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jubjub
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jubjub/src/fr.rs

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use core::fmt;
use core::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
use byteorder::{ByteOrder, LittleEndian};
use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
use crate::util::{adc, mac, sbb};
/// Represents an element of `GF(r)`.
// The internal representation of this type is four 64-bit unsigned
// integers in little-endian order. Elements of Fr are always in
// Montgomery form; i.e., Fr(a) = aR mod r, with R = 2^256.
#[derive(Clone, Copy, Eq)]
pub struct Fr(pub(crate) [u64; 4]);
impl fmt::Debug for Fr {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
let tmp = self.to_bytes();
write!(f, "0x")?;
for &b in tmp.iter().rev() {
write!(f, "{:02x}", b)?;
}
Ok(())
}
}
impl From<u64> for Fr {
fn from(val: u64) -> Fr {
Fr([val, 0, 0, 0]) * R2
}
}
impl ConstantTimeEq for Fr {
fn ct_eq(&self, other: &Self) -> Choice {
self.0[0].ct_eq(&other.0[0])
& self.0[1].ct_eq(&other.0[1])
& self.0[2].ct_eq(&other.0[2])
& self.0[3].ct_eq(&other.0[3])
}
}
impl PartialEq for Fr {
fn eq(&self, other: &Self) -> bool {
self.ct_eq(other).unwrap_u8() == 1
}
}
impl ConditionallySelectable for Fr {
fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
Fr([
u64::conditional_select(&a.0[0], &b.0[0], choice),
u64::conditional_select(&a.0[1], &b.0[1], choice),
u64::conditional_select(&a.0[2], &b.0[2], choice),
u64::conditional_select(&a.0[3], &b.0[3], choice),
])
}
}
/// Constant representing the modulus
/// r = 0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7
pub const MODULUS: Fr = Fr([
0xd0970e5ed6f72cb7,
0xa6682093ccc81082,
0x06673b0101343b00,
0x0e7db4ea6533afa9,
]);
impl<'a> Neg for &'a Fr {
type Output = Fr;
#[inline]
fn neg(self) -> Fr {
// Subtract `self` from `MODULUS` to negate. Ignore the final
// borrow because it cannot underflow; self is guaranteed to
// be in the field.
let (d0, borrow) = sbb(MODULUS.0[0], self.0[0], 0);
let (d1, borrow) = sbb(MODULUS.0[1], self.0[1], borrow);
let (d2, borrow) = sbb(MODULUS.0[2], self.0[2], borrow);
let (d3, _) = sbb(MODULUS.0[3], self.0[3], borrow);
// `tmp` could be `MODULUS` if `self` was zero. Create a mask that is
// zero if `self` was zero, and `u64::max_value()` if self was nonzero.
let mask = u64::from((self.0[0] | self.0[1] | self.0[2] | self.0[3]) == 0).wrapping_sub(1);
Fr([d0 & mask, d1 & mask, d2 & mask, d3 & mask])
}
}
impl Neg for Fr {
type Output = Fr;
#[inline]
fn neg(self) -> Fr {
-&self
}
}
impl<'a, 'b> Sub<&'b Fr> for &'a Fr {
type Output = Fr;
#[inline]
fn sub(self, rhs: &'b Fr) -> Fr {
self.subtract(rhs)
}
}
impl<'a, 'b> Add<&'b Fr> for &'a Fr {
type Output = Fr;
#[inline]
fn add(self, rhs: &'b Fr) -> Fr {
let (d0, carry) = adc(self.0[0], rhs.0[0], 0);
let (d1, carry) = adc(self.0[1], rhs.0[1], carry);
let (d2, carry) = adc(self.0[2], rhs.0[2], carry);
let (d3, _) = adc(self.0[3], rhs.0[3], carry);
// Attempt to subtract the modulus, to ensure the value
// is smaller than the modulus.
Fr([d0, d1, d2, d3]) - &MODULUS
}
}
impl<'a, 'b> Mul<&'b Fr> for &'a Fr {
type Output = Fr;
#[inline]
fn mul(self, rhs: &'b Fr) -> Fr {
// Schoolbook multiplication
self.multiply(rhs)
}
}
impl_binops_additive!(Fr, Fr);
impl_binops_multiplicative!(Fr, Fr);
/// INV = -(r^{-1} mod 2^64) mod 2^64
const INV: u64 = 0x1ba3a358ef788ef9;
/// R = 2^256 mod r
const R: Fr = Fr([
0x25f80bb3b99607d9,
0xf315d62f66b6e750,
0x932514eeeb8814f4,
0x09a6fc6f479155c6,
]);
/// R^2 = 2^512 mod r
const R2: Fr = Fr([
0x67719aa495e57731,
0x51b0cef09ce3fc26,
0x69dab7fac026e9a5,
0x04f6547b8d127688,
]);
/// R^2 = 2^768 mod r
const R3: Fr = Fr([
0xe0d6c6563d830544,
0x323e3883598d0f85,
0xf0fea3004c2e2ba8,
0x05874f84946737ec,
]);
impl Default for Fr {
fn default() -> Self {
Self::zero()
}
}
impl Fr {
/// Returns zero, the additive identity.
#[inline]
pub fn zero() -> Fr {
Fr([0, 0, 0, 0])
}
/// Returns one, the multiplicative identity.
#[inline]
pub fn one() -> Fr {
R
}
/// Doubles this field element.
#[inline]
pub fn double(&self) -> Fr {
self + self
}
/// Attempts to convert a little-endian byte representation of
/// a field element into an element of `Fr`, failing if the input
/// is not canonical (is not smaller than r).
pub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Fr> {
let mut tmp = Fr([0, 0, 0, 0]);
tmp.0[0] = LittleEndian::read_u64(&bytes[0..8]);
tmp.0[1] = LittleEndian::read_u64(&bytes[8..16]);
tmp.0[2] = LittleEndian::read_u64(&bytes[16..24]);
tmp.0[3] = LittleEndian::read_u64(&bytes[24..32]);
// Try to subtract the modulus
let (_, borrow) = sbb(tmp.0[0], MODULUS.0[0], 0);
let (_, borrow) = sbb(tmp.0[1], MODULUS.0[1], borrow);
let (_, borrow) = sbb(tmp.0[2], MODULUS.0[2], borrow);
let (_, borrow) = sbb(tmp.0[3], MODULUS.0[3], borrow);
// If the element is smaller than MODULUS then the
// subtraction will underflow, producing a borrow value
// of 0xffff...ffff. Otherwise, it'll be zero.
let is_some = (borrow as u8) & 1;
// Convert to Montgomery form by computing
// (a.R^0 * R^2) / R = a.R
tmp *= &R2;
CtOption::new(tmp, Choice::from(is_some))
}
/// Converts an element of `Fr` into a byte representation in
/// little-endian byte order.
pub fn to_bytes(&self) -> [u8; 32] {
// Turn into canonical form by computing
// (a.R) / R = a
let tmp = Fr::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);
let mut res = [0; 32];
LittleEndian::write_u64(&mut res[0..8], tmp.0[0]);
LittleEndian::write_u64(&mut res[8..16], tmp.0[1]);
LittleEndian::write_u64(&mut res[16..24], tmp.0[2]);
LittleEndian::write_u64(&mut res[24..32], tmp.0[3]);
res
}
/// Converts a 512-bit little endian integer into
/// an element of Fr by reducing modulo r.
pub fn from_bytes_wide(bytes: &[u8; 64]) -> Fr {
Fr::from_u512([
LittleEndian::read_u64(&bytes[0..8]),
LittleEndian::read_u64(&bytes[8..16]),
LittleEndian::read_u64(&bytes[16..24]),
LittleEndian::read_u64(&bytes[24..32]),
LittleEndian::read_u64(&bytes[32..40]),
LittleEndian::read_u64(&bytes[40..48]),
LittleEndian::read_u64(&bytes[48..56]),
LittleEndian::read_u64(&bytes[56..64]),
])
}
fn from_u512(limbs: [u64; 8]) -> Fr {
// We reduce an arbitrary 512-bit number by decomposing it into two 256-bit digits
// with the higher bits multiplied by 2^256. Thus, we perform two reductions
//
// 1. the lower bits are multiplied by R^2, as normal
// 2. the upper bits are multiplied by R^2 * 2^256 = R^3
//
// and computing their sum in the field. It remains to see that arbitrary 256-bit
// numbers can be placed into Montgomery form safely using the reduction. The
// reduction works so long as the product is less than R=2^256 multipled by
// the modulus. This holds because for any `c` smaller than the modulus, we have
// that (2^256 - 1)*c is an acceptable product for the reduction. Therefore, the
// reduction always works so long as `c` is in the field; in this case it is either the
// constant `R2` or `R3`.
let d0 = Fr([limbs[0], limbs[1], limbs[2], limbs[3]]);
let d1 = Fr([limbs[4], limbs[5], limbs[6], limbs[7]]);
// Convert to Montgomery form
d0 * R2 + d1 * R3
}
/// Converts from an integer represented in little endian
/// into its (congruent) representation in Fr.
pub const fn from_raw(val: [u64; 4]) -> Self {
Fr(val).multiply(&R2)
}
/// Squares this element.
#[inline]
pub const fn square(&self) -> Fr {
let (r1, carry) = mac(0, self.0[0], self.0[1], 0);
let (r2, carry) = mac(0, self.0[0], self.0[2], carry);
let (r3, r4) = mac(0, self.0[0], self.0[3], carry);
let (r3, carry) = mac(r3, self.0[1], self.0[2], 0);
let (r4, r5) = mac(r4, self.0[1], self.0[3], carry);
let (r5, r6) = mac(r5, self.0[2], self.0[3], 0);
let r7 = r6 >> 63;
let r6 = (r6 << 1) | (r5 >> 63);
let r5 = (r5 << 1) | (r4 >> 63);
let r4 = (r4 << 1) | (r3 >> 63);
let r3 = (r3 << 1) | (r2 >> 63);
let r2 = (r2 << 1) | (r1 >> 63);
let r1 = r1 << 1;
let (r0, carry) = mac(0, self.0[0], self.0[0], 0);
let (r1, carry) = adc(0, r1, carry);
let (r2, carry) = mac(r2, self.0[1], self.0[1], carry);
let (r3, carry) = adc(0, r3, carry);
let (r4, carry) = mac(r4, self.0[2], self.0[2], carry);
let (r5, carry) = adc(0, r5, carry);
let (r6, carry) = mac(r6, self.0[3], self.0[3], carry);
let (r7, _) = adc(0, r7, carry);
Fr::montgomery_reduce(r0, r1, r2, r3, r4, r5, r6, r7)
}
/// Computes the square root of this element, if it exists.
pub fn sqrt(&self) -> CtOption<Self> {
// Because r = 3 (mod 4)
// sqrt can be done with only one exponentiation,
// via the computation of self^((r + 1) // 4) (mod r)
let sqrt = self.pow_vartime(&[
0xb425c397b5bdcb2e,
0x299a0824f3320420,
0x4199cec0404d0ec0,
0x039f6d3a994cebea,
]);
CtOption::new(
sqrt,
(&sqrt * &sqrt).ct_eq(self), // Only return Some if it's the square root.
)
}
/// Exponentiates `self` by `by`, where `by` is a
/// little-endian order integer exponent.
pub fn pow(&self, by: &[u64; 4]) -> Self {
let mut res = Self::one();
for e in by.iter().rev() {
for i in (0..64).rev() {
res = res.square();
let mut tmp = res;
tmp.mul_assign(self);
res.conditional_assign(&tmp, (((*e >> i) & 0x1) as u8).into());
}
}
res
}
/// Exponentiates `self` by `by`, where `by` is a
/// little-endian order integer exponent.
///
/// **This operation is variable time with respect
/// to the exponent.** If the exponent is fixed,
/// this operation is effectively constant time.
pub fn pow_vartime(&self, by: &[u64; 4]) -> Self {
let mut res = Self::one();
for e in by.iter().rev() {
for i in (0..64).rev() {
res = res.square();
if ((*e >> i) & 1) == 1 {
res.mul_assign(self);
}
}
}
res
}
/// Computes the multiplicative inverse of this element,
/// failing if the element is zero.
pub fn invert(&self) -> CtOption<Self> {
#[inline(always)]
fn square_assign_multi(n: &mut Fr, num_times: usize) {
for _ in 0..num_times {
*n = n.square();
}
}
// found using https://github.com/kwantam/addchain
let mut t1 = self.square();
let mut t0 = t1.square();
let mut t3 = t0 * &t1;
let t6 = t3 * self;
let t7 = t6 * &t1;
let t12 = t7 * &t3;
let t13 = t12 * &t0;
let t16 = t12 * &t3;
let t2 = t13 * &t3;
let t15 = t16 * &t3;
let t19 = t2 * &t0;
let t9 = t15 * &t3;
let t18 = t9 * &t3;
let t14 = t18 * &t1;
let t4 = t18 * &t0;
let t8 = t18 * &t3;
let t17 = t14 * &t3;
let t11 = t8 * &t3;
t1 = t17 * &t3;
let t5 = t11 * &t3;
t3 = t5 * &t0;
t0 = t5.square();
square_assign_multi(&mut t0, 5);
t0.mul_assign(&t3);
square_assign_multi(&mut t0, 6);
t0.mul_assign(&t8);
square_assign_multi(&mut t0, 7);
t0.mul_assign(&t19);
square_assign_multi(&mut t0, 6);
t0.mul_assign(&t13);
square_assign_multi(&mut t0, 8);
t0.mul_assign(&t14);
square_assign_multi(&mut t0, 6);
t0.mul_assign(&t18);
square_assign_multi(&mut t0, 7);
t0.mul_assign(&t17);
square_assign_multi(&mut t0, 5);
t0.mul_assign(&t16);
square_assign_multi(&mut t0, 3);
t0.mul_assign(self);
square_assign_multi(&mut t0, 11);
t0.mul_assign(&t11);
square_assign_multi(&mut t0, 8);
t0.mul_assign(&t5);
square_assign_multi(&mut t0, 5);
t0.mul_assign(&t15);
square_assign_multi(&mut t0, 8);
t0.mul_assign(self);
square_assign_multi(&mut t0, 12);
t0.mul_assign(&t13);
square_assign_multi(&mut t0, 7);
t0.mul_assign(&t9);
square_assign_multi(&mut t0, 5);
t0.mul_assign(&t15);
square_assign_multi(&mut t0, 14);
t0.mul_assign(&t14);
square_assign_multi(&mut t0, 5);
t0.mul_assign(&t13);
square_assign_multi(&mut t0, 2);
t0.mul_assign(self);
square_assign_multi(&mut t0, 6);
t0.mul_assign(self);
square_assign_multi(&mut t0, 9);
t0.mul_assign(&t7);
square_assign_multi(&mut t0, 6);
t0.mul_assign(&t12);
square_assign_multi(&mut t0, 8);
t0.mul_assign(&t11);
square_assign_multi(&mut t0, 3);
t0.mul_assign(self);
square_assign_multi(&mut t0, 12);
t0.mul_assign(&t9);
square_assign_multi(&mut t0, 11);
t0.mul_assign(&t8);
square_assign_multi(&mut t0, 8);
t0.mul_assign(&t7);
square_assign_multi(&mut t0, 4);
t0.mul_assign(&t6);
square_assign_multi(&mut t0, 10);
t0.mul_assign(&t5);
square_assign_multi(&mut t0, 7);
t0.mul_assign(&t3);
square_assign_multi(&mut t0, 6);
t0.mul_assign(&t4);
square_assign_multi(&mut t0, 7);
t0.mul_assign(&t3);
square_assign_multi(&mut t0, 5);
t0.mul_assign(&t2);
square_assign_multi(&mut t0, 6);
t0.mul_assign(&t2);
square_assign_multi(&mut t0, 7);
t0.mul_assign(&t1);
CtOption::new(t0, !self.ct_eq(&Self::zero()))
}
#[inline]
const fn montgomery_reduce(
r0: u64,
r1: u64,
r2: u64,
r3: u64,
r4: u64,
r5: u64,
r6: u64,
r7: u64,
) -> Self {
// The Montgomery reduction here is based on Algorithm 14.32 in
// Handbook of Applied Cryptography
// <http://cacr.uwaterloo.ca/hac/about/chap14.pdf>.
let k = r0.wrapping_mul(INV);
let (_, carry) = mac(r0, k, MODULUS.0[0], 0);
let (r1, carry) = mac(r1, k, MODULUS.0[1], carry);
let (r2, carry) = mac(r2, k, MODULUS.0[2], carry);
let (r3, carry) = mac(r3, k, MODULUS.0[3], carry);
let (r4, carry2) = adc(r4, 0, carry);
let k = r1.wrapping_mul(INV);
let (_, carry) = mac(r1, k, MODULUS.0[0], 0);
let (r2, carry) = mac(r2, k, MODULUS.0[1], carry);
let (r3, carry) = mac(r3, k, MODULUS.0[2], carry);
let (r4, carry) = mac(r4, k, MODULUS.0[3], carry);
let (r5, carry2) = adc(r5, carry2, carry);
let k = r2.wrapping_mul(INV);
let (_, carry) = mac(r2, k, MODULUS.0[0], 0);
let (r3, carry) = mac(r3, k, MODULUS.0[1], carry);
let (r4, carry) = mac(r4, k, MODULUS.0[2], carry);
let (r5, carry) = mac(r5, k, MODULUS.0[3], carry);
let (r6, carry2) = adc(r6, carry2, carry);
let k = r3.wrapping_mul(INV);
let (_, carry) = mac(r3, k, MODULUS.0[0], 0);
let (r4, carry) = mac(r4, k, MODULUS.0[1], carry);
let (r5, carry) = mac(r5, k, MODULUS.0[2], carry);
let (r6, carry) = mac(r6, k, MODULUS.0[3], carry);
let (r7, _) = adc(r7, carry2, carry);
// Result may be within MODULUS of the correct value
Fr([r4, r5, r6, r7]).subtract(&MODULUS)
}
#[inline]
const fn multiply(&self, rhs: &Self) -> Self {
// Schoolbook multiplication
let (r0, carry) = mac(0, self.0[0], rhs.0[0], 0);
let (r1, carry) = mac(0, self.0[0], rhs.0[1], carry);
let (r2, carry) = mac(0, self.0[0], rhs.0[2], carry);
let (r3, r4) = mac(0, self.0[0], rhs.0[3], carry);
let (r1, carry) = mac(r1, self.0[1], rhs.0[0], 0);
let (r2, carry) = mac(r2, self.0[1], rhs.0[1], carry);
let (r3, carry) = mac(r3, self.0[1], rhs.0[2], carry);
let (r4, r5) = mac(r4, self.0[1], rhs.0[3], carry);
let (r2, carry) = mac(r2, self.0[2], rhs.0[0], 0);
let (r3, carry) = mac(r3, self.0[2], rhs.0[1], carry);
let (r4, carry) = mac(r4, self.0[2], rhs.0[2], carry);
let (r5, r6) = mac(r5, self.0[2], rhs.0[3], carry);
let (r3, carry) = mac(r3, self.0[3], rhs.0[0], 0);
let (r4, carry) = mac(r4, self.0[3], rhs.0[1], carry);
let (r5, carry) = mac(r5, self.0[3], rhs.0[2], carry);
let (r6, r7) = mac(r6, self.0[3], rhs.0[3], carry);
Fr::montgomery_reduce(r0, r1, r2, r3, r4, r5, r6, r7)
}
#[inline]
const fn subtract(&self, rhs: &Self) -> Self {
let (d0, borrow) = sbb(self.0[0], rhs.0[0], 0);
let (d1, borrow) = sbb(self.0[1], rhs.0[1], borrow);
let (d2, borrow) = sbb(self.0[2], rhs.0[2], borrow);
let (d3, borrow) = sbb(self.0[3], rhs.0[3], borrow);
// If underflow occurred on the final limb, borrow = 0xfff...fff, otherwise
// borrow = 0x000...000. Thus, we use it as a mask to conditionally add the modulus.
let (d0, carry) = adc(d0, MODULUS.0[0] & borrow, 0);
let (d1, carry) = adc(d1, MODULUS.0[1] & borrow, carry);
let (d2, carry) = adc(d2, MODULUS.0[2] & borrow, carry);
let (d3, _) = adc(d3, MODULUS.0[3] & borrow, carry);
Fr([d0, d1, d2, d3])
}
}
impl<'a> From<&'a Fr> for [u8; 32] {
fn from(value: &'a Fr) -> [u8; 32] {
value.to_bytes()
}
}
#[test]
fn test_inv() {
// Compute -(r^{-1} mod 2^64) mod 2^64 by exponentiating
// by totient(2**64) - 1
let mut inv = 1u64;
for _ in 0..63 {
inv = inv.wrapping_mul(inv);
inv = inv.wrapping_mul(MODULUS.0[0]);
}
inv = inv.wrapping_neg();
assert_eq!(inv, INV);
}
#[cfg(feature = "std")]
#[test]
fn test_debug() {
assert_eq!(
format!("{:?}", Fr::zero()),
"0x0000000000000000000000000000000000000000000000000000000000000000"
);
assert_eq!(
format!("{:?}", Fr::one()),
"0x0000000000000000000000000000000000000000000000000000000000000001"
);
assert_eq!(
format!("{:?}", R2),
"0x09a6fc6f479155c6932514eeeb8814f4f315d62f66b6e75025f80bb3b99607d9"
);
}
#[test]
fn test_equality() {
assert_eq!(Fr::zero(), Fr::zero());
assert_eq!(Fr::one(), Fr::one());
assert_eq!(R2, R2);
assert!(Fr::zero() != Fr::one());
assert!(Fr::one() != R2);
}
#[test]
fn test_to_bytes() {
assert_eq!(
Fr::zero().to_bytes(),
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0
]
);
assert_eq!(
Fr::one().to_bytes(),
[
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0
]
);
assert_eq!(
R2.to_bytes(),
[
217, 7, 150, 185, 179, 11, 248, 37, 80, 231, 182, 102, 47, 214, 21, 243, 244, 20, 136,
235, 238, 20, 37, 147, 198, 85, 145, 71, 111, 252, 166, 9
]
);
assert_eq!(
(-&Fr::one()).to_bytes(),
[
182, 44, 247, 214, 94, 14, 151, 208, 130, 16, 200, 204, 147, 32, 104, 166, 0, 59, 52,
1, 1, 59, 103, 6, 169, 175, 51, 101, 234, 180, 125, 14
]
);
}
#[test]
fn test_from_bytes() {
assert_eq!(
Fr::from_bytes(&[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0
])
.unwrap(),
Fr::zero()
);
assert_eq!(
Fr::from_bytes(&[
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0
])
.unwrap(),
Fr::one()
);
assert_eq!(
Fr::from_bytes(&[
217, 7, 150, 185, 179, 11, 248, 37, 80, 231, 182, 102, 47, 214, 21, 243, 244, 20, 136,
235, 238, 20, 37, 147, 198, 85, 145, 71, 111, 252, 166, 9
])
.unwrap(),
R2
);
// -1 should work
assert!(
Fr::from_bytes(&[
182, 44, 247, 214, 94, 14, 151, 208, 130, 16, 200, 204, 147, 32, 104, 166, 0, 59, 52,
1, 1, 59, 103, 6, 169, 175, 51, 101, 234, 180, 125, 14
])
.is_some()
.unwrap_u8()
== 1
);
// modulus is invalid
assert!(
Fr::from_bytes(&[
183, 44, 247, 214, 94, 14, 151, 208, 130, 16, 200, 204, 147, 32, 104, 166, 0, 59, 52,
1, 1, 59, 103, 6, 169, 175, 51, 101, 234, 180, 125, 14
])
.is_none()
.unwrap_u8()
== 1
);
// Anything larger than the modulus is invalid
assert!(
Fr::from_bytes(&[
184, 44, 247, 214, 94, 14, 151, 208, 130, 16, 200, 204, 147, 32, 104, 166, 0, 59, 52,
1, 1, 59, 103, 6, 169, 175, 51, 101, 234, 180, 125, 14
])
.is_none()
.unwrap_u8()
== 1
);
assert!(
Fr::from_bytes(&[
183, 44, 247, 214, 94, 14, 151, 208, 130, 16, 200, 204, 147, 32, 104, 166, 0, 59, 52,
1, 1, 59, 104, 6, 169, 175, 51, 101, 234, 180, 125, 14
])
.is_none()
.unwrap_u8()
== 1
);
assert!(
Fr::from_bytes(&[
183, 44, 247, 214, 94, 14, 151, 208, 130, 16, 200, 204, 147, 32, 104, 166, 0, 59, 52,
1, 1, 59, 103, 6, 169, 175, 51, 101, 234, 180, 125, 15
])
.is_none()
.unwrap_u8()
== 1
);
}
#[test]
fn test_from_u512_zero() {
assert_eq!(
Fr::zero(),
Fr::from_u512([
MODULUS.0[0],
MODULUS.0[1],
MODULUS.0[2],
MODULUS.0[3],
0,
0,
0,
0
])
);
}
#[test]
fn test_from_u512_r() {
assert_eq!(R, Fr::from_u512([1, 0, 0, 0, 0, 0, 0, 0]));
}
#[test]
fn test_from_u512_r2() {
assert_eq!(R2, Fr::from_u512([0, 0, 0, 0, 1, 0, 0, 0]));
}
#[test]
fn test_from_u512_max() {
let max_u64 = 0xffffffffffffffff;
assert_eq!(
R3 - R,
Fr::from_u512([max_u64, max_u64, max_u64, max_u64, max_u64, max_u64, max_u64, max_u64])
);
}
#[test]
fn test_from_bytes_wide_r2() {
assert_eq!(
R2,
Fr::from_bytes_wide(&[
217, 7, 150, 185, 179, 11, 248, 37, 80, 231, 182, 102, 47, 214, 21, 243, 244, 20, 136,
235, 238, 20, 37, 147, 198, 85, 145, 71, 111, 252, 166, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
])
);
}
#[test]
fn test_from_bytes_wide_negative_one() {
assert_eq!(
-&Fr::one(),
Fr::from_bytes_wide(&[
182, 44, 247, 214, 94, 14, 151, 208, 130, 16, 200, 204, 147, 32, 104, 166, 0, 59, 52,
1, 1, 59, 103, 6, 169, 175, 51, 101, 234, 180, 125, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
])
);
}
#[test]
fn test_from_bytes_wide_maximum() {
assert_eq!(
Fr([
0x8b75c9015ae42a22,
0xe59082e7bf9e38b8,
0x6440c91261da51b3,
0xa5e07ffb20991cf
]),
Fr::from_bytes_wide(&[0xff; 64])
);
}
#[test]
fn test_zero() {
assert_eq!(Fr::zero(), -&Fr::zero());
assert_eq!(Fr::zero(), Fr::zero() + Fr::zero());
assert_eq!(Fr::zero(), Fr::zero() - Fr::zero());
assert_eq!(Fr::zero(), Fr::zero() * Fr::zero());
}
#[cfg(test)]
const LARGEST: Fr = Fr([
0xd0970e5ed6f72cb6,
0xa6682093ccc81082,
0x06673b0101343b00,
0x0e7db4ea6533afa9,
]);
#[test]
fn test_addition() {
let mut tmp = LARGEST;
tmp += &LARGEST;
assert_eq!(
tmp,
Fr([
0xd0970e5ed6f72cb5,
0xa6682093ccc81082,
0x06673b0101343b00,
0x0e7db4ea6533afa9
])
);
let mut tmp = LARGEST;
tmp += &Fr([1, 0, 0, 0]);
assert_eq!(tmp, Fr::zero());
}
#[test]
fn test_negation() {
let tmp = -&LARGEST;
assert_eq!(tmp, Fr([1, 0, 0, 0]));
let tmp = -&Fr::zero();
assert_eq!(tmp, Fr::zero());
let tmp = -&Fr([1, 0, 0, 0]);
assert_eq!(tmp, LARGEST);
}
#[test]
fn test_subtraction() {
let mut tmp = LARGEST;
tmp -= &LARGEST;
assert_eq!(tmp, Fr::zero());
let mut tmp = Fr::zero();
tmp -= &LARGEST;
let mut tmp2 = MODULUS;
tmp2 -= &LARGEST;
assert_eq!(tmp, tmp2);
}
#[test]
fn test_multiplication() {
let mut cur = LARGEST;
for _ in 0..100 {
let mut tmp = cur;
tmp *= &cur;
let mut tmp2 = Fr::zero();
for b in cur
.to_bytes()
.iter()
.rev()
.flat_map(|byte| (0..8).rev().map(move |i| ((byte >> i) & 1u8) == 1u8))
{
let tmp3 = tmp2;
tmp2.add_assign(&tmp3);
if b {
tmp2.add_assign(&cur);
}
}
assert_eq!(tmp, tmp2);
cur.add_assign(&LARGEST);
}
}
#[test]
fn test_squaring() {
let mut cur = LARGEST;
for _ in 0..100 {
let mut tmp = cur;
tmp = tmp.square();
let mut tmp2 = Fr::zero();
for b in cur
.to_bytes()
.iter()
.rev()
.flat_map(|byte| (0..8).rev().map(move |i| ((byte >> i) & 1u8) == 1u8))
{
let tmp3 = tmp2;
tmp2.add_assign(&tmp3);
if b {
tmp2.add_assign(&cur);
}
}
assert_eq!(tmp, tmp2);
cur.add_assign(&LARGEST);
}
}
#[test]
fn test_inversion() {
assert_eq!(Fr::zero().invert().is_none().unwrap_u8(), 1);
assert_eq!(Fr::one().invert().unwrap(), Fr::one());
assert_eq!((-&Fr::one()).invert().unwrap(), -&Fr::one());
let mut tmp = R2;
for _ in 0..100 {
let mut tmp2 = tmp.invert().unwrap();
tmp2.mul_assign(&tmp);
assert_eq!(tmp2, Fr::one());
tmp.add_assign(&R2);
}
}
#[test]
fn test_invert_is_pow() {
let r_minus_2 = [
0xd0970e5ed6f72cb5,
0xa6682093ccc81082,
0x06673b0101343b00,
0x0e7db4ea6533afa9,
];
let mut r1 = R;
let mut r2 = R;
let mut r3 = R;
for _ in 0..100 {
r1 = r1.invert().unwrap();
r2 = r2.pow_vartime(&r_minus_2);
r3 = r3.pow(&r_minus_2);
assert_eq!(r1, r2);
assert_eq!(r2, r3);
// Add R so we check something different next time around
r1.add_assign(&R);
r2 = r1;
r3 = r1;
}
}
#[test]
fn test_sqrt() {
let mut square = Fr([
// r - 2
0xd0970e5ed6f72cb5,
0xa6682093ccc81082,
0x06673b0101343b00,
0x0e7db4ea6533afa9,
]);
let mut none_count = 0;
for _ in 0..100 {
let square_root = square.sqrt();
if square_root.is_none().unwrap_u8() == 1 {
none_count += 1;
} else {
assert_eq!(square_root.unwrap() * square_root.unwrap(), square);
}
square -= Fr::one();
}
assert_eq!(47, none_count);
}
#[test]
fn test_from_raw() {
assert_eq!(
Fr::from_raw([
0x25f80bb3b99607d8,
0xf315d62f66b6e750,
0x932514eeeb8814f4,
0x9a6fc6f479155c6
]),
Fr::from_raw([0xffffffffffffffff; 4])
);
assert_eq!(Fr::from_raw(MODULUS.0), Fr::zero());
assert_eq!(Fr::from_raw([1, 0, 0, 0]), R);
}
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