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work on tensor, fix mul by constant(plaintext)

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arnaucube
2025-06-22 18:42:50 +02:00
parent d2fc32ac0c
commit 7740a3ef3e
4 changed files with 135 additions and 196 deletions
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5
README.md
View File

@@ -1,4 +1,5 @@
# fhe-study
Code done while studying some FHE papers, with the idea of doing implementations from scratch.
Implementations from scratch done while studying some FHE papers.
- arithmetic: contains $\mathbb{Z}_q$ and $\mathbb{Z}_q[X]/(X^N+1)$ arithmetic implementations, together with the NTT implementation.
- arithmetic: contains $\mathbb{Z}_q$, $R_q=\mathbb{Z}_q[X]/(X^N+1)$ and $R=\mathbb{Z}[X]/(X^N+1)$ arithmetic implementations, together with the NTT implementation.
- bfv: https://eprint.iacr.org/2012/144.pdf scheme implementation

36
arithmetic/src/ring.rs
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@@ -59,6 +59,7 @@ impl<const N: usize> R<N> {
crate::Rq::<Q, N>::from_vec_f64(r)
}
}
pub fn mul_div_round<const Q: u64, const N: usize>(
v: Vec<i64>,
num: u64,
@@ -73,6 +74,7 @@ pub fn mul_div_round<const Q: u64, const N: usize>(
crate::Rq::<Q, N>::from_vec_f64(r)
}
// TODO rename to make it clear that is not mod q, but mod X^N+1
// apply mod (X^N+1)
pub fn modulus<const N: usize>(p: &mut Vec<i64>) {
if p.len() < N {
@@ -84,6 +86,16 @@ pub fn modulus<const N: usize>(p: &mut Vec<i64>) {
}
p.truncate(N);
}
pub fn modulus_i128<const N: usize>(p: &mut Vec<i128>) {
if p.len() < N {
return;
}
for i in N..p.len() {
p[i - N] = p[i - N].clone() - p[i].clone();
p[i] = 0;
}
p.truncate(N);
}
impl<const N: usize> PartialEq for R<N> {
fn eq(&self, other: &Self) -> bool {
@@ -133,7 +145,7 @@ impl<const N: usize> ops::Mul<&R<N>> for &R<N> {
}
}
// TODO with NTT(?)
// TODO WIP
pub fn naive_poly_mul<const N: usize>(poly1: &R<N>, poly2: &R<N>) -> R<N> {
let poly1: Vec<i128> = poly1.0.iter().map(|c| *c as i128).collect();
let poly2: Vec<i128> = poly2.0.iter().map(|c| *c as i128).collect();
@@ -147,15 +159,35 @@ pub fn naive_poly_mul<const N: usize>(poly1: &R<N>, poly2: &R<N>) -> R<N> {
// apply mod (X^N + 1))
R::<N>::from_vec(result.iter().map(|c| *c as i64).collect())
}
pub fn naive_mul<const N: usize>(poly1: &R<N>, poly2: &R<N>) -> Vec<i64> {
let poly1: Vec<i128> = poly1.0.iter().map(|c| *c as i128).collect();
let poly2: Vec<i128> = poly2.0.iter().map(|c| *c as i128).collect();
let mut result = vec![0; (N * 2) - 1];
let mut result: Vec<i128> = vec![0; (N * 2) - 1];
for i in 0..N {
for j in 0..N {
result[i + j] = result[i + j] + poly1[i] * poly2[j];
}
}
modulus_i128::<N>(&mut result);
// for c_i in result.iter() {
// println!("---");
// println!("{:?}", &c_i);
// println!("{:?}", *c_i as i64);
// println!("{:?}", (*c_i as i64) as i128);
// assert_eq!(*c_i, (*c_i as i64) as i128, "{:?}", c_i);
// }
// let q: i128 = 65537;
// let result: Vec<i64> = result
// .iter()
// // .map(|c_i| ((c_i % q + q) % q) as i64)
// .map(|c_i| (c_i % q) as i64)
// // .map(|c_i| *c_i as i64)
// .collect();
// result
result.iter().map(|c| *c as i64).collect()
}

7
arithmetic/src/ringq.rs
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@@ -56,6 +56,13 @@ impl<const Q: u64, const N: usize> Rq<Q, N> {
crate::R::<N>::from(self)
}
pub fn zero() -> Self {
let coeffs = array::from_fn(|_| Zq::zero());
Self {
coeffs,
evals: None,
}
}
pub fn from_vec(coeffs: Vec<Zq<Q>>) -> Self {
let mut p = coeffs;
modulus::<Q, N>(&mut p);

265
bfv/src/lib.rs
View File

@@ -10,12 +10,13 @@ use rand::Rng;
use rand_distr::{Normal, Uniform};
use std::ops;
use arithmetic::{Rq, Zq, R};
use arithmetic::{Rq, R};
// error deviation for the Gaussian(Normal) distribution
// sigma=3.2 from: https://eprint.iacr.org/2022/162.pdf page 5
const ERR_SIGMA: f64 = 3.2;
// const ERR_SIGMA: f64 = 0.0; // TODO WIP
// const ERR_SIGMA: f64 = 1.0; // TODO WIP
#[derive(Clone, Debug)]
pub struct SecretKey<const Q: u64, const N: usize>(Rq<Q, N>);
@@ -48,21 +49,23 @@ impl<const Q: u64, const N: usize> RLWE<Q, N> {
}
fn tensor<const PQ: u64, const T: u64>(a: &Self, b: &Self) -> (Rq<Q, N>, Rq<Q, N>, Rq<Q, N>) {
// expand Q->PQ // TODO rm
// get the coefficients in Z, ie. interpret a,b \in R (instead of R_q)
let a0: R<N> = a.0.to_r();
let a1: R<N> = a.1.to_r();
let b0: R<N> = b.0.to_r();
let b1: R<N> = b.1.to_r();
// tensor (\in R)
// tensor (\in R) (2021-204 p.9)
use arithmetic::ring::naive_mul;
// (here can use *, but want to make it explicit that we're using the naive mul)
let c0: Vec<i64> = naive_mul(&a0, &b0);
let c1_l: Vec<i64> = naive_mul(&a0, &b1);
let c1_r = naive_mul(&a1, &b0);
let c1: Vec<i64> = itertools::zip_eq(c1_l, c1_r).map(|(l, r)| l + r).collect();
let c2: Vec<i64> = naive_mul(&a1, &b1);
// scale down, module Q, so result is \in R_q
// scale down, then reduce module Q, so result is \in R_q
let c0: Rq<Q, N> = arithmetic::ring::mul_div_round::<Q, N>(c0, T, Q);
let c1: Rq<Q, N> = arithmetic::ring::mul_div_round::<Q, N>(c1, T, Q);
let c2: Rq<Q, N> = arithmetic::ring::mul_div_round::<Q, N>(c2, T, Q);
@@ -119,76 +122,73 @@ impl<const Q: u64, const N: usize, const T: u64> ops::Add<&Rq<T, N>> for &RLWE<Q
BFV::<Q, N, T>::add_const(self, rhs)
}
}
impl<const Q: u64, const N: usize, const T: u64> ops::Mul<&Rq<T, N>> for &RLWE<Q, N> {
type Output = RLWE<Q, N>;
fn mul(self, rhs: &Rq<T, N>) -> Self::Output {
BFV::<Q, N, T>::mul_const(&self, rhs)
}
}
// impl<const Q: u64, const N: usize, const T: u64> ops::Mul<&Rq<T, N>> for &RLWE<Q, N> {
// type Output = RLWE<Q, N>;
// fn mul(self, rhs: &Rq<T, N>) -> Self::Output {
// BFV::<Q, N, T>::mul_const(&self, rhs)
// }
// }
pub struct BFV<const Q: u64, const N: usize, const T: u64> {}
impl<const Q: u64, const N: usize, const T: u64> BFV<Q, N, T> {
const DELTA: u64 = Q / T;
const DELTA: u64 = Q / T; // floor
/// generate a new key pair (privK, pubK)
pub fn new_key(mut rng: impl Rng) -> Result<(SecretKey<Q, N>, PublicKey<Q, N>)> {
// WIP: review probabilities
// let Xi_key = Uniform::new(-1_f64, 1_f64);
let Xi_key = Uniform::new(0_u64, 2_u64);
let Xi_key = Uniform::new(-1_f64, 1_f64);
// let Xi_key = Uniform::new(0_u64, 2_u64);
// use rand::distributions::Bernoulli;
// let Xi_key = Bernoulli::new(0.5)?;
let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
// let Xi_err = Normal::new(0_f64, 0.0)?;
// secret key
let s = Rq::<Q, N>::rand_u64(&mut rng, Xi_key)?;
let s = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;
// let s = Rq::<Q, N>::rand_u64(&mut rng, Xi_key)?;
#[cfg(test)] // sanity check
assert!(s.infinity_norm() <= 1, "{:?}", s.coeffs());
// #[cfg(test)] // sanity check
// assert!(
// s.infinity_norm() <= 1,
// "s.infinity_norm check failed {:?}",
// s.coeffs()
// );
// pk = (-a * s + e, a)
let a = Rq::<Q, N>::rand_u64(&mut rng, Uniform::new(0_u64, Q))?;
let e = Rq::<Q, N>::rand_f64(&mut rng, Xi_err)?;
// println!("e{:?}", e.coeffs());
let pk: PublicKey<Q, N> = PublicKey((&(-a) * &s) + e, a.clone());
Ok((SecretKey(s), pk))
}
pub fn encrypt(mut rng: impl Rng, pk: &PublicKey<Q, N>, m: &Rq<T, N>) -> Result<RLWE<Q, N>> {
// let Xi_key = Uniform::new(-1_f64, 1_f64);
// let Xi_key = Uniform::new(0_f64, 2_f64);
let Xi_key = Uniform::new(0_u64, 2_u64);
let Xi_key = Uniform::new(-1_f64, 1_f64);
// let Xi_key = Uniform::new(0_u64, 2_u64);
let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;
// let Xi_err = Normal::new(0_f64, 0.0)?;
let u = Rq::<Q, N>::rand_u64(&mut rng, Xi_key)?;
let e_1 = Rq::<Q, N>::rand_f64_abs(&mut rng, Xi_err)?;
let e_2 = Rq::<Q, N>::rand_f64_abs(&mut rng, Xi_err)?;
let u = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;
// let u = Rq::<Q, N>::rand_u64(&mut rng, Xi_key)?;
let e_1 = Rq::<Q, N>::rand_f64(&mut rng, Xi_err)?;
let e_2 = Rq::<Q, N>::rand_f64(&mut rng, Xi_err)?;
// println!("e_1{:?}", e_1.coeffs());
// println!("e_2{:?}", e_2.coeffs());
// println!("{:?}", &e_1.coeffs());
// println!("{:?}", &e_2.coeffs());
#[cfg(test)] // sanity check
assert!(u.infinity_norm() <= 1, "{:?}", u.coeffs());
// #[cfg(test)] // sanity check
// assert!(
// u.infinity_norm() <= 1,
// "u.infinity_norm check failed {:?}",
// u.coeffs()
// );
// migrate m's coeffs to the bigger modulus Q (from T)
let m = m.remodule::<Q>();
#[cfg(test)]
{
// sanity check // TODO rm
let m_remod_naive =
Rq::<Q, N>::from_vec_u64(m.coeffs().iter().map(|m_i| m_i.0).collect());
assert_eq!(m_remod_naive, m);
}
// let c0 = &pk.0 * &u + e_1 + m * Self::DELTA;
let c0 = &pk.0 * &u + e_1 + m.mul_div_round(Q, T); // TODO use DELTA?
// let c0 = &pk.0 * &u + e_1 + m.mul_div_round(Q, T);
let c0 = &pk.0 * &u + e_1 + m * Self::DELTA;
// let D: u64 = (Q as f64 / T as f64).floor() as u64;
// let c0 = &pk.0 * &u + e_1 + m * D; // TODO use DELTA?
let c1 = &pk.1 * &u + e_2;
// let c0 = tmp_naive_mul(pk.0, u) + e_1 + m * Self::DELTA;
// let c0 = tmp_naive_mul(pk.0, u) + e_1 + m.mul_div_round(Q, T);
// let c1 = tmp_naive_mul(pk.1, u)
// // &pk.1 * &u
// + e_2;
Ok(RLWE::<Q, N>(c0, c1))
}
@@ -216,10 +216,13 @@ impl<const Q: u64, const N: usize, const T: u64> BFV<Q, N, T> {
let m = m.remodule::<Q>();
RLWE::<Q, N>(c.0 + m * Self::DELTA, c.1)
}
fn mul_const(c: &RLWE<Q, N>, m: &Rq<T, N>) -> RLWE<Q, N> {
fn mul_const<const PQ: u64>(rlk: &RLK<PQ, N>, c: &RLWE<Q, N>, m: &Rq<T, N>) -> RLWE<Q, N> {
// assuming T<Q, move m from Zq<T> to Zq<Q>
let m = m.remodule::<Q>();
RLWE::<Q, N>(c.0 * m * Self::DELTA, c.1)
// encrypt m*Delta without noise, and then perform normal ciphertext multiplication
let md = RLWE::<Q, N>(m * Self::DELTA, Rq::zero());
RLWE::<Q, N>::mul::<PQ, T>(&rlk, &c, &md)
}
fn rlk_key<const PQ: u64>(mut rng: impl Rng, s: &SecretKey<Q, N>) -> Result<RLK<PQ, N>> {
@@ -232,11 +235,11 @@ impl<const Q: u64, const N: usize, const T: u64> BFV<Q, N, T> {
// let rlk_1: Rq<PQ, N> = (&(-a) * &s) - e + (s * s) * P;
let P = PQ / Q;
// let rlk: RLK<PQ, N> = RLK::<PQ, N>((&(-a) * &s) - e + (s * s) * P, a.clone());
let rlk: RLK<PQ, N> = RLK::<PQ, N>(
-(tmp_naive_mul(a, s) + e) + tmp_naive_mul(s, s) * P,
a.clone(),
);
let rlk: RLK<PQ, N> = RLK::<PQ, N>((&(-a) * &s) - e + (s * s) * P, a.clone());
// let rlk: RLK<PQ, N> = RLK::<PQ, N>(
// -(tmp_naive_mul(a, s) + e) + tmp_naive_mul(s, s) * P,
// a.clone(),
// );
// let rlk: RLK<PQ, N> = RLK::<PQ, N>(-(&a * &s + e) + (s * s) * P, a.clone());
// let pq = P * Q;
@@ -292,17 +295,8 @@ impl<const Q: u64, const N: usize, const T: u64> BFV<Q, N, T> {
// let c2rlk0: Vec<f64> = (c2.remodule::<PQ>() * rlk.0)
use arithmetic::ring::naive_mul;
let c2rlk0: Vec<i64> = naive_mul(&c2.to_r(), &rlk.0.to_r());
// .coeffs()
// .iter()
// .map(|e| (*e as f64 / P as f64).round())
// .collect();
let c2rlk1: Vec<i64> = naive_mul(&c2.to_r(), &rlk.1.to_r());
// .coeffs()
// .iter()
// .map(|e| (*e as f64 / P as f64).round())
// .collect();
//
let r0: Rq<Q, N> = arithmetic::ring::mul_div_round::<Q, N>(c2rlk0, 1, P);
let r1: Rq<Q, N> = arithmetic::ring::mul_div_round::<Q, N>(c2rlk1, 1, P);
@@ -348,13 +342,13 @@ mod tests {
#[test]
fn test_addition() -> Result<()> {
const Q: u64 = 2u64.pow(16) + 1;
// const N: usize = 32;
const N: usize = 4;
const N: usize = 32;
const T: u64 = 4; // plaintext modulus
type S = BFV<Q, N, T>;
let mut rng = rand::thread_rng();
for _ in 0..1_000 {
let (sk, pk) = S::new_key(&mut rng)?;
let msg_dist = Uniform::new(0_u64, T);
@@ -369,15 +363,16 @@ mod tests {
let m3_recovered = S::decrypt(&sk, &c3);
assert_eq!(m1 + m2, m3_recovered);
}
Ok(())
}
#[test]
fn test_constant_add() -> Result<()> {
fn test_constant_add_mul() -> Result<()> {
const Q: u64 = 2u64.pow(16) + 1;
const N: usize = 32;
const T: u64 = 4; // plaintext modulus
const T: u64 = 8; // plaintext modulus
type S = BFV<Q, N, T>;
let mut rng = rand::thread_rng();
@@ -387,25 +382,25 @@ mod tests {
let msg_dist = Uniform::new(0_u64, T);
let m1 = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
let m2_const = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
let c1 = S::encrypt(&mut rng, &pk, &m1)?;
let c3_add = &c1 + &m2_const;
// let c3_mul = &c1 * &m2_const;
let m3_add_recovered = S::decrypt(&sk, &c3_add);
// let m3_mul_recovered = S::decrypt(&sk, &c3_mul);
assert_eq!(m1 + m2_const, m3_add_recovered);
//
// let mut mul_res = naive_poly_mul::<T>(&m1.coeffs().to_vec(), &m2_const.coeffs().to_vec());
// arithmetic::ring::modulus::<T, N>(&mut mul_res);
// dbg!(&mul_res);
// let mul_res_2 =
// naive_poly_mul_2::<T, N>(&m1.coeffs().to_vec(), &m2_const.coeffs().to_vec());
// assert_eq!(mul_res, mul_res_2);
// let mul_res = PR::<T, N>::from_vec(mul_res);
// assert_eq!(mul_res.coeffs(), m3_mul_recovered.coeffs());
// test multiplication of a ciphertext by a constant
const P: u64 = Q * Q;
const PQ: u64 = P * Q;
let rlk = BFV::<Q, N, T>::rlk_key::<PQ>(&mut rng, &sk)?;
let c3_mul = S::mul_const(&rlk, &c1, &m2_const);
let m3_mul_recovered = S::decrypt(&sk, &c3_mul);
assert_eq!(
(m1.to_r() * m2_const.to_r()).to_rq::<T>().coeffs(),
m3_mul_recovered.coeffs()
);
Ok(())
}
@@ -413,12 +408,11 @@ mod tests {
#[test]
fn test_tensor() -> Result<()> {
const Q: u64 = 2u64.pow(16) + 1; // q prime, and 2^q + 1 shape
const N: usize = 8;
const T: u64 = 4; // plaintext modulus
const N: usize = 32;
const T: u64 = 8; // plaintext modulus
// const P: u64 = Q;
const P: u64 = Q * Q;
// const P: u64 = 2_u64.pow(13) * Q + 1;
const PQ: u64 = P * Q;
let mut rng = rand::thread_rng();
@@ -447,7 +441,13 @@ mod tests {
// decrypt non-relinearized mul result
let m3: Rq<Q, N> = c_a + c_b * sk.0 + c_c * sk.0 * sk.0;
let m3: Rq<Q, N> = m3.mul_div_round(T, Q);
// let m3: Rq<Q, N> = c_a
// + Rq::<Q, N>::from_vec_i64(arithmetic::ring::naive_mul(&c_b.to_r(), &sk.0.to_r()))
// + Rq::<Q, N>::from_vec_i64(arithmetic::ring::naive_mul(
// &c_c.to_r(),
// &R::<N>::from_vec(arithmetic::ring::naive_mul(&sk.0.to_r(), &sk.0.to_r())),
// ));
let m3: Rq<Q, N> = m3.mul_div_round(T, Q); // descale
let m3 = m3.remodule::<T>();
let naive = (m1.to_r() * m2.to_r()).to_rq::<T>();
@@ -538,7 +538,7 @@ mod tests {
let c1 = BFV::<Q, N, T>::encrypt(&mut rng, &pk, &m1)?;
let c2 = BFV::<Q, N, T>::encrypt(&mut rng, &pk, &m2)?;
let c3 = RLWE::<Q, N>::mul::<PQ, T>(&rlk, &c1, &c2);
let c3 = RLWE::<Q, N>::mul::<PQ, T>(&rlk, &c1, &c2); // uses relinearize internally
let m3 = BFV::<Q, N, T>::decrypt(&sk, &c3);
@@ -551,105 +551,4 @@ mod tests {
Ok(())
}
#[test]
fn test_naive_mul() -> Result<()> {
const Q: u64 = 2u64.pow(16) + 1; // prime, and 2^q + 1 shape
const N: usize = 4;
const T: u64 = 4; // plaintext modulus
let mut rng = rand::thread_rng();
let msg_dist = Uniform::new(0_u64, T);
// for _ in 0..10_000 {
for _ in 0..2 {
println!("---");
// let a = Rq::<Q, N>::rand_u64(&mut rng, msg_dist)?;
// let b = Rq::<Q, N>::rand_u64(&mut rng, msg_dist)?;
// let a = Rq::<Q, N>::from_vec_u64(vec![Q - 1, Q - 2, Q - 3, Q - 3]);
// let b = Rq::<Q, N>::from_vec_u64(vec![Q - 3, Q - 3, Q - 2, Q - 1]);
let a = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
let b = Rq::<T, N>::rand_u64(&mut rng, msg_dist)?;
dbg!(&a);
dbg!(&b);
let (_, pk) = BFV::<Q, N, T>::new_key(&mut rng)?;
let ciph1 = BFV::<Q, N, T>::encrypt(&mut rng, &pk, &a)?;
let ciph2 = BFV::<Q, N, T>::encrypt(&mut rng, &pk, &b)?;
let a = ciph1.0;
let b = ciph2.0;
dbg!(&a);
dbg!(&b);
let c0: Vec<i64> = arithmetic::ring::naive_mul(&a.to_r(), &b.to_r());
let c0 = Rq::<Q, N>::from_vec_i64(c0);
let c1 = tmp_naive_mul(a, b); // naive mul
let c2: Rq<Q, N> = a * b; // NTT mul
println!("{:?}", c0.coeffs());
println!("{:?}", c1.coeffs());
println!("{:?}", c2.coeffs());
assert_eq!(c0, c2);
assert_eq!(c1, c2);
// scale by Delta=Q/T
let a = a.mul_div_round(Q, T);
let b = b.mul_div_round(Q, T);
dbg!(&a);
dbg!(&b);
let c0: Vec<i64> = arithmetic::ring::naive_mul(&a.to_r(), &b.to_r());
let c0 = Rq::<Q, N>::from_vec_i64(c0);
let c1 = tmp_naive_mul(a, b); // naive mul
let c2: Rq<Q, N> = a * b; // NTT mul
println!("{:?}", c0.coeffs());
println!("{:?}", c1.coeffs());
println!("{:?}", c2.coeffs());
assert_eq!(c0, c2);
assert_eq!(c1, c2);
let c0 = c0.mul_div_round(T, Q);
let c1 = c1.mul_div_round(T, Q);
let c2 = c2.mul_div_round(T, Q);
println!("{:?}", c0.coeffs());
println!("{:?}", c1.coeffs());
println!("{:?}", c2.coeffs());
assert_eq!(c0, c2);
assert_eq!(c1, c2);
/*
// now same as before, but multiplying by T/Q
let c0: Vec<i64> = arithmetic::ring::naive_mul(&a.to_r(), &b.to_r());
let c0: Vec<f64> = c0
.iter()
.map(|e| ((T as f64 * *e as f64) / Q as f64).round())
.collect();
let c0 = Rq::<Q, N>::from_vec_f64(c0);
dbg!(&c0.coeffs());
let a = a.mul_div_round(T, Q);
let b = b.mul_div_round(T, Q);
println!("a{:?}", a.coeffs());
println!("b{:?}", b.coeffs());
let c4: Vec<i64> = arithmetic::ring::naive_mul(&a.to_r(), &b.to_r());
let c4 = Rq::<Q, N>::from_vec_i64(c4);
let c4 = c4.mul_div_round(T, Q);
let c1 = tmp_naive_mul(a, b); // naive mul
let c1 = c1.mul_div_round(T, Q);
let c2 = a * b; // NTT mul
let c2 = c2.mul_div_round(T, Q);
println!("{:?}", c0.coeffs());
println!("{:?}", c1.coeffs());
println!("{:?}", c2.coeffs());
println!("{:?}", c4.coeffs());
assert_eq!(c0, c2);
assert_eq!(c4, c2);
assert_eq!(c1, c2);
*/
}
Ok(())
}
}