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Add initial CCS mod: (#6)
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- port initial CCS structure with methods from multifolding-poc
- add R1CS helper methods, which will be used in Nova impl
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arnaucube authored Aug 23, 2023
1 parent bc81fbe commit 240b916
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123 changes: 123 additions & 0 deletions src/ccs/mod.rs
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use ark_ec::CurveGroup;
use ark_std::log2;
use ark_std::{One, Zero};
use std::ops::Neg;

use crate::utils::vec::*;
use crate::Error;

pub mod r1cs;
use r1cs::R1CS;

/// CCS represents the Customizable Constraint Systems structure defined in
/// https://eprint.iacr.org/2023/552
#[derive(Debug, Clone, Eq, PartialEq)]
pub struct CCS<C: CurveGroup> {
/// m: number of columns in M_i (such that M_i \in F^{m, n})
pub m: usize,
/// n = |z|, number of rows in M_i
pub n: usize,
/// l = |io|, size of public input/output
pub l: usize,
/// t = |M|, number of matrices
pub t: usize,
/// q = |c| = |S|, number of multisets
pub q: usize,
/// d: max degree in each variable
pub d: usize,
/// s = log(m), dimension of x
pub s: usize,
/// s_prime = log(n), dimension of y
pub s_prime: usize,

/// vector of matrices
pub M: Vec<SparseMatrix<C::ScalarField>>,
/// vector of multisets
pub S: Vec<Vec<usize>>,
/// vector of coefficients
pub c: Vec<C::ScalarField>,
}

impl<C: CurveGroup> CCS<C> {
/// check that a CCS structure is satisfied by a z vector. Only for testing.
pub fn check_relation(&self, z: &[C::ScalarField]) -> Result<(), Error> {
let mut result = vec![C::ScalarField::zero(); self.m];

for i in 0..self.q {
// extract the needed M_j matrices out of S_i
let vec_M_j: Vec<&SparseMatrix<C::ScalarField>> =
self.S[i].iter().map(|j| &self.M[*j]).collect();

// complete the hadamard chain
let mut hadamard_result = vec![C::ScalarField::one(); self.m];
for M_j in vec_M_j.into_iter() {
hadamard_result = hadamard(&hadamard_result, &mat_vec_mul_sparse(M_j, z));
}

// multiply by the coefficient of this step
let c_M_j_z = vec_scalar_mul(&hadamard_result, &self.c[i]);

// add it to the final vector
result = vec_add(&result, &c_M_j_z);
}

// make sure the final vector is all zeroes
for e in result {
if !e.is_zero() {
return Err(Error::NotSatisfied);
}
}

Ok(())
}
}

impl<C: CurveGroup> CCS<C> {
pub fn from_r1cs(r1cs: R1CS<C::ScalarField>, io_len: usize) -> Self {
let m = r1cs.A.n_cols;
let n = r1cs.A.n_rows;
CCS {
m,
n,
l: io_len,
s: log2(m) as usize,
s_prime: log2(n) as usize,
t: 3,
q: 2,
d: 2,

S: vec![vec![0, 1], vec![2]],
c: vec![C::ScalarField::one(), C::ScalarField::one().neg()],
M: vec![r1cs.A, r1cs.B, r1cs.C],
}
}
pub fn to_r1cs(self) -> R1CS<C::ScalarField> {
R1CS::<C::ScalarField> {
l: self.l,
A: self.M[0].clone(),
B: self.M[1].clone(),
C: self.M[2].clone(),
}
}
}

#[cfg(test)]
mod tests {
use super::*;
use crate::ccs::r1cs::tests::{get_test_r1cs, get_test_z};
use ark_bls12_377::G1Projective;

pub fn get_test_ccs<C: CurveGroup>() -> CCS<C> {
let r1cs = get_test_r1cs::<C::ScalarField>();
CCS::<C>::from_r1cs(r1cs, 1)
}

/// Test that a basic CCS relation can be satisfied
#[test]
fn test_ccs_relation() {
let ccs = get_test_ccs::<G1Projective>();
let z = get_test_z(3);

ccs.check_relation(&z).unwrap();
}
}
79 changes: 79 additions & 0 deletions src/ccs/r1cs.rs
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use ark_ff::PrimeField;

use crate::utils::vec::*;

#[derive(Debug, Clone, Eq, PartialEq)]
pub struct R1CS<F: PrimeField> {
pub l: usize, // io len
pub A: SparseMatrix<F>,
pub B: SparseMatrix<F>,
pub C: SparseMatrix<F>,
}
impl<F: PrimeField> R1CS<F> {
/// returns a tuple containing (w, x) (witness and public inputs respectively)
pub fn split_z(&self, z: &[F]) -> (Vec<F>, Vec<F>) {
(z[self.l + 1..].to_vec(), z[1..self.l + 1].to_vec())
}
}

#[cfg(test)]
pub mod tests {
use super::*;

pub fn to_F_matrix<F: PrimeField>(M: Vec<Vec<usize>>) -> Vec<Vec<F>> {
let mut R: Vec<Vec<F>> = vec![Vec::new(); M.len()];
for i in 0..M.len() {
R[i] = vec![F::zero(); M[i].len()];
for j in 0..M[i].len() {
R[i][j] = F::from(M[i][j] as u64);
}
}
R
}
pub fn to_F_vec<F: PrimeField>(z: Vec<usize>) -> Vec<F> {
let mut r: Vec<F> = vec![F::zero(); z.len()];
for i in 0..z.len() {
r[i] = F::from(z[i] as u64);
}
r
}

pub fn get_test_r1cs<F: PrimeField>() -> R1CS<F> {
// R1CS for: x^3 + x + 5 = y (example from article
// https://www.vitalik.ca/general/2016/12/10/qap.html )
let A = dense_matrix_to_sparse(to_F_matrix::<F>(vec![
vec![0, 1, 0, 0, 0, 0],
vec![0, 0, 0, 1, 0, 0],
vec![0, 1, 0, 0, 1, 0],
vec![5, 0, 0, 0, 0, 1],
]));
let B = dense_matrix_to_sparse(to_F_matrix::<F>(vec![
vec![0, 1, 0, 0, 0, 0],
vec![0, 1, 0, 0, 0, 0],
vec![1, 0, 0, 0, 0, 0],
vec![1, 0, 0, 0, 0, 0],
]));
let C = dense_matrix_to_sparse(to_F_matrix::<F>(vec![
vec![0, 0, 0, 1, 0, 0],
vec![0, 0, 0, 0, 1, 0],
vec![0, 0, 0, 0, 0, 1],
vec![0, 0, 1, 0, 0, 0],
]));

R1CS::<F> { l: 1, A, B, C }
}

pub fn get_test_z<F: PrimeField>(input: usize) -> Vec<F> {
// z = (1, io, w)
to_F_vec(vec![
1,
input, // io
input * input * input + input + 5, // x^3 + x + 5
input * input, // x^2
input * input * input, // x^2 * x
input * input * input + input, // x^3 + x
0, // pad to pow of 2
0,
])
}
}
1 change: 1 addition & 0 deletions src/lib.rs
Original file line number Diff line number Diff line change
Expand Up @@ -8,6 +8,7 @@ use thiserror::Error;

pub mod transcript;
use transcript::Transcript;
pub mod ccs;
pub mod pedersen;
pub mod utils;

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