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implemented parallelized kate division, with a lot of TODOs

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This commit is contained in:
Alex Vlasov 2019-03-11 14:57:14 +01:00
parent 9f887847f7
commit 2a5dc08cf6
9 changed files with 505 additions and 148 deletions
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12
src/sonic/README.md
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@ -20,8 +20,14 @@ Initial SONIC proof system integration using the code from the [original impleme
- [x] Basic Ethereum smart-contract
- [x] Add blinding factors
- [ ] Implement unhelped version
- [x] Implement a part of S poly precomputation (S2)
- [x] Implement a part of S poly precomputation (S_2)
- [x] Implement a "well formed" argument
- [x] Implement a coefficients product argument
- [ ] Implement a premutation argument
- [ ] Implement synthesizer for proper form of S polynomial
- [x] Implement a premutation argument
- [ ] Implement synthesizer for proper form of S polynomial
- [ ] Finer tuning
- [x] Parallelized evaluation of S polynomial
- [ ] Parallelize some polynomial operations in the protocol itself
- [x] Parallelized kate division
- [ ] Implement specialized version of polynomial multiplication by degree 1 polynomial
- [ ] Non-assigning variant of the "adaptor" (may require a change of SONIC CS trait)

48
src/sonic/cs/mod.rs
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@ -207,50 +207,6 @@ impl SynthesisDriver for Basic {
circuit.synthesize(&mut tmp)?;
// let blindings_to_add = 6;
// for i in 0..blindings_to_add {
// match tmp.current_variable.take() {
// Some(index) => {
// let var_a = Variable::A(index);
// let var_b = Variable::B(index);
// let var_c = Variable::C(index);
// let mut product = None;
// let value_a = tmp.backend.get_var(var_a);
// tmp.backend.set_var(var_b, || {
// let value_b = E::Fr::one();
// product = Some(value_a.ok_or(SynthesisError::AssignmentMissing)?);
// product.as_mut().map(|product| product.mul_assign(&value_b));
// Ok(value_b)
// })?;
// tmp.backend.set_var(var_c, || {
// product.ok_or(SynthesisError::AssignmentMissing)
// })?;
// tmp.current_variable = None;
// },
// None => {
// self.n += 1;
// let index = self.n ;
// tmp.backend.new_multiplication_gate();
// let var_a = Variable::A(index);
// tmp.backend.set_var(var_a, value)?;
// tmp.current_variable = Some(index);
// }
// }
// }
// TODO: add blinding factors so we actually get zero-knowledge
Ok(())
}
}
@ -355,10 +311,6 @@ impl SynthesisDriver for Nonassigning {
circuit.synthesize(&mut tmp)?;
// TODO: add blinding factors so we actually get zero-knowledge
// println!("n = {}", tmp.n);
Ok(())
}
}

1
src/sonic/helped/generator.rs
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@ -383,7 +383,6 @@ pub fn generate_parameters<E, C>(
{
let circuit_parameters = get_circuit_parameters::<E, C>(circuit)?;
let min_d = circuit_parameters.n * 4 + 2*NUM_BLINDINGS;
println!{"Mid d = {}", min_d};
let srs = generate_srs(alpha, x, min_d)?;

37
src/sonic/helped/helper.rs
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@ -62,7 +62,7 @@ pub fn create_aggregate_on_srs<E: Engine, C: Circuit<E>, S: SynthesisDriver>(
}
}
let mut tmp = CountN{n:0,q:0};
let mut tmp = CountN{n:0, q:0};
S::synthesize(&mut tmp, circuit).unwrap(); // TODO
(tmp.n, tmp.q)
@ -139,23 +139,28 @@ pub fn create_aggregate_on_srs_using_information<E: Engine, C: Circuit<E>, S: Sy
// Let's open up C to every y.
fn compute_value<E: Engine>(y: &E::Fr, poly_positive: &[E::Fr], poly_negative: &[E::Fr]) -> E::Fr {
let mut value = E::Fr::zero();
let yinv = y.inverse().unwrap(); // TODO
let mut tmp = yinv;
for &coeff in poly_negative {
let mut coeff = coeff;
coeff.mul_assign(&tmp);
value.add_assign(&coeff);
tmp.mul_assign(&yinv);
}
let mut tmp = *y;
for &coeff in poly_positive {
let mut coeff = coeff;
coeff.mul_assign(&tmp);
value.add_assign(&coeff);
tmp.mul_assign(&y);
}
let positive_powers_contrib = evaluate_at_consequitive_powers(poly_positive, *y, *y);
let negative_powers_contrib = evaluate_at_consequitive_powers(poly_negative, yinv, yinv);
value.add_assign(&positive_powers_contrib);
value.add_assign(&negative_powers_contrib);
// let mut tmp = yinv;
// for &coeff in poly_negative {
// let mut coeff = coeff;
// coeff.mul_assign(&tmp);
// value.add_assign(&coeff);
// tmp.mul_assign(&yinv);
// }
// let mut tmp = *y;
// for &coeff in poly_positive {
// let mut coeff = coeff;
// coeff.mul_assign(&tmp);
// value.add_assign(&coeff);
// tmp.mul_assign(&y);
// }
value
}

74
src/sonic/helped/poly.rs
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@ -4,6 +4,7 @@ use std::marker::PhantomData;
use crate::sonic::cs::{Backend};
use crate::sonic::cs::{Coeff, Variable, LinearCombination};
use crate::sonic::util::*;
/*
s(X, Y) = \sum\limits_{i=1}^N u_i(Y) X^{-i}
@ -71,26 +72,33 @@ impl<E: Engine> SxEval<E> {
pub fn finalize(self, x: E::Fr) -> E::Fr {
let x_inv = x.inverse().unwrap(); // TODO
let mut tmp = x_inv;
let mut acc = E::Fr::zero();
for mut u in self.u {
u.mul_assign(&tmp);
acc.add_assign(&u);
tmp.mul_assign(&x_inv);
}
let mut tmp = x_inv;
acc.add_assign(&evaluate_at_consequitive_powers(& self.u[..], tmp, tmp));
let mut tmp = x;
for mut v in self.v {
v.mul_assign(&tmp);
acc.add_assign(&v);
tmp.mul_assign(&x);
}
for mut w in self.w {
w.mul_assign(&tmp);
acc.add_assign(&w);
tmp.mul_assign(&x);
}
acc.add_assign(&evaluate_at_consequitive_powers(& self.v[..], tmp, tmp));
let mut tmp = x.pow(&[(self.v.len()+1) as u64]);
acc.add_assign(&evaluate_at_consequitive_powers(& self.w[..], tmp, x));
// let mut tmp = x_inv;
// for mut u in self.u {
// u.mul_assign(&tmp);
// acc.add_assign(&u);
// tmp.mul_assign(&x_inv);
// }
// let mut tmp = x;
// for mut v in self.v {
// v.mul_assign(&tmp);
// acc.add_assign(&v);
// tmp.mul_assign(&x);
// }
// for mut w in self.w {
// w.mul_assign(&tmp);
// acc.add_assign(&w);
// tmp.mul_assign(&x);
// }
acc
}
@ -209,20 +217,26 @@ impl<E: Engine> SyEval<E> {
pub fn finalize(self, y: E::Fr) -> E::Fr {
let mut acc = E::Fr::zero();
let mut tmp = y;
for mut coeff in self.positive_coeffs {
coeff.mul_assign(&tmp);
acc.add_assign(&coeff);
tmp.mul_assign(&y);
}
let yinv = y.inverse().unwrap(); // TODO
let mut tmp = yinv;
for mut coeff in self.negative_coeffs {
coeff.mul_assign(&tmp);
acc.add_assign(&coeff);
tmp.mul_assign(&yinv);
}
let positive_powers_contrib = evaluate_at_consequitive_powers(& self.positive_coeffs[..], y, y);
let negative_powers_contrib = evaluate_at_consequitive_powers(& self.negative_coeffs[..], yinv, yinv);
acc.add_assign(&positive_powers_contrib);
acc.add_assign(&negative_powers_contrib);
// let mut tmp = y;
// for mut coeff in self.positive_coeffs {
// coeff.mul_assign(&tmp);
// acc.add_assign(&coeff);
// tmp.mul_assign(&y);
// }
// let mut tmp = yinv;
// for mut coeff in self.negative_coeffs {
// coeff.mul_assign(&tmp);
// acc.add_assign(&coeff);
// tmp.mul_assign(&yinv);
// }
acc
}

22
src/sonic/helped/prover.rs
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@ -310,23 +310,6 @@ pub fn create_proof_on_srs<E: Engine, C: Circuit<E>, S: SynthesisDriver>(
evaluate_at_consequitive_powers(&rx1, tmp, z)
};
// {
// rx1[(2 * n + NUM_BLINDINGS)].sub_assign(&rz);
// let opening = polynomial_commitment_opening(
// 2 * n + NUM_BLINDINGS,
// n,
// rx1.iter(),
// z,
// srs
// );
// let valid_rz_commitment = check_polynomial_commitment(&r, &z, &rz, &opening, n, &srs);
// assert!(valid_rz_commitment);
// rx1[(2 * n + NUM_BLINDINGS)].add_assign(&rz);
// }
// rzy is evaluation of r(X, Y) at z, y
let rzy = {
let tmp = z_inv.pow(&[(2*n + NUM_BLINDINGS) as u64]);
@ -385,11 +368,6 @@ pub fn create_proof_on_srs<E: Engine, C: Circuit<E>, S: SynthesisDriver>(
srs)
};
// let mut zy = z;
// zy.mul_assign(&y);
// let valid_rzy_commitment = check_polynomial_commitment(&r, &zy, &rzy, &zy_opening, n, &srs);
// assert!(valid_rzy_commitment);
Ok(Proof {
r, rz, rzy, t, z_opening, zy_opening
})

1
src/sonic/tests/mod.rs Normal file
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@ -0,0 +1 @@
mod sonics;

154
src/sonic/tests/sonics.rs
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@ -23,23 +23,131 @@ use crate::pairing::bn256::{
};
// We'll use these interfaces to construct our circuit.
use bellman::{
use crate::{
Circuit,
ConstraintSystem,
SynthesisError
};
// We're going to use the Groth16 proving system.
use bellman::groth16::{
Proof,
generate_random_parameters,
prepare_verifying_key,
create_random_proof,
verify_proof,
};
const MIMC_ROUNDS: usize = 322;
fn mimc<E: Engine>(
mut xl: E::Fr,
mut xr: E::Fr,
constants: &[E::Fr]
) -> E::Fr
{
assert_eq!(constants.len(), MIMC_ROUNDS);
for i in 0..MIMC_ROUNDS {
let mut tmp1 = xl;
tmp1.add_assign(&constants[i]);
let mut tmp2 = tmp1;
tmp2.square();
tmp2.mul_assign(&tmp1);
tmp2.add_assign(&xr);
xr = xl;
xl = tmp2;
}
xl
}
/// This is our demo circuit for proving knowledge of the
/// preimage of a MiMC hash invocation.
#[derive(Clone)]
struct MiMCDemo<'a, E: Engine> {
xl: Option<E::Fr>,
xr: Option<E::Fr>,
constants: &'a [E::Fr]
}
/// Our demo circuit implements this `Circuit` trait which
/// is used during paramgen and proving in order to
/// synthesize the constraint system.
impl<'a, E: Engine> Circuit<E> for MiMCDemo<'a, E> {
fn synthesize<CS: ConstraintSystem<E>>(
self,
cs: &mut CS
) -> Result<(), SynthesisError>
{
assert_eq!(self.constants.len(), MIMC_ROUNDS);
// Allocate the first component of the preimage.
let mut xl_value = self.xl;
let mut xl = cs.alloc(|| "preimage xl", || {
xl_value.ok_or(SynthesisError::AssignmentMissing)
})?;
// Allocate the second component of the preimage.
let mut xr_value = self.xr;
let mut xr = cs.alloc(|| "preimage xr", || {
xr_value.ok_or(SynthesisError::AssignmentMissing)
})?;
for i in 0..MIMC_ROUNDS {
// xL, xR := xR + (xL + Ci)^3, xL
let cs = &mut cs.namespace(|| format!("round {}", i));
// tmp = (xL + Ci)^2
let tmp_value = xl_value.map(|mut e| {
e.add_assign(&self.constants[i]);
e.square();
e
});
let tmp = cs.alloc(|| "tmp", || {
tmp_value.ok_or(SynthesisError::AssignmentMissing)
})?;
cs.enforce(
|| "tmp = (xL + Ci)^2",
|lc| lc + xl + (self.constants[i], CS::one()),
|lc| lc + xl + (self.constants[i], CS::one()),
|lc| lc + tmp
);
// new_xL = xR + (xL + Ci)^3
// new_xL = xR + tmp * (xL + Ci)
// new_xL - xR = tmp * (xL + Ci)
let new_xl_value = xl_value.map(|mut e| {
e.add_assign(&self.constants[i]);
e.mul_assign(&tmp_value.unwrap());
e.add_assign(&xr_value.unwrap());
e
});
let new_xl = if i == (MIMC_ROUNDS-1) {
// This is the last round, xL is our image and so
// we allocate a public input.
cs.alloc_input(|| "image", || {
new_xl_value.ok_or(SynthesisError::AssignmentMissing)
})?
} else {
cs.alloc(|| "new_xl", || {
new_xl_value.ok_or(SynthesisError::AssignmentMissing)
})?
};
cs.enforce(
|| "new_xL = xR + (xL + Ci)^3",
|lc| lc + tmp,
|lc| lc + xl + (self.constants[i], CS::one()),
|lc| lc + new_xl - xr
);
// xR = xL
xr = xl;
xr_value = xl_value;
// xL = new_xL
xl = new_xl;
xl_value = new_xl_value;
}
Ok(())
}
}
/// This is our demo circuit for proving knowledge of the
/// preimage of a MiMC hash invocation.
#[derive(Clone)]
@ -143,7 +251,7 @@ fn test_sonic_mimc() {
use crate::pairing::{Engine, CurveAffine, CurveProjective};
use crate::pairing::bls12_381::{Bls12, Fr};
use std::time::{Instant};
use bellman::sonic::srs::SRS;
use crate::sonic::srs::SRS;
let srs_x = Fr::from_str("23923").unwrap();
let srs_alpha = Fr::from_str("23728792").unwrap();
@ -174,11 +282,11 @@ fn test_sonic_mimc() {
constants: &constants
};
use bellman::sonic::cs::Basic;
use bellman::sonic::sonic::AdaptorCircuit;
use bellman::sonic::helped::prover::{create_advice_on_srs, create_proof_on_srs};
use bellman::sonic::helped::{MultiVerifier, get_circuit_parameters};
use bellman::sonic::helped::helper::{create_aggregate_on_srs};
use crate::sonic::cs::Basic;
use crate::sonic::sonic::AdaptorCircuit;
use crate::sonic::helped::prover::{create_advice_on_srs, create_proof_on_srs};
use crate::sonic::helped::{MultiVerifier, get_circuit_parameters};
use crate::sonic::helped::helper::{create_aggregate_on_srs};
println!("creating proof");
let start = Instant::now();
@ -248,7 +356,7 @@ fn test_inputs_into_sonic_mimc() {
use crate::pairing::bn256::{Bn256, Fr};
// use crate::pairing::bls12_381::{Bls12, Fr};
use std::time::{Instant};
use bellman::sonic::srs::SRS;
use crate::sonic::srs::SRS;
let srs_x = Fr::from_str("23923").unwrap();
let srs_alpha = Fr::from_str("23728792").unwrap();
@ -278,11 +386,11 @@ fn test_inputs_into_sonic_mimc() {
constants: &constants
};
use bellman::sonic::cs::Basic;
use bellman::sonic::sonic::AdaptorCircuit;
use bellman::sonic::helped::prover::{create_advice_on_srs, create_proof_on_srs};
use bellman::sonic::helped::{MultiVerifier, get_circuit_parameters};
use bellman::sonic::helped::helper::{create_aggregate_on_srs};
use crate::sonic::cs::Basic;
use crate::sonic::sonic::AdaptorCircuit;
use crate::sonic::helped::prover::{create_advice_on_srs, create_proof_on_srs};
use crate::sonic::helped::{MultiVerifier, get_circuit_parameters};
use crate::sonic::helped::helper::{create_aggregate_on_srs};
let info = get_circuit_parameters::<Bn256, _>(circuit.clone()).expect("Must get circuit info");
println!("{:?}", info);
@ -352,7 +460,7 @@ fn test_inputs_into_sonic_mimc() {
fn test_high_level_sonic_api() {
use crate::pairing::bn256::{Bn256};
use std::time::{Instant};
use bellman::sonic::helped::{
use crate::sonic::helped::{
generate_random_parameters,
verify_aggregate,
verify_proofs,

304
src/sonic/util.rs
View File

@ -123,10 +123,12 @@ pub fn polynomial_commitment_opening<
) -> E::G1Affine
where I::IntoIter: DoubleEndedIterator + ExactSizeIterator,
{
let poly = kate_divison(
polynomial_coefficients,
point,
);
let poly = parallel_kate_divison::<E, _>(polynomial_coefficients, point);
// let poly = kate_divison(
// polynomial_coefficients,
// point,
// );
let negative_poly = poly[0..largest_negative_power].iter().rev();
let positive_poly = poly[largest_negative_power..].iter();
@ -400,6 +402,75 @@ where
q
}
/// Divides polynomial `a` in `x` by `x - b` with
/// no remainder using fft.
pub fn parallel_kate_divison<'a, E: Engine, I: IntoIterator<Item = &'a E::Fr>>(a: I, mut b: E::Fr) -> Vec<E::Fr>
where
I::IntoIter: DoubleEndedIterator + ExactSizeIterator,
{
// this implementation is only for division by `x - b` form polynomail,
// so we can manuall calculate the reciproical poly of the form `x^2/(x-b)`
// and the reminder
// x^2 /(x - b) = x + b*x/(x - b) = (x + b) + b^2/(x - b)
let reciproical = vec![b, E::Fr::one()]; // x + b
// and remainder b^2
let mut b_squared = b;
b_squared.square();
let mut b_neg = b;
b_neg.negate();
let divisor = vec![b_neg, E::Fr::one()];
let poly: Vec<E::Fr> = a.into_iter().map(|el| el.clone()).collect();
let (q, _) = kate_divison_inner::<E>(poly, divisor, reciproical, b_squared);
// assert_eq!(r.len(), 0);
q
}
fn kate_divison_inner<E: Engine>(
poly: Vec<E::Fr>,
divisor: Vec<E::Fr>,
reciproical: Vec<E::Fr>,
remainder: E::Fr
) -> (Vec<E::Fr>, Vec<E::Fr>) {
if poly.len() == 1 {
return (vec![], poly);
}
// TODO: Change generic multiplications by multiplications by degree 1 polynomial
let poly_degree = poly.len() - 1;
let mut q = multiply_polynomials::<E>(poly.clone(), reciproical.clone());
q.drain(0..2);
// recursion step
if poly_degree > 2 {
let mut rec_step = poly.clone();
mul_polynomial_by_scalar(&mut rec_step[..], remainder);
// truncate low order terms
rec_step.drain(0..2);
let (q2, _) = kate_divison_inner::<E>(rec_step, divisor.clone(), reciproical, remainder);
// length of q2 is smaller
add_polynomials(&mut q[..q2.len()], &q2[..]);
}
// although r must be zero, calculate it for now
if q.len() == 0 {
return (q, poly);
}
// r = u - v*q
let mut poly = poly;
let tmp = multiply_polynomials::<E>(divisor, q.clone());
sub_polynomials(&mut poly[..], &tmp[..]);
return (q, poly);
}
/// Convenience function to check polynomail commitment
pub fn check_polynomial_commitment<E: Engine>(
commitment: &E::G1Affine,
@ -524,6 +595,90 @@ pub fn multiply_polynomials<E: Engine>(a: Vec<E::Fr>, b: Vec<E::Fr>) -> Vec<E::F
mul_result
}
// alternative implementation that does not require an `Evaluation domain` struct
pub fn multiply_polynomials_fft<E: Engine>(a: Vec<E::Fr>, b: Vec<E::Fr>) -> Vec<E::Fr> {
use crate::multicore::Worker;
use crate::domain::{best_fft, Scalar};
use crate::group::Group;
let result_len = a.len() + b.len() - 1;
// m is a size of domain where Z polynomial does NOT vanish
// in normal domain Z is in a form of (X-1)(X-2)...(X-N)
let mut m = 1;
let mut exp = 0;
let mut omega = E::Fr::root_of_unity();
let max_degree = (1 << E::Fr::S) - 1;
if result_len > max_degree {
panic!("multiplication result degree is too large");
}
while m < result_len {
m *= 2;
exp += 1;
// The pairing-friendly curve may not be able to support
// large enough (radix2) evaluation domains.
if exp > E::Fr::S {
panic!("multiplication result degree is too large");
}
}
// If full domain is not needed - limit it,
// e.g. if (2^N)th power is not required, just double omega and get 2^(N-1)th
// Compute omega, the 2^exp primitive root of unity
for _ in exp..E::Fr::S {
omega.square();
}
let omegainv = omega.inverse().unwrap();
let minv = E::Fr::from_str(&format!("{}", m)).unwrap().inverse().unwrap();
let worker = Worker::new();
let mut scalars_a: Vec<Scalar<E>> = a.into_iter().map(|e| Scalar::<E>(e)).collect();
let mut scalars_b: Vec<Scalar<E>> = b.into_iter().map(|e| Scalar::<E>(e)).collect();
scalars_a.resize(m, Scalar::<E>(E::Fr::zero()));
scalars_b.resize(m, Scalar::<E>(E::Fr::zero()));
best_fft(&mut scalars_a[..], &worker, &omega, exp);
best_fft(&mut scalars_b[..], &worker, &omega, exp);
// do the convolution
worker.scope(scalars_a.len(), |scope, chunk| {
for (a, b) in scalars_a.chunks_mut(chunk).zip(scalars_b.chunks(chunk)) {
scope.spawn(move |_| {
for (a, b) in a.iter_mut().zip(b.iter()) {
a.group_mul_assign(&b.0);
}
});
}
});
// no longer need it
drop(scalars_b);
best_fft(&mut scalars_a[..], &worker, &omegainv, exp);
worker.scope(scalars_a.len(), |scope, chunk| {
for v in scalars_a.chunks_mut(chunk) {
scope.spawn(move |_| {
for v in v {
v.group_mul_assign(&minv);
}
});
}
});
let mut mul_result: Vec<E::Fr> = scalars_a.into_iter().map(|e| e.0).collect();
mul_result.truncate(result_len);
mul_result
}
pub fn multiply_polynomials_serial<E: Engine>(mut a: Vec<E::Fr>, mut b: Vec<E::Fr>) -> Vec<E::Fr> {
let result_len = a.len() + b.len() - 1;
@ -574,6 +729,7 @@ pub fn multiply_polynomials_serial<E: Engine>(mut a: Vec<E::Fr>, mut b: Vec<E::F
a
}
// add polynomails in coefficient form
pub fn add_polynomials<F: Field>(a: &mut [F], b: &[F]) {
use crate::multicore::Worker;
use crate::domain::{EvaluationDomain, Scalar};
@ -594,6 +750,28 @@ pub fn add_polynomials<F: Field>(a: &mut [F], b: &[F]) {
});
}
// subtract polynomails in coefficient form
pub fn sub_polynomials<F: Field>(a: &mut [F], b: &[F]) {
use crate::multicore::Worker;
use crate::domain::{EvaluationDomain, Scalar};
let worker = Worker::new();
assert_eq!(a.len(), b.len());
worker.scope(a.len(), |scope, chunk| {
for (a, b) in a.chunks_mut(chunk).zip(b.chunks(chunk))
{
scope.spawn(move |_| {
for (a, b) in a.iter_mut().zip(b.iter()) {
a.sub_assign(b);
}
});
}
});
}
// multiply coefficients of the polynomial by the scalar
pub fn mul_polynomial_by_scalar<F: Field>(a: &mut [F], b: F) {
use crate::multicore::Worker;
use crate::domain::{EvaluationDomain, Scalar};
@ -612,6 +790,8 @@ pub fn mul_polynomial_by_scalar<F: Field>(a: &mut [F], b: F) {
});
}
// elementwise add coeffs of one polynomial with coeffs of other, that are
// first multiplied by a scalar
pub fn mul_add_polynomials<F: Field>(a: &mut [F], b: &[F], c: F) {
use crate::multicore::Worker;
use crate::domain::{EvaluationDomain, Scalar};
@ -693,7 +873,6 @@ impl<T> OptionExt<T> for Option<T> {
}
#[test]
fn test_mul() {
use rand::{self, Rand};
use crate::pairing::bls12_381::Bls12;
@ -804,4 +983,119 @@ fn test_mut_distribute_powers() {
mut_distribute_consequitive_powers(&mut b[..], first_power, x);
assert!(a == b);
}
#[test]
fn test_trivial_parallel_kate_division() {
use pairing::ff::PrimeField;
use pairing::bls12_381::{Bls12, Fr};
let mut minus_one = Fr::one();
minus_one.negate();
let z = Fr::one();
// this is x^2 - 1
let poly = vec![
minus_one,
Fr::from_str("0").unwrap(),
Fr::from_str("1").unwrap(),
];
let quotient_poly = kate_divison(&poly, z);
let parallel_q_poly = parallel_kate_divison::<Bls12, _>(&poly, z);
assert_eq!(quotient_poly, parallel_q_poly);
}
#[test]
fn test_less_trivial_parallel_kate_division() {
use pairing::ff::PrimeField;
use pairing::bls12_381::{Bls12, Fr};
let z = Fr::one();
let mut poly = vec![
Fr::from_str("328947234").unwrap(),
Fr::from_str("3545623451111").unwrap(),
Fr::from_str("5").unwrap(),
Fr::from_str("55555").unwrap(),
Fr::from_str("1235685").unwrap(),
];
fn eval(poly: &[Fr], point: Fr) -> Fr {
let mut acc = Fr::zero();
let mut tmp = Fr::one();
for p in &poly[..] {
let mut t = *p;
t.mul_assign(&tmp);
acc.add_assign(&t);
tmp.mul_assign(&point);
}
acc
}
let p_at_z = eval(&poly, z);
// poly = poly(X) - poly(z)
poly[0].sub_assign(&p_at_z);
let quotient_poly = kate_divison(&poly, z);
let parallel_q_poly = parallel_kate_divison::<Bls12, _>(&poly, z);
assert_eq!(quotient_poly, parallel_q_poly);
}
#[test]
fn test_parallel_kate_division() {
use pairing::ff::PrimeField;
use pairing::bls12_381::{Bls12, Fr};
let mut poly = vec![
Fr::from_str("328947234").unwrap(),
Fr::from_str("3545623451111").unwrap(),
Fr::from_str("0").unwrap(),
Fr::from_str("55555").unwrap(),
Fr::from_str("1235685").unwrap(),
];
fn eval(poly: &[Fr], point: Fr) -> Fr {
let point_inv = point.inverse().unwrap();
let mut acc = Fr::zero();
let mut tmp = Fr::one();
for p in &poly[2..] {
let mut t = *p;
t.mul_assign(&tmp);
acc.add_assign(&t);
tmp.mul_assign(&point);
}
let mut tmp = point_inv;
for p in poly[0..2].iter().rev() {
let mut t = *p;
t.mul_assign(&tmp);
acc.add_assign(&t);
tmp.mul_assign(&point_inv);
}
acc
}
let z = Fr::from_str("2000").unwrap();
let p_at_z = eval(&poly, z);
// poly = poly(X) - poly(z)
poly[2].sub_assign(&p_at_z);
let quotient_poly = kate_divison(&poly, z);
let parallel_q_poly = parallel_kate_divison::<Bls12, _>(&poly, z);
assert_eq!(quotient_poly, parallel_q_poly);
}