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ark-curves-cherry-picked/bn254/src/fields/tests.rs
Weikeng Chen 74f6efb821 Replace rand with ark_std::rand (#42) 
* replace rand

* update CHANGELOG

* fmt

* fix

* fix
2021-02-04 20:12:47 -08:00

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use ark_ff::{
biginteger::{BigInteger, BigInteger256},
fields::{
fp6_3over2::Fp6Parameters, FftField, FftParameters, Field, FpParameters, PrimeField,
SquareRootField,
},
One, UniformRand, Zero,
};
use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
use ark_std::rand::Rng;
use ark_std::test_rng;
use core::{
cmp::Ordering,
ops::{AddAssign, MulAssign, SubAssign},
};
use crate::{Fq, Fq12, Fq2, Fq6, Fq6Parameters, FqParameters, Fr};
use ark_algebra_test_templates::fields::*;
pub(crate) const ITERATIONS: usize = 5;
#[test]
fn test_fr() {
let mut rng = test_rng();
for _ in 0..ITERATIONS {
let a: Fr = rng.gen();
let b: Fr = rng.gen();
field_test(a, b);
primefield_test::<Fr>();
sqrt_field_test(b);
let byte_size = a.serialized_size();
field_serialization_test::<Fr>(byte_size);
}
}
#[test]
fn test_fq() {
let mut rng = test_rng();
for _ in 0..ITERATIONS {
let a: Fq = rng.gen();
let b: Fq = rng.gen();
field_test(a, b);
primefield_test::<Fq>();
sqrt_field_test(a);
let byte_size = a.serialized_size();
let (_, buffer_size) = buffer_bit_byte_size(Fq::size_in_bits());
assert_eq!(byte_size, buffer_size);
field_serialization_test::<Fq>(byte_size);
}
}
#[test]
fn test_fq2() {
let mut rng = test_rng();
for _ in 0..ITERATIONS {
let a: Fq2 = rng.gen();
let b: Fq2 = rng.gen();
field_test(a, b);
sqrt_field_test(a);
}
frobenius_test::<Fq2, _>(Fq::characteristic(), 13);
let byte_size = Fq2::zero().serialized_size();
field_serialization_test::<Fq2>(byte_size);
}
#[test]
fn test_fq6() {
let mut rng = test_rng();
for _ in 0..ITERATIONS {
let g: Fq6 = rng.gen();
let h: Fq6 = rng.gen();
field_test(g, h);
}
frobenius_test::<Fq6, _>(Fq::characteristic(), 13);
let byte_size = Fq6::zero().serialized_size();
field_serialization_test::<Fq6>(byte_size);
}
#[test]
fn test_fq12() {
let mut rng = test_rng();
for _ in 0..ITERATIONS {
let g: Fq12 = rng.gen();
let h: Fq12 = rng.gen();
field_test(g, h);
}
frobenius_test::<Fq12, _>(Fq::characteristic(), 13);
let byte_size = Fq12::zero().serialized_size();
field_serialization_test::<Fq12>(byte_size);
}
#[test]
fn test_fq_repr_from() {
assert_eq!(BigInteger256::from(100), BigInteger256([100, 0, 0, 0]));
}
#[test]
fn test_fq_repr_is_odd() {
assert!(!BigInteger256::from(0).is_odd());
assert!(BigInteger256::from(0).is_even());
assert!(BigInteger256::from(1).is_odd());
assert!(!BigInteger256::from(1).is_even());
assert!(!BigInteger256::from(324834872).is_odd());
assert!(BigInteger256::from(324834872).is_even());
assert!(BigInteger256::from(324834873).is_odd());
assert!(!BigInteger256::from(324834873).is_even());
}
#[test]
fn test_fq_repr_is_zero() {
assert!(BigInteger256::from(0).is_zero());
assert!(!BigInteger256::from(1).is_zero());
assert!(!BigInteger256([0, 0, 1, 0]).is_zero());
}
#[test]
fn test_fq_repr_num_bits() {
let mut a = BigInteger256::from(0);
assert_eq!(0, a.num_bits());
a = BigInteger256::from(1);
for i in 1..257 {
assert_eq!(i, a.num_bits());
a.mul2();
}
assert_eq!(0, a.num_bits());
}
#[test]
fn test_fq_add_assign() {
// Test associativity
let mut rng = ark_std::test_rng();
for _ in 0..1000 {
// Generate a, b, c and ensure (a + b) + c == a + (b + c).
let a = Fq::rand(&mut rng);
let b = Fq::rand(&mut rng);
let c = Fq::rand(&mut rng);
let mut tmp1 = a;
tmp1.add_assign(&b);
tmp1.add_assign(&c);
let mut tmp2 = b;
tmp2.add_assign(&c);
tmp2.add_assign(&a);
assert_eq!(tmp1, tmp2);
}
}
#[test]
fn test_fq_sub_assign() {
let mut rng = ark_std::test_rng();
for _ in 0..1000 {
// Ensure that (a - b) + (b - a) = 0.
let a = Fq::rand(&mut rng);
let b = Fq::rand(&mut rng);
let mut tmp1 = a;
tmp1.sub_assign(&b);
let mut tmp2 = b;
tmp2.sub_assign(&a);
tmp1.add_assign(&tmp2);
assert!(tmp1.is_zero());
}
}
#[test]
fn test_fq_mul_assign() {
let mut rng = ark_std::test_rng();
for _ in 0..1000000 {
// Ensure that (a * b) * c = a * (b * c)
let a = Fq::rand(&mut rng);
let b = Fq::rand(&mut rng);
let c = Fq::rand(&mut rng);
let mut tmp1 = a;
tmp1.mul_assign(&b);
tmp1.mul_assign(&c);
let mut tmp2 = b;
tmp2.mul_assign(&c);
tmp2.mul_assign(&a);
assert_eq!(tmp1, tmp2);
}
for _ in 0..1000000 {
// Ensure that r * (a + b + c) = r*a + r*b + r*c
let r = Fq::rand(&mut rng);
let mut a = Fq::rand(&mut rng);
let mut b = Fq::rand(&mut rng);
let mut c = Fq::rand(&mut rng);
let mut tmp1 = a;
tmp1.add_assign(&b);
tmp1.add_assign(&c);
tmp1.mul_assign(&r);
a.mul_assign(&r);
b.mul_assign(&r);
c.mul_assign(&r);
a.add_assign(&b);
a.add_assign(&c);
assert_eq!(tmp1, a);
}
}
#[test]
fn test_fq_squaring() {
let mut rng = ark_std::test_rng();
for _ in 0..1000000 {
// Ensure that (a * a) = a^2
let a = Fq::rand(&mut rng);
let mut tmp = a;
tmp.square_in_place();
let mut tmp2 = a;
tmp2.mul_assign(&a);
assert_eq!(tmp, tmp2);
}
}
#[test]
fn test_fq_inverse() {
assert!(Fq::zero().inverse().is_none());
let mut rng = ark_std::test_rng();
let one = Fq::one();
for _ in 0..1000 {
// Ensure that a * a^-1 = 1
let mut a = Fq::rand(&mut rng);
let ainv = a.inverse().unwrap();
a.mul_assign(&ainv);
assert_eq!(a, one);
}
}
#[test]
fn test_fq_double_in_place() {
let mut rng = ark_std::test_rng();
for _ in 0..1000 {
// Ensure doubling a is equivalent to adding a to itself.
let mut a = Fq::rand(&mut rng);
let mut b = a;
b.add_assign(&a);
a.double_in_place();
assert_eq!(a, b);
}
}
#[test]
fn test_fq_negate() {
{
let a = -Fq::zero();
assert!(a.is_zero());
}
let mut rng = ark_std::test_rng();
for _ in 0..1000 {
// Ensure (a - (-a)) = 0.
let mut a = Fq::rand(&mut rng);
let b = -a;
a.add_assign(&b);
assert!(a.is_zero());
}
}
#[test]
fn test_fq_pow() {
let mut rng = ark_std::test_rng();
for i in 0..1000 {
// Exponentiate by various small numbers and ensure it consists with repeated
// multiplication.
let a = Fq::rand(&mut rng);
let target = a.pow(&[i]);
let mut c = Fq::one();
for _ in 0..i {
c.mul_assign(&a);
}
assert_eq!(c, target);
}
for _ in 0..1000 {
// Exponentiating by the modulus should have no effect in a prime field.
let a = Fq::rand(&mut rng);
assert_eq!(a, a.pow(Fq::characteristic()));
}
}
#[test]
fn test_fq_sqrt() {
let mut rng = ark_std::test_rng();
assert_eq!(Fq::zero().sqrt().unwrap(), Fq::zero());
for _ in 0..1000 {
// Ensure sqrt(a^2) = a or -a
let a = Fq::rand(&mut rng);
let nega = -a;
let mut b = a;
b.square_in_place();
let b = b.sqrt().unwrap();
assert!(a == b || nega == b);
}
for _ in 0..1000 {
// Ensure sqrt(a)^2 = a for random a
let a = Fq::rand(&mut rng);
if let Some(mut tmp) = a.sqrt() {
tmp.square_in_place();
assert_eq!(a, tmp);
}
}
}
#[test]
fn test_fq_num_bits() {
assert_eq!(FqParameters::MODULUS_BITS, 254);
assert_eq!(FqParameters::CAPACITY, 253);
}
#[test]
fn test_fq_root_of_unity() {
assert_eq!(FqParameters::TWO_ADICITY, 1);
assert_eq!(
Fq::multiplicative_generator().pow([
0x9e10460b6c3e7ea3,
0xcbc0b548b438e546,
0xdc2822db40c0ac2e,
0x183227397098d014,
]),
Fq::two_adic_root_of_unity()
);
assert_eq!(
Fq::two_adic_root_of_unity().pow([1 << FqParameters::TWO_ADICITY]),
Fq::one()
);
assert!(Fq::multiplicative_generator().sqrt().is_none());
}
#[test]
fn test_fq_ordering() {
// BigInteger256's ordering is well-tested, but we still need to make sure the
// Fq elements aren't being compared in Montgomery form.
for i in 0..100 {
assert!(Fq::from(BigInteger256::from(i + 1)) > Fq::from(BigInteger256::from(i)));
}
}
#[test]
fn test_fq_legendre() {
use ark_ff::fields::LegendreSymbol::*;
assert_eq!(QuadraticResidue, Fq::one().legendre());
assert_eq!(Zero, Fq::zero().legendre());
assert_eq!(
QuadraticResidue,
Fq::from(BigInteger256::from(4)).legendre()
);
assert_eq!(
QuadraticNonResidue,
Fq::from(BigInteger256::from(5)).legendre()
);
}
#[test]
fn test_fq2_ordering() {
let mut a = Fq2::new(Fq::zero(), Fq::zero());
let mut b = a.clone();
assert!(a.cmp(&b) == Ordering::Equal);
b.c0.add_assign(&Fq::one());
assert!(a.cmp(&b) == Ordering::Less);
a.c0.add_assign(&Fq::one());
assert!(a.cmp(&b) == Ordering::Equal);
b.c1.add_assign(&Fq::one());
assert!(a.cmp(&b) == Ordering::Less);
a.c0.add_assign(&Fq::one());
assert!(a.cmp(&b) == Ordering::Less);
a.c1.add_assign(&Fq::one());
assert!(a.cmp(&b) == Ordering::Greater);
b.c0.add_assign(&Fq::one());
assert!(a.cmp(&b) == Ordering::Equal);
}
#[test]
fn test_fq2_basics() {
assert_eq!(Fq2::new(Fq::zero(), Fq::zero(),), Fq2::zero());
assert_eq!(Fq2::new(Fq::one(), Fq::zero(),), Fq2::one());
assert!(Fq2::zero().is_zero());
assert!(!Fq2::one().is_zero());
assert!(!Fq2::new(Fq::zero(), Fq::one(),).is_zero());
}
#[test]
fn test_fq2_legendre() {
use ark_ff::fields::LegendreSymbol::*;
assert_eq!(Zero, Fq2::zero().legendre());
// i^2 = -1
let mut m1 = -Fq2::one();
assert_eq!(QuadraticResidue, m1.legendre());
m1 = Fq6Parameters::mul_fp2_by_nonresidue(&m1);
assert_eq!(QuadraticNonResidue, m1.legendre());
}
#[test]
fn test_fq6_mul_by_1() {
let mut rng = ark_std::test_rng();
for _ in 0..1000 {
let c1 = Fq2::rand(&mut rng);
let mut a = Fq6::rand(&mut rng);
let mut b = a;
a.mul_by_1(&c1);
b.mul_assign(&Fq6::new(Fq2::zero(), c1, Fq2::zero()));
assert_eq!(a, b);
}
}
#[test]
fn test_fq6_mul_by_01() {
let mut rng = ark_std::test_rng();
for _ in 0..1000 {
let c0 = Fq2::rand(&mut rng);
let c1 = Fq2::rand(&mut rng);
let mut a = Fq6::rand(&mut rng);
let mut b = a;
a.mul_by_01(&c0, &c1);
b.mul_assign(&Fq6::new(c0, c1, Fq2::zero()));
assert_eq!(a, b);
}
}
#[test]
fn test_fq12_mul_by_014() {
let mut rng = ark_std::test_rng();
for _ in 0..1000 {
let c0 = Fq2::rand(&mut rng);
let c1 = Fq2::rand(&mut rng);
let c5 = Fq2::rand(&mut rng);
let mut a = Fq12::rand(&mut rng);
let mut b = a;
a.mul_by_014(&c0, &c1, &c5);
b.mul_assign(&Fq12::new(
Fq6::new(c0, c1, Fq2::zero()),
Fq6::new(Fq2::zero(), c5, Fq2::zero()),
));
assert_eq!(a, b);
}
}
#[test]
fn test_fq12_mul_by_034() {
let mut rng = ark_std::test_rng();
for _ in 0..1000 {
let c0 = Fq2::rand(&mut rng);
let c3 = Fq2::rand(&mut rng);
let c4 = Fq2::rand(&mut rng);
let mut a = Fq12::rand(&mut rng);
let mut b = a;
a.mul_by_034(&c0, &c3, &c4);
b.mul_assign(&Fq12::new(
Fq6::new(c0, Fq2::zero(), Fq2::zero()),
Fq6::new(c3, c4, Fq2::zero()),
));
assert_eq!(a, b);
}
}
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