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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" + diff --git a/README.md b/README.md new file mode 100644 index 0000000..dd3a86d --- /dev/null +++ b/README.md @@ -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)?; + ``` diff --git a/src/lib.rs b/src/lib.rs new file mode 100644 index 0000000..e8ca5ca --- /dev/null +++ b/src/lib.rs @@ -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( + cs: ConstraintSystemRef, + z: Vec>, +) -> Result>, SynthesisError> { + let five = NonNativeFieldVar::::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( + m: SparseMatrixVar, + v: Vec>, +) -> Vec> { + let mut res = vec![NonNativeFieldVar::::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 { + _cf: PhantomData, + pub A: SparseMatrix, + pub z: Vec, + pub y: Vec, +} +impl ConstraintSynthesizer for MatrixVectorCircuit { + fn generate_constraints(self, cs: ConstraintSystemRef) -> Result<(), SynthesisError> { + // set A as circuit constants + let A = SparseMatrixVar::::new_constant(cs.clone(), self.A)?; + // set z and y as witness (private inputs) + let z: Vec> = Vec::new_witness(cs.clone(), || Ok(self.z.clone()))?; + let y: Vec> = 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::(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::::new_ref(); + let circuit = MatrixVectorCircuit:: { + _cf: PhantomData, + A, + z, + y, + }; + circuit.generate_constraints(cs.clone()).unwrap(); + println!("Number of constraints: {}", cs.num_constraints()); + assert!(cs.is_satisfied().unwrap()); + } +} diff --git a/src/utils.rs b/src/utils.rs new file mode 100644 index 0000000..2e7da15 --- /dev/null +++ b/src/utils.rs @@ -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 { + pub n_rows: usize, + pub n_cols: usize, + /// coeffs = R1CSMatrix = Vec>, which contains each row and the F is the value + /// of the coefficient and the usize indicates the column position + pub coeffs: R1CSMatrix, +} + +#[derive(Debug, Clone)] +pub struct SparseMatrixVar { + _f: PhantomData, + _cf: PhantomData, + pub n_rows: usize, + pub n_cols: usize, + // same format as the native SparseMatrix (which follows ark_relations::r1cs::Matrix format + pub coeffs: Vec, usize)>>, +} + +impl AllocVar, CF> for SparseMatrixVar +where + F: PrimeField, + CF: PrimeField, +{ + fn new_variable>>( + cs: impl Into>, + f: impl FnOnce() -> Result, + mode: AllocationMode, + ) -> Result { + f().and_then(|val| { + let cs = cs.into(); + + let mut coeffs: Vec, usize)>> = Vec::new(); + for row in val.borrow().coeffs.iter() { + let mut rowVar: Vec<(NonNativeFieldVar, usize)> = Vec::new(); + for &(value, col_i) in row.iter() { + let coeffVar = + NonNativeFieldVar::::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(M: &SparseMatrix, z: &[F]) -> Vec { + 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(m: Vec>) -> SparseMatrix { + let mut r = SparseMatrix:: { + 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(M: Vec>) -> SparseMatrix { + dense_matrix_to_sparse(to_F_dense_matrix(M)) +} +pub fn to_F_dense_matrix(M: Vec>) -> Vec> { + M.iter() + .map(|m| m.iter().map(|r| F::from(*r as u64)).collect()) + .collect() +} +pub fn to_F_vec(z: Vec) -> Vec { + z.iter().map(|c| F::from(*c as u64)).collect() +}