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source = "registry+https://github.com/rust-lang/crates.io-index" |
|||
checksum = "c06d3da6113f116aaee68e4d601191614c9053067f9ab7f6edbcb161237daa54" |
|||
|
|||
[[package]] |
|||
name = "typenum" |
|||
version = "1.17.0" |
|||
source = "registry+https://github.com/rust-lang/crates.io-index" |
|||
checksum = "42ff0bf0c66b8238c6f3b578df37d0b7848e55df8577b3f74f92a69acceeb825" |
|||
|
|||
[[package]] |
|||
name = "unicode-ident" |
|||
version = "1.0.12" |
|||
source = "registry+https://github.com/rust-lang/crates.io-index" |
|||
checksum = "3354b9ac3fae1ff6755cb6db53683adb661634f67557942dea4facebec0fee4b" |
|||
|
|||
[[package]] |
|||
name = "version_check" |
|||
version = "0.9.4" |
|||
source = "registry+https://github.com/rust-lang/crates.io-index" |
|||
checksum = "49874b5167b65d7193b8aba1567f5c7d93d001cafc34600cee003eda787e483f" |
|||
|
|||
[[package]] |
|||
name = "wasi" |
|||
version = "0.11.0+wasi-snapshot-preview1" |
|||
source = "registry+https://github.com/rust-lang/crates.io-index" |
|||
checksum = "9c8d87e72b64a3b4db28d11ce29237c246188f4f51057d65a7eab63b7987e423" |
|||
|
|||
[[package]] |
|||
name = "zerocopy" |
|||
version = "0.7.32" |
|||
source = "registry+https://github.com/rust-lang/crates.io-index" |
|||
checksum = "74d4d3961e53fa4c9a25a8637fc2bfaf2595b3d3ae34875568a5cf64787716be" |
|||
dependencies = [ |
|||
"zerocopy-derive", |
|||
] |
|||
|
|||
[[package]] |
|||
name = "zerocopy-derive" |
|||
version = "0.7.32" |
|||
source = "registry+https://github.com/rust-lang/crates.io-index" |
|||
checksum = "9ce1b18ccd8e73a9321186f97e46f9f04b778851177567b1975109d26a08d2a6" |
|||
dependencies = [ |
|||
"proc-macro2", |
|||
"quote", |
|||
"syn 2.0.48", |
|||
] |
|||
|
|||
[[package]] |
|||
name = "zeroize" |
|||
version = "1.7.0" |
|||
source = "registry+https://github.com/rust-lang/crates.io-index" |
|||
checksum = "525b4ec142c6b68a2d10f01f7bbf6755599ca3f81ea53b8431b7dd348f5fdb2d" |
|||
dependencies = [ |
|||
"zeroize_derive", |
|||
] |
|||
|
|||
[[package]] |
|||
name = "zeroize_derive" |
|||
version = "1.4.2" |
|||
source = "registry+https://github.com/rust-lang/crates.io-index" |
|||
checksum = "ce36e65b0d2999d2aafac989fb249189a141aee1f53c612c1f37d72631959f69" |
|||
dependencies = [ |
|||
"proc-macro2", |
|||
"quote", |
|||
"syn 2.0.48", |
|||
] |
|||
@ -0,0 +1,23 @@ |
|||
[package] |
|||
name = "mat-vec-prod-exp" |
|||
version = "0.1.0" |
|||
edition = "2021" |
|||
|
|||
[dependencies] |
|||
ark-ec = "^0.4.0" |
|||
ark-ff = "^0.4.0" |
|||
ark-poly = "^0.4.0" |
|||
ark-std = "^0.4.0" |
|||
ark-relations = { version = "^0.4.0", default-features = false } |
|||
ark-r1cs-std = { version = "0.4.0", default-features = false } # this is patched at the workspace level |
|||
ark-snark = { version = "^0.4.0"} |
|||
ark-serialize = "^0.4.0" |
|||
thiserror = "1.0" |
|||
num-bigint = "0.4" |
|||
|
|||
|
|||
[dev-dependencies] |
|||
ark-pallas = {version="0.4.0", features=["r1cs"]} |
|||
ark-vesta = {version="0.4.0", features=["r1cs"]} |
|||
rand = "0.8.5" |
|||
|
|||
@ -0,0 +1,11 @@ |
|||
# mat-vec-prod-exp |
|||
*Matrix vector product experiments* |
|||
|
|||
Instructions: |
|||
|
|||
- Just run `cargo test -- --nocapture` and the number of constraints will be printed |
|||
- Can comment & uncomment `lib.rs` lines `71` & `72` to test the different approaches: |
|||
```rust |
|||
let Az = mat_vec_mul_sparse_gadget(A, z); |
|||
// let Az = handcrafted_A_by_z(cs, z)?; |
|||
``` |
|||
@ -0,0 +1,113 @@ |
|||
#![allow(non_snake_case)]
|
|||
#![allow(unused_doc_comments)]
|
|||
#![allow(dead_code)]
|
|||
|
|||
use ark_ff::PrimeField;
|
|||
use ark_r1cs_std::fields::nonnative::NonNativeFieldVar;
|
|||
use ark_r1cs_std::{alloc::AllocVar, eq::EqGadget, fields::FieldVar, R1CSVar};
|
|||
use ark_relations::r1cs::{ConstraintSynthesizer, ConstraintSystemRef, SynthesisError};
|
|||
use core::marker::PhantomData;
|
|||
use std::ops::Mul;
|
|||
|
|||
mod utils;
|
|||
use utils::*;
|
|||
|
|||
/// - F stands for the field that we represent
|
|||
/// - CF stands for the ConstraintField over which we do the operations
|
|||
|
|||
/// Implements the A * z matrix-vector-product by fixing the combinations of 'z'.
|
|||
fn handcrafted_A_by_z<F: PrimeField, CF: PrimeField>(
|
|||
cs: ConstraintSystemRef<CF>,
|
|||
z: Vec<NonNativeFieldVar<F, CF>>,
|
|||
) -> Result<Vec<NonNativeFieldVar<F, CF>>, SynthesisError> {
|
|||
let five = NonNativeFieldVar::<F, CF>::new_constant(cs.clone(), F::from(5u32))?;
|
|||
// directly hand-craft the output vector containing the operations in-place:
|
|||
Ok(vec![
|
|||
z[1].clone() + five.clone() * z[4].clone(),
|
|||
z[1].clone() + z[3].clone(),
|
|||
z[1].clone() + z[4].clone(),
|
|||
five * z[0].clone() + z[4].clone() + z[5].clone(),
|
|||
]
|
|||
.clone())
|
|||
}
|
|||
|
|||
/// Implements the A * z matrix-vector-product by doing the sparse matrix by vector algorithm, and
|
|||
/// assuming that the elements of the matrix A are constants of the system.
|
|||
pub fn mat_vec_mul_sparse_gadget<F: PrimeField, CF: PrimeField>(
|
|||
m: SparseMatrixVar<F, CF>,
|
|||
v: Vec<NonNativeFieldVar<F, CF>>,
|
|||
) -> Vec<NonNativeFieldVar<F, CF>> {
|
|||
let mut res = vec![NonNativeFieldVar::<F, CF>::zero(); m.n_rows];
|
|||
for (row_i, row) in m.coeffs.iter().enumerate() {
|
|||
for (value, col_i) in row.iter() {
|
|||
if value.value().unwrap() == F::one() {
|
|||
res[row_i] += v[*col_i].clone(); // when value==1, no need to multiply by it
|
|||
continue;
|
|||
}
|
|||
res[row_i] += value.clone().mul(&v[*col_i].clone());
|
|||
}
|
|||
}
|
|||
res
|
|||
}
|
|||
|
|||
/// Circuit that takes as constants the sparse matrix A, and as inputs the vectors z and y. It
|
|||
/// computes the matrix by vector product between A and z, and checks that is equal to y
|
|||
/// (ie. y == A*z)
|
|||
struct MatrixVectorCircuit<F: PrimeField, CF: PrimeField> {
|
|||
_cf: PhantomData<CF>,
|
|||
pub A: SparseMatrix<F>,
|
|||
pub z: Vec<F>,
|
|||
pub y: Vec<F>,
|
|||
}
|
|||
impl<F: PrimeField, CF: PrimeField> ConstraintSynthesizer<CF> for MatrixVectorCircuit<F, CF> {
|
|||
fn generate_constraints(self, cs: ConstraintSystemRef<CF>) -> Result<(), SynthesisError> {
|
|||
// set A as circuit constants
|
|||
let A = SparseMatrixVar::<F, CF>::new_constant(cs.clone(), self.A)?;
|
|||
// set z and y as witness (private inputs)
|
|||
let z: Vec<NonNativeFieldVar<F, CF>> = Vec::new_witness(cs.clone(), || Ok(self.z.clone()))?;
|
|||
let y: Vec<NonNativeFieldVar<F, CF>> = Vec::new_witness(cs.clone(), || Ok(self.y.clone()))?;
|
|||
|
|||
/// The next two lines are the ones that can be swapped to see the number of constraints
|
|||
/// taken by the two approaches:
|
|||
let Az = mat_vec_mul_sparse_gadget(A, z);
|
|||
// let Az = handcrafted_A_by_z(cs, z)?;
|
|||
|
|||
Az.enforce_equal(&y)?;
|
|||
Ok(())
|
|||
}
|
|||
}
|
|||
|
|||
#[cfg(test)]
|
|||
mod tests {
|
|||
use super::*;
|
|||
use ark_pallas::{Fq, Fr};
|
|||
use ark_relations::r1cs::ConstraintSystem;
|
|||
|
|||
#[test]
|
|||
fn test_relaxed_r1cs_nonnative_matrix_vector_product() {
|
|||
let A = to_F_matrix::<Fq>(vec![
|
|||
vec![0, 1, 0, 0, 5, 0],
|
|||
vec![0, 1, 0, 1, 0, 0],
|
|||
vec![0, 1, 0, 0, 1, 0],
|
|||
vec![5, 0, 0, 0, 1, 1],
|
|||
]);
|
|||
let z = to_F_vec(vec![1, 123, 35, 53, 80, 30]);
|
|||
let y = mat_vec_mul_sparse(&A, &z); // y = A*z
|
|||
println!("Matrix of size {} x {}", A.n_rows, A.n_cols);
|
|||
println!("Vector of size {}", z.len());
|
|||
|
|||
println!(
|
|||
"Build the circuit that computes the matrix-vector-product over a non-native field"
|
|||
);
|
|||
let cs = ConstraintSystem::<Fr>::new_ref();
|
|||
let circuit = MatrixVectorCircuit::<Fq, Fr> {
|
|||
_cf: PhantomData,
|
|||
A,
|
|||
z,
|
|||
y,
|
|||
};
|
|||
circuit.generate_constraints(cs.clone()).unwrap();
|
|||
println!("Number of constraints: {}", cs.num_constraints());
|
|||
assert!(cs.is_satisfied().unwrap());
|
|||
}
|
|||
}
|
|||
@ -0,0 +1,101 @@ |
|||
use ark_ff::PrimeField;
|
|||
use ark_r1cs_std::{
|
|||
alloc::{AllocVar, AllocationMode},
|
|||
fields::nonnative::NonNativeFieldVar,
|
|||
};
|
|||
use ark_relations::r1cs::{Matrix as R1CSMatrix, Namespace, SynthesisError};
|
|||
use core::{borrow::Borrow, marker::PhantomData};
|
|||
|
|||
pub struct SparseMatrix<F: PrimeField> {
|
|||
pub n_rows: usize,
|
|||
pub n_cols: usize,
|
|||
/// coeffs = R1CSMatrix = Vec<Vec<(F, usize)>>, which contains each row and the F is the value
|
|||
/// of the coefficient and the usize indicates the column position
|
|||
pub coeffs: R1CSMatrix<F>,
|
|||
}
|
|||
|
|||
#[derive(Debug, Clone)]
|
|||
pub struct SparseMatrixVar<F: PrimeField, CF: PrimeField> {
|
|||
_f: PhantomData<F>,
|
|||
_cf: PhantomData<CF>,
|
|||
pub n_rows: usize,
|
|||
pub n_cols: usize,
|
|||
// same format as the native SparseMatrix (which follows ark_relations::r1cs::Matrix format
|
|||
pub coeffs: Vec<Vec<(NonNativeFieldVar<F, CF>, usize)>>,
|
|||
}
|
|||
|
|||
impl<F, CF> AllocVar<SparseMatrix<F>, CF> for SparseMatrixVar<F, CF>
|
|||
where
|
|||
F: PrimeField,
|
|||
CF: PrimeField,
|
|||
{
|
|||
fn new_variable<T: Borrow<SparseMatrix<F>>>(
|
|||
cs: impl Into<Namespace<CF>>,
|
|||
f: impl FnOnce() -> Result<T, SynthesisError>,
|
|||
mode: AllocationMode,
|
|||
) -> Result<Self, SynthesisError> {
|
|||
f().and_then(|val| {
|
|||
let cs = cs.into();
|
|||
|
|||
let mut coeffs: Vec<Vec<(NonNativeFieldVar<F, CF>, usize)>> = Vec::new();
|
|||
for row in val.borrow().coeffs.iter() {
|
|||
let mut rowVar: Vec<(NonNativeFieldVar<F, CF>, usize)> = Vec::new();
|
|||
for &(value, col_i) in row.iter() {
|
|||
let coeffVar =
|
|||
NonNativeFieldVar::<F, CF>::new_variable(cs.clone(), || Ok(value), mode)?;
|
|||
rowVar.push((coeffVar, col_i));
|
|||
}
|
|||
coeffs.push(rowVar);
|
|||
}
|
|||
|
|||
Ok(Self {
|
|||
_f: PhantomData,
|
|||
_cf: PhantomData,
|
|||
n_rows: val.borrow().n_rows,
|
|||
n_cols: val.borrow().n_cols,
|
|||
coeffs,
|
|||
})
|
|||
})
|
|||
}
|
|||
}
|
|||
|
|||
pub fn mat_vec_mul_sparse<F: PrimeField>(M: &SparseMatrix<F>, z: &[F]) -> Vec<F> {
|
|||
assert_eq!(M.n_cols, z.len());
|
|||
let mut res = vec![F::zero(); M.n_rows];
|
|||
for (row_i, row) in M.coeffs.iter().enumerate() {
|
|||
for &(value, col_i) in row.iter() {
|
|||
res[row_i] += value * z[col_i];
|
|||
}
|
|||
}
|
|||
res
|
|||
}
|
|||
pub fn dense_matrix_to_sparse<F: PrimeField>(m: Vec<Vec<F>>) -> SparseMatrix<F> {
|
|||
let mut r = SparseMatrix::<F> {
|
|||
n_rows: m.len(),
|
|||
n_cols: m[0].len(),
|
|||
coeffs: Vec::new(),
|
|||
};
|
|||
for m_row in m.iter() {
|
|||
let mut row: Vec<(F, usize)> = Vec::new();
|
|||
for (col_i, value) in m_row.iter().enumerate() {
|
|||
if !value.is_zero() {
|
|||
row.push((*value, col_i));
|
|||
}
|
|||
}
|
|||
r.coeffs.push(row);
|
|||
}
|
|||
r
|
|||
}
|
|||
|
|||
// just some helpers to define matrices and vectors by hand
|
|||
pub fn to_F_matrix<F: PrimeField>(M: Vec<Vec<usize>>) -> SparseMatrix<F> {
|
|||
dense_matrix_to_sparse(to_F_dense_matrix(M))
|
|||
}
|
|||
pub fn to_F_dense_matrix<F: PrimeField>(M: Vec<Vec<usize>>) -> Vec<Vec<F>> {
|
|||
M.iter()
|
|||
.map(|m| m.iter().map(|r| F::from(*r as u64)).collect())
|
|||
.collect()
|
|||
}
|
|||
pub fn to_F_vec<F: PrimeField>(z: Vec<usize>) -> Vec<F> {
|
|||
z.iter().map(|c| F::from(*c as u64)).collect()
|
|||
}
|
|||