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r1csinstance.rs
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r1csinstance.rs
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use crate::transcript::AppendToTranscript;
use super::dense_mlpoly::DensePolynomial;
use super::errors::ProofVerifyError;
use super::math::Math;
use super::random::RandomTape;
use super::scalar::Scalar;
use super::sparse_mlpoly::{
MultiSparseMatPolynomialAsDense, SparseMatEntry, SparseMatPolyCommitment,
SparseMatPolyCommitmentGens, SparseMatPolyEvalProof, SparseMatPolynomial,
};
use super::timer::Timer;
use flate2::{write::ZlibEncoder, Compression};
use merlin::Transcript;
use rand::rngs::OsRng;
use serde::{Deserialize, Serialize};
#[derive(Debug, Serialize, Deserialize)]
pub struct R1CSInstance {
num_cons: usize,
num_vars: usize,
num_inputs: usize,
A: SparseMatPolynomial,
B: SparseMatPolynomial,
C: SparseMatPolynomial,
}
pub struct R1CSCommitmentGens {
gens: SparseMatPolyCommitmentGens,
}
impl R1CSCommitmentGens {
pub fn new(
label: &'static [u8],
num_cons: usize,
num_vars: usize,
num_inputs: usize,
num_nz_entries: usize,
) -> R1CSCommitmentGens {
assert!(num_inputs < num_vars);
let num_poly_vars_x = num_cons.log_2();
let num_poly_vars_y = (2 * num_vars).log_2();
let gens =
SparseMatPolyCommitmentGens::new(label, num_poly_vars_x, num_poly_vars_y, num_nz_entries, 3);
R1CSCommitmentGens { gens }
}
}
#[derive(Debug, Serialize, Deserialize)]
pub struct R1CSCommitment {
num_cons: usize,
num_vars: usize,
num_inputs: usize,
comm: SparseMatPolyCommitment,
}
impl AppendToTranscript for R1CSCommitment {
fn append_to_transcript(&self, _label: &'static [u8], transcript: &mut Transcript) {
transcript.append_u64(b"num_cons", self.num_cons as u64);
transcript.append_u64(b"num_vars", self.num_vars as u64);
transcript.append_u64(b"num_inputs", self.num_inputs as u64);
self.comm.append_to_transcript(b"comm", transcript);
}
}
pub struct R1CSDecommitment {
dense: MultiSparseMatPolynomialAsDense,
}
impl R1CSCommitment {
pub fn get_num_cons(&self) -> usize {
self.num_cons
}
pub fn get_num_vars(&self) -> usize {
self.num_vars
}
pub fn get_num_inputs(&self) -> usize {
self.num_inputs
}
}
impl R1CSInstance {
pub fn new(
num_cons: usize,
num_vars: usize,
num_inputs: usize,
A: &[(usize, usize, Scalar)],
B: &[(usize, usize, Scalar)],
C: &[(usize, usize, Scalar)],
) -> R1CSInstance {
Timer::print(&format!("number_of_constraints {num_cons}"));
Timer::print(&format!("number_of_variables {num_vars}"));
Timer::print(&format!("number_of_inputs {num_inputs}"));
Timer::print(&format!("number_non-zero_entries_A {}", A.len()));
Timer::print(&format!("number_non-zero_entries_B {}", B.len()));
Timer::print(&format!("number_non-zero_entries_C {}", C.len()));
// check that num_cons is a power of 2
assert_eq!(num_cons.next_power_of_two(), num_cons);
// check that num_vars is a power of 2
assert_eq!(num_vars.next_power_of_two(), num_vars);
// check that number_inputs + 1 <= num_vars
assert!(num_inputs < num_vars);
// no errors, so create polynomials
let num_poly_vars_x = num_cons.log_2();
let num_poly_vars_y = (2 * num_vars).log_2();
let mat_A = A
.iter()
.map(|(row, col, val)| SparseMatEntry::new(*row, *col, *val))
.collect::<Vec<SparseMatEntry>>();
let mat_B = B
.iter()
.map(|(row, col, val)| SparseMatEntry::new(*row, *col, *val))
.collect::<Vec<SparseMatEntry>>();
let mat_C = C
.iter()
.map(|(row, col, val)| SparseMatEntry::new(*row, *col, *val))
.collect::<Vec<SparseMatEntry>>();
let poly_A = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, mat_A);
let poly_B = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, mat_B);
let poly_C = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, mat_C);
Self {
num_cons,
num_vars,
num_inputs,
A: poly_A,
B: poly_B,
C: poly_C,
}
}
pub fn get_num_vars(&self) -> usize {
self.num_vars
}
pub fn get_num_cons(&self) -> usize {
self.num_cons
}
pub fn get_num_inputs(&self) -> usize {
self.num_inputs
}
pub fn get_digest(&self) -> Vec<u8> {
let mut encoder = ZlibEncoder::new(Vec::new(), Compression::default());
bincode::serialize_into(&mut encoder, &self).unwrap();
encoder.finish().unwrap()
}
pub fn produce_synthetic_r1cs(
num_cons: usize,
num_vars: usize,
num_inputs: usize,
) -> (R1CSInstance, Vec<Scalar>, Vec<Scalar>) {
Timer::print(&format!("number_of_constraints {num_cons}"));
Timer::print(&format!("number_of_variables {num_vars}"));
Timer::print(&format!("number_of_inputs {num_inputs}"));
let mut csprng: OsRng = OsRng;
// assert num_cons and num_vars are power of 2
assert_eq!((num_cons.log_2()).pow2(), num_cons);
assert_eq!((num_vars.log_2()).pow2(), num_vars);
// num_inputs + 1 <= num_vars
assert!(num_inputs < num_vars);
// z is organized as [vars,1,io]
let size_z = num_vars + num_inputs + 1;
// produce a random satisfying assignment
let Z = {
let mut Z: Vec<Scalar> = (0..size_z)
.map(|_i| Scalar::random(&mut csprng))
.collect::<Vec<Scalar>>();
Z[num_vars] = Scalar::one(); // set the constant term to 1
Z
};
// three sparse matrices
let mut A: Vec<SparseMatEntry> = Vec::new();
let mut B: Vec<SparseMatEntry> = Vec::new();
let mut C: Vec<SparseMatEntry> = Vec::new();
let one = Scalar::one();
for i in 0..num_cons {
let A_idx = i % size_z;
let B_idx = (i + 2) % size_z;
A.push(SparseMatEntry::new(i, A_idx, one));
B.push(SparseMatEntry::new(i, B_idx, one));
let AB_val = Z[A_idx] * Z[B_idx];
let C_idx = (i + 3) % size_z;
let C_val = Z[C_idx];
if C_val == Scalar::zero() {
C.push(SparseMatEntry::new(i, num_vars, AB_val));
} else {
C.push(SparseMatEntry::new(
i,
C_idx,
AB_val * C_val.invert().unwrap(),
));
}
}
Timer::print(&format!("number_non-zero_entries_A {}", A.len()));
Timer::print(&format!("number_non-zero_entries_B {}", B.len()));
Timer::print(&format!("number_non-zero_entries_C {}", C.len()));
let num_poly_vars_x = num_cons.log_2();
let num_poly_vars_y = (2 * num_vars).log_2();
let poly_A = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, A);
let poly_B = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, B);
let poly_C = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, C);
let inst = R1CSInstance {
num_cons,
num_vars,
num_inputs,
A: poly_A,
B: poly_B,
C: poly_C,
};
assert!(inst.is_sat(&Z[..num_vars], &Z[num_vars + 1..]));
(inst, Z[..num_vars].to_vec(), Z[num_vars + 1..].to_vec())
}
pub fn is_sat(&self, vars: &[Scalar], input: &[Scalar]) -> bool {
assert_eq!(vars.len(), self.num_vars);
assert_eq!(input.len(), self.num_inputs);
let z = {
let mut z = vars.to_vec();
z.extend(&vec![Scalar::one()]);
z.extend(input);
z
};
// verify if Az * Bz - Cz = [0...]
let Az = self
.A
.multiply_vec(self.num_cons, self.num_vars + self.num_inputs + 1, &z);
let Bz = self
.B
.multiply_vec(self.num_cons, self.num_vars + self.num_inputs + 1, &z);
let Cz = self
.C
.multiply_vec(self.num_cons, self.num_vars + self.num_inputs + 1, &z);
assert_eq!(Az.len(), self.num_cons);
assert_eq!(Bz.len(), self.num_cons);
assert_eq!(Cz.len(), self.num_cons);
(0..self.num_cons).all(|i| Az[i] * Bz[i] == Cz[i])
}
pub fn multiply_vec(
&self,
num_rows: usize,
num_cols: usize,
z: &[Scalar],
) -> (DensePolynomial, DensePolynomial, DensePolynomial) {
assert_eq!(num_rows, self.num_cons);
assert_eq!(z.len(), num_cols);
assert!(num_cols > self.num_vars);
(
DensePolynomial::new(self.A.multiply_vec(num_rows, num_cols, z)),
DensePolynomial::new(self.B.multiply_vec(num_rows, num_cols, z)),
DensePolynomial::new(self.C.multiply_vec(num_rows, num_cols, z)),
)
}
pub fn compute_eval_table_sparse(
&self,
num_rows: usize,
num_cols: usize,
evals: &[Scalar],
) -> (Vec<Scalar>, Vec<Scalar>, Vec<Scalar>) {
assert_eq!(num_rows, self.num_cons);
assert!(num_cols > self.num_vars);
let evals_A = self.A.compute_eval_table_sparse(evals, num_rows, num_cols);
let evals_B = self.B.compute_eval_table_sparse(evals, num_rows, num_cols);
let evals_C = self.C.compute_eval_table_sparse(evals, num_rows, num_cols);
(evals_A, evals_B, evals_C)
}
pub fn evaluate(&self, rx: &[Scalar], ry: &[Scalar]) -> (Scalar, Scalar, Scalar) {
let evals = SparseMatPolynomial::multi_evaluate(&[&self.A, &self.B, &self.C], rx, ry);
(evals[0], evals[1], evals[2])
}
pub fn commit(&self, gens: &R1CSCommitmentGens) -> (R1CSCommitment, R1CSDecommitment) {
let (comm, dense) = SparseMatPolynomial::multi_commit(&[&self.A, &self.B, &self.C], &gens.gens);
let r1cs_comm = R1CSCommitment {
num_cons: self.num_cons,
num_vars: self.num_vars,
num_inputs: self.num_inputs,
comm,
};
let r1cs_decomm = R1CSDecommitment { dense };
(r1cs_comm, r1cs_decomm)
}
}
#[derive(Debug, Serialize, Deserialize)]
pub struct R1CSEvalProof {
proof: SparseMatPolyEvalProof,
}
impl R1CSEvalProof {
pub fn prove(
decomm: &R1CSDecommitment,
rx: &[Scalar], // point at which the polynomial is evaluated
ry: &[Scalar],
evals: &(Scalar, Scalar, Scalar),
gens: &R1CSCommitmentGens,
transcript: &mut Transcript,
random_tape: &mut RandomTape,
) -> R1CSEvalProof {
let timer = Timer::new("R1CSEvalProof::prove");
let proof = SparseMatPolyEvalProof::prove(
&decomm.dense,
rx,
ry,
&[evals.0, evals.1, evals.2],
&gens.gens,
transcript,
random_tape,
);
timer.stop();
R1CSEvalProof { proof }
}
pub fn verify(
&self,
comm: &R1CSCommitment,
rx: &[Scalar], // point at which the R1CS matrix polynomials are evaluated
ry: &[Scalar],
evals: &(Scalar, Scalar, Scalar),
gens: &R1CSCommitmentGens,
transcript: &mut Transcript,
) -> Result<(), ProofVerifyError> {
self.proof.verify(
&comm.comm,
rx,
ry,
&[evals.0, evals.1, evals.2],
&gens.gens,
transcript,
)
}
}