|||
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
|
|||
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
|
|||
fn setup<R: RngCore>(rng: &mut R, num_vars: usize) -> Result<Self::SRS, PCSErrors>;
|
|||
|
|||
/// Generate a commitment for a polynomial
|
|||
fn commit(
|
|||
prover_param: &Self::ProverParam,
|
|||
poly: &impl MultilinearExtension<E::Fr>,
|
|||
) -> Result<Self::Commitment, PCSErrors>;
|
|||
|
|||
/// On input a polynomial `p` and a point `point`, outputs a proof for the
|
|||
/// same.
|
|||
fn open(
|
|||
prover_param: &Self::ProverParam,
|
|||
polynomial: &impl MultilinearExtension<E::Fr>,
|
|||
point: &[E::Fr],
|
|||
) -> Result<Self::Proof, PCSErrors>;
|
|||
|
|||
/// Verifies that `value` is the evaluation at `x` of the polynomial
|
|||
/// committed inside `comm`.
|
|||
fn verify(
|
|||
verifier_param: &Self::VerifierParam,
|
|||
commitment: &Self::Commitment,
|
|||
point: &[E::Fr],
|
|||
value: E::Fr,
|
|||
proof: &Self::Proof,
|
|||
) -> Result<bool, PCSErrors>;
|
|||
}
|
@ -0,0 +1,259 @@ |
|||
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_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> {
|
|||
pub evals: Vec<C>,
|
|||
}
|
|||
|
|||
/// Universal Parameter
|
|||
#[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
|
|||
pub struct UniversalParams<E: PairingEngine> {
|
|||
/// prover parameters
|
|||
pub prover_param: ProverParam<E>,
|
|||
/// g^randomness: g^t1, g^t2, ...
|
|||
pub g_mask: Vec<E::G1Affine>,
|
|||
}
|
|||
|
|||
/// 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>>,
|
|||
/// `pp_{num_vars}`, `pp_{num_vars - 1}`, `pp_{num_vars - 2}`, ..., defined
|
|||
/// by XZZPD19
|
|||
pub powers_of_h: Vec<Evaluations<E::G2Affine>>,
|
|||
/// 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,
|
|||
/// g^t1, g^t2, ...
|
|||
pub g_mask: Vec<E::G1Affine>,
|
|||
}
|
|||
|
|||
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,
|
|||
g_mask: self.g_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_h: self.prover_param.powers_of_h[to_reduce..].to_vec(),
|
|||
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,
|
|||
g_mask: self.g_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 mut powers_of_h = 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 h_table = FixedBaseMSM::get_window_table(scalar_bits, window_size, h);
|
|||
|
|||
let pp_g = E::G1Projective::batch_normalization_into_affine(
|
|||
&FixedBaseMSM::multi_scalar_mul(scalar_bits, window_size, &g_table, &pp_powers),
|
|||
);
|
|||
let pp_h = E::G2Projective::batch_normalization_into_affine(
|
|||
&FixedBaseMSM::multi_scalar_mul(scalar_bits, window_size, &h_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(),
|
|||
};
|
|||
let pp_k_h = Evaluations {
|
|||
evals: pp_h[start..(start + size)].to_vec(),
|
|||
};
|
|||
powers_of_g.push(pp_k_g);
|
|||
powers_of_h.push(pp_k_h);
|
|||
start += size;
|
|||
}
|
|||
|
|||
let pp = ProverParam {
|
|||
num_vars,
|
|||
g: g.into_affine(),
|
|||
h: h.into_affine(),
|
|||
powers_of_g,
|
|||
powers_of_h,
|
|||
};
|
|||
|
|||
end_timer!(pp_generation_timer);
|
|||
|
|||
let vp_generation_timer = start_timer!(|| "VP generation");
|
|||
let g_mask = {
|
|||
let window_size = FixedBaseMSM::get_mul_window_size(num_vars);
|
|||
let g_table = FixedBaseMSM::get_window_table(scalar_bits, window_size, g);
|
|||
E::G1Projective::batch_normalization_into_affine(&FixedBaseMSM::multi_scalar_mul(
|
|||
scalar_bits,
|
|||
window_size,
|
|||
&g_table,
|
|||
&t,
|
|||
))
|
|||
};
|
|||
end_timer!(vp_generation_timer);
|
|||
end_timer!(total_timer);
|
|||
Ok(Self {
|
|||
prover_param: pp,
|
|||
g_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(())
|
|||
}
|
|||
}
|