mirror of
https://github.com/Qortal/pirate-librustzcash.git
synced 2025-07-30 03:51:22 +00:00
1718 lines
42 KiB
Rust
1718 lines
42 KiB
Rust
use byteorder::{ByteOrder, LittleEndian};
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use ff::{
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adc, mac_with_carry, sbb, BitIterator, Field,
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LegendreSymbol::{self, *},
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PrimeField, PrimeFieldDecodingError, PrimeFieldRepr, SqrtField,
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};
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use rand_core::RngCore;
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use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
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use super::ToUniform;
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// s = 6554484396890773809930967563523245729705921265872317281365359162392183254199
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const MODULUS: FsRepr = FsRepr([
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0xd0970e5ed6f72cb7,
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0xa6682093ccc81082,
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0x6673b0101343b00,
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0xe7db4ea6533afa9,
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]);
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// The number of bits needed to represent the modulus.
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const MODULUS_BITS: u32 = 252;
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// The number of bits that must be shaved from the beginning of
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// the representation when randomly sampling.
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const REPR_SHAVE_BITS: u32 = 4;
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// R = 2**256 % s
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const R: FsRepr = FsRepr([
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0x25f80bb3b99607d9,
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0xf315d62f66b6e750,
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0x932514eeeb8814f4,
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0x9a6fc6f479155c6,
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]);
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// R2 = R^2 % s
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const R2: FsRepr = FsRepr([
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0x67719aa495e57731,
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0x51b0cef09ce3fc26,
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0x69dab7fac026e9a5,
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0x4f6547b8d127688,
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]);
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// INV = -(s^{-1} mod 2^64) mod s
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const INV: u64 = 0x1ba3a358ef788ef9;
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// GENERATOR = 6 (multiplicative generator of r-1 order, that is also quadratic nonresidue)
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const GENERATOR: FsRepr = FsRepr([
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0x720b1b19d49ea8f1,
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0xbf4aa36101f13a58,
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0x5fa8cc968193ccbb,
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0xe70cbdc7dccf3ac,
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]);
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// 2^S * t = MODULUS - 1 with t odd
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const S: u32 = 1;
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// 2^S root of unity computed by GENERATOR^t
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const ROOT_OF_UNITY: FsRepr = FsRepr([
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0xaa9f02ab1d6124de,
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0xb3524a6466112932,
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0x7342261215ac260b,
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0x4d6b87b1da259e2,
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]);
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// -((2**256) mod s) mod s
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const NEGATIVE_ONE: Fs = Fs(FsRepr([
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0xaa9f02ab1d6124de,
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0xb3524a6466112932,
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0x7342261215ac260b,
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0x4d6b87b1da259e2,
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]));
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/// This is the underlying representation of an element of `Fs`.
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#[derive(Copy, Clone, PartialEq, Eq, Default, Debug)]
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pub struct FsRepr(pub [u64; 4]);
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impl ::std::fmt::Display for FsRepr {
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fn fmt(&self, f: &mut ::std::fmt::Formatter<'_>) -> ::std::fmt::Result {
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write!(f, "0x")?;
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for i in self.0.iter().rev() {
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write!(f, "{:016x}", *i)?;
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}
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Ok(())
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}
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}
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impl AsRef<[u64]> for FsRepr {
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#[inline(always)]
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fn as_ref(&self) -> &[u64] {
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&self.0
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}
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}
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impl AsMut<[u64]> for FsRepr {
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#[inline(always)]
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fn as_mut(&mut self) -> &mut [u64] {
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&mut self.0
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}
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}
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impl From<u64> for FsRepr {
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#[inline(always)]
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fn from(val: u64) -> FsRepr {
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let mut repr = Self::default();
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repr.0[0] = val;
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repr
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}
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}
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impl Ord for FsRepr {
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#[inline(always)]
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fn cmp(&self, other: &FsRepr) -> ::std::cmp::Ordering {
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for (a, b) in self.0.iter().rev().zip(other.0.iter().rev()) {
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if a < b {
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return ::std::cmp::Ordering::Less;
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} else if a > b {
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return ::std::cmp::Ordering::Greater;
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}
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}
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::std::cmp::Ordering::Equal
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}
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}
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impl PartialOrd for FsRepr {
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#[inline(always)]
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fn partial_cmp(&self, other: &FsRepr) -> Option<::std::cmp::Ordering> {
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Some(self.cmp(other))
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}
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}
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impl PrimeFieldRepr for FsRepr {
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#[inline(always)]
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fn is_odd(&self) -> bool {
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self.0[0] & 1 == 1
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}
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#[inline(always)]
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fn is_even(&self) -> bool {
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!self.is_odd()
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}
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#[inline(always)]
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fn is_zero(&self) -> bool {
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self.0.iter().all(|&e| e == 0)
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}
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#[inline(always)]
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fn shr(&mut self, mut n: u32) {
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if n >= 64 * 4 {
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*self = Self::from(0);
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return;
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}
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while n >= 64 {
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let mut t = 0;
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for i in self.0.iter_mut().rev() {
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::std::mem::swap(&mut t, i);
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}
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n -= 64;
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}
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if n > 0 {
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let mut t = 0;
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for i in self.0.iter_mut().rev() {
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let t2 = *i << (64 - n);
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*i >>= n;
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*i |= t;
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t = t2;
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}
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}
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}
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#[inline(always)]
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fn div2(&mut self) {
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let mut t = 0;
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for i in self.0.iter_mut().rev() {
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let t2 = *i << 63;
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*i >>= 1;
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*i |= t;
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t = t2;
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}
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}
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#[inline(always)]
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fn mul2(&mut self) {
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let mut last = 0;
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for i in &mut self.0 {
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let tmp = *i >> 63;
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*i <<= 1;
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*i |= last;
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last = tmp;
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}
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}
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#[inline(always)]
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fn shl(&mut self, mut n: u32) {
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if n >= 64 * 4 {
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*self = Self::from(0);
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return;
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}
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while n >= 64 {
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let mut t = 0;
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for i in &mut self.0 {
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::std::mem::swap(&mut t, i);
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}
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n -= 64;
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}
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if n > 0 {
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let mut t = 0;
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for i in &mut self.0 {
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let t2 = *i >> (64 - n);
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*i <<= n;
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*i |= t;
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t = t2;
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}
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}
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}
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#[inline(always)]
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fn num_bits(&self) -> u32 {
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let mut ret = (4 as u32) * 64;
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for i in self.0.iter().rev() {
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let leading = i.leading_zeros();
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ret -= leading;
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if leading != 64 {
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break;
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}
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}
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ret
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}
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#[inline(always)]
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fn add_nocarry(&mut self, other: &FsRepr) {
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let mut carry = 0;
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for (a, b) in self.0.iter_mut().zip(other.0.iter()) {
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*a = adc(*a, *b, &mut carry);
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}
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}
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#[inline(always)]
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fn sub_noborrow(&mut self, other: &FsRepr) {
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let mut borrow = 0;
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for (a, b) in self.0.iter_mut().zip(other.0.iter()) {
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*a = sbb(*a, *b, &mut borrow);
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}
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}
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}
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/// This is an element of the scalar field of the Jubjub curve.
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#[derive(Copy, Clone, PartialEq, Eq, Debug)]
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pub struct Fs(FsRepr);
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impl ::std::fmt::Display for Fs {
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fn fmt(&self, f: &mut ::std::fmt::Formatter<'_>) -> ::std::fmt::Result {
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write!(f, "Fs({})", self.into_repr())
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}
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}
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impl From<Fs> for FsRepr {
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fn from(e: Fs) -> FsRepr {
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e.into_repr()
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}
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}
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impl Neg for Fs {
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type Output = Self;
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#[inline]
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fn neg(mut self) -> Self {
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if !self.is_zero() {
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let mut tmp = MODULUS;
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tmp.sub_noborrow(&self.0);
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self.0 = tmp;
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}
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self
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}
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}
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impl<'r> Add<&'r Fs> for Fs {
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type Output = Self;
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#[inline]
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fn add(self, other: &Self) -> Self {
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let mut ret = self;
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ret.add_assign(other);
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ret
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}
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}
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impl Add for Fs {
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type Output = Self;
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#[inline]
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fn add(self, other: Self) -> Self {
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self + &other
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}
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}
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impl<'r> AddAssign<&'r Fs> for Fs {
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#[inline]
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fn add_assign(&mut self, other: &Self) {
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// This cannot exceed the backing capacity.
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self.0.add_nocarry(&other.0);
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// However, it may need to be reduced.
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self.reduce();
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}
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}
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impl AddAssign for Fs {
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#[inline]
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fn add_assign(&mut self, other: Self) {
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self.add_assign(&other);
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}
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}
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impl<'r> Sub<&'r Fs> for Fs {
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type Output = Self;
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#[inline]
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fn sub(self, other: &Self) -> Self {
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let mut ret = self;
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ret.sub_assign(other);
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ret
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}
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}
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impl Sub for Fs {
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type Output = Self;
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#[inline]
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fn sub(self, other: Self) -> Self {
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self - &other
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}
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}
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impl<'r> SubAssign<&'r Fs> for Fs {
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#[inline]
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fn sub_assign(&mut self, other: &Self) {
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// If `other` is larger than `self`, we'll need to add the modulus to self first.
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if other.0 > self.0 {
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self.0.add_nocarry(&MODULUS);
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}
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self.0.sub_noborrow(&other.0);
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}
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}
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impl SubAssign for Fs {
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#[inline]
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fn sub_assign(&mut self, other: Self) {
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self.sub_assign(&other);
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}
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}
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impl<'r> Mul<&'r Fs> for Fs {
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type Output = Self;
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#[inline]
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fn mul(self, other: &Self) -> Self {
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let mut ret = self;
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ret.mul_assign(other);
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ret
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}
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}
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impl Mul for Fs {
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type Output = Self;
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#[inline]
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fn mul(self, other: Self) -> Self {
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self * &other
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}
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}
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impl<'r> MulAssign<&'r Fs> for Fs {
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#[inline]
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fn mul_assign(&mut self, other: &Self) {
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let mut carry = 0;
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let r0 = mac_with_carry(0, (self.0).0[0], (other.0).0[0], &mut carry);
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let r1 = mac_with_carry(0, (self.0).0[0], (other.0).0[1], &mut carry);
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let r2 = mac_with_carry(0, (self.0).0[0], (other.0).0[2], &mut carry);
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let r3 = mac_with_carry(0, (self.0).0[0], (other.0).0[3], &mut carry);
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let r4 = carry;
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let mut carry = 0;
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let r1 = mac_with_carry(r1, (self.0).0[1], (other.0).0[0], &mut carry);
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let r2 = mac_with_carry(r2, (self.0).0[1], (other.0).0[1], &mut carry);
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let r3 = mac_with_carry(r3, (self.0).0[1], (other.0).0[2], &mut carry);
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let r4 = mac_with_carry(r4, (self.0).0[1], (other.0).0[3], &mut carry);
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let r5 = carry;
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let mut carry = 0;
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let r2 = mac_with_carry(r2, (self.0).0[2], (other.0).0[0], &mut carry);
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let r3 = mac_with_carry(r3, (self.0).0[2], (other.0).0[1], &mut carry);
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let r4 = mac_with_carry(r4, (self.0).0[2], (other.0).0[2], &mut carry);
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let r5 = mac_with_carry(r5, (self.0).0[2], (other.0).0[3], &mut carry);
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let r6 = carry;
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let mut carry = 0;
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let r3 = mac_with_carry(r3, (self.0).0[3], (other.0).0[0], &mut carry);
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let r4 = mac_with_carry(r4, (self.0).0[3], (other.0).0[1], &mut carry);
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let r5 = mac_with_carry(r5, (self.0).0[3], (other.0).0[2], &mut carry);
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let r6 = mac_with_carry(r6, (self.0).0[3], (other.0).0[3], &mut carry);
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let r7 = carry;
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self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7);
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}
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}
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impl MulAssign for Fs {
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#[inline]
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fn mul_assign(&mut self, other: Self) {
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self.mul_assign(&other);
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}
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}
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impl PrimeField for Fs {
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type Repr = FsRepr;
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fn from_repr(r: FsRepr) -> Result<Fs, PrimeFieldDecodingError> {
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let mut r = Fs(r);
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if r.is_valid() {
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r.mul_assign(&Fs(R2));
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Ok(r)
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} else {
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Err(PrimeFieldDecodingError::NotInField(format!("{}", r.0)))
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}
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}
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fn into_repr(&self) -> FsRepr {
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let mut r = *self;
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r.mont_reduce(
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(self.0).0[0],
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(self.0).0[1],
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(self.0).0[2],
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(self.0).0[3],
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0,
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0,
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0,
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0,
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);
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r.0
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}
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fn char() -> FsRepr {
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MODULUS
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}
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const NUM_BITS: u32 = MODULUS_BITS;
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const CAPACITY: u32 = Self::NUM_BITS - 1;
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fn multiplicative_generator() -> Self {
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Fs(GENERATOR)
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}
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const S: u32 = S;
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fn root_of_unity() -> Self {
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Fs(ROOT_OF_UNITY)
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}
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}
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impl Field for Fs {
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fn random<R: RngCore>(rng: &mut R) -> Self {
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loop {
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let mut tmp = {
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let mut repr = [0u64; 4];
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for limb in &mut repr {
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*limb = rng.next_u64();
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}
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Fs(FsRepr(repr))
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};
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// Mask away the unused most-significant bits.
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tmp.0.as_mut()[3] &= 0xffffffffffffffff >> REPR_SHAVE_BITS;
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if tmp.is_valid() {
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return tmp;
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}
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}
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}
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#[inline]
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fn zero() -> Self {
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Fs(FsRepr::from(0))
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}
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#[inline]
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fn one() -> Self {
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Fs(R)
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}
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#[inline]
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fn is_zero(&self) -> bool {
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self.0.is_zero()
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}
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#[inline]
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fn double(&self) -> Self {
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let mut ret = *self;
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|
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// This cannot exceed the backing capacity.
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ret.0.mul2();
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// However, it may need to be reduced.
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ret.reduce();
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ret
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}
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|
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fn inverse(&self) -> Option<Self> {
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if self.is_zero() {
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None
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} else {
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// Guajardo Kumar Paar Pelzl
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|
// Efficient Software-Implementation of Finite Fields with Applications to Cryptography
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// Algorithm 16 (BEA for Inversion in Fp)
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|
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let one = FsRepr::from(1);
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let mut u = self.0;
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let mut v = MODULUS;
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let mut b = Fs(R2); // Avoids unnecessary reduction step.
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let mut c = Self::zero();
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|
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while u != one && v != one {
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while u.is_even() {
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u.div2();
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if b.0.is_even() {
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b.0.div2();
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} else {
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b.0.add_nocarry(&MODULUS);
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b.0.div2();
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}
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}
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|
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while v.is_even() {
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v.div2();
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|
|
if c.0.is_even() {
|
|
c.0.div2();
|
|
} else {
|
|
c.0.add_nocarry(&MODULUS);
|
|
c.0.div2();
|
|
}
|
|
}
|
|
|
|
if v < u {
|
|
u.sub_noborrow(&v);
|
|
b.sub_assign(&c);
|
|
} else {
|
|
v.sub_noborrow(&u);
|
|
c.sub_assign(&b);
|
|
}
|
|
}
|
|
|
|
if u == one {
|
|
Some(b)
|
|
} else {
|
|
Some(c)
|
|
}
|
|
}
|
|
}
|
|
|
|
#[inline(always)]
|
|
fn frobenius_map(&mut self, _: usize) {
|
|
// This has no effect in a prime field.
|
|
}
|
|
|
|
#[inline]
|
|
fn square(&mut self) {
|
|
let mut carry = 0;
|
|
let r1 = mac_with_carry(0, (self.0).0[0], (self.0).0[1], &mut carry);
|
|
let r2 = mac_with_carry(0, (self.0).0[0], (self.0).0[2], &mut carry);
|
|
let r3 = mac_with_carry(0, (self.0).0[0], (self.0).0[3], &mut carry);
|
|
let r4 = carry;
|
|
let mut carry = 0;
|
|
let r3 = mac_with_carry(r3, (self.0).0[1], (self.0).0[2], &mut carry);
|
|
let r4 = mac_with_carry(r4, (self.0).0[1], (self.0).0[3], &mut carry);
|
|
let r5 = carry;
|
|
let mut carry = 0;
|
|
let r5 = mac_with_carry(r5, (self.0).0[2], (self.0).0[3], &mut carry);
|
|
let r6 = carry;
|
|
|
|
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 mut carry = 0;
|
|
let r0 = mac_with_carry(0, (self.0).0[0], (self.0).0[0], &mut carry);
|
|
let r1 = adc(r1, 0, &mut carry);
|
|
let r2 = mac_with_carry(r2, (self.0).0[1], (self.0).0[1], &mut carry);
|
|
let r3 = adc(r3, 0, &mut carry);
|
|
let r4 = mac_with_carry(r4, (self.0).0[2], (self.0).0[2], &mut carry);
|
|
let r5 = adc(r5, 0, &mut carry);
|
|
let r6 = mac_with_carry(r6, (self.0).0[3], (self.0).0[3], &mut carry);
|
|
let r7 = adc(r7, 0, &mut carry);
|
|
self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7);
|
|
}
|
|
}
|
|
|
|
impl Fs {
|
|
/// Determines if the element is really in the field. This is only used
|
|
/// internally.
|
|
#[inline(always)]
|
|
fn is_valid(&self) -> bool {
|
|
self.0 < MODULUS
|
|
}
|
|
|
|
/// Subtracts the modulus from this element if this element is not in the
|
|
/// field. Only used internally.
|
|
#[inline(always)]
|
|
fn reduce(&mut self) {
|
|
if !self.is_valid() {
|
|
self.0.sub_noborrow(&MODULUS);
|
|
}
|
|
}
|
|
|
|
#[inline(always)]
|
|
fn mont_reduce(
|
|
&mut self,
|
|
r0: u64,
|
|
mut r1: u64,
|
|
mut r2: u64,
|
|
mut r3: u64,
|
|
mut r4: u64,
|
|
mut r5: u64,
|
|
mut r6: u64,
|
|
mut r7: u64,
|
|
) {
|
|
// 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 mut carry = 0;
|
|
mac_with_carry(r0, k, MODULUS.0[0], &mut carry);
|
|
r1 = mac_with_carry(r1, k, MODULUS.0[1], &mut carry);
|
|
r2 = mac_with_carry(r2, k, MODULUS.0[2], &mut carry);
|
|
r3 = mac_with_carry(r3, k, MODULUS.0[3], &mut carry);
|
|
r4 = adc(r4, 0, &mut carry);
|
|
let carry2 = carry;
|
|
let k = r1.wrapping_mul(INV);
|
|
let mut carry = 0;
|
|
mac_with_carry(r1, k, MODULUS.0[0], &mut carry);
|
|
r2 = mac_with_carry(r2, k, MODULUS.0[1], &mut carry);
|
|
r3 = mac_with_carry(r3, k, MODULUS.0[2], &mut carry);
|
|
r4 = mac_with_carry(r4, k, MODULUS.0[3], &mut carry);
|
|
r5 = adc(r5, carry2, &mut carry);
|
|
let carry2 = carry;
|
|
let k = r2.wrapping_mul(INV);
|
|
let mut carry = 0;
|
|
mac_with_carry(r2, k, MODULUS.0[0], &mut carry);
|
|
r3 = mac_with_carry(r3, k, MODULUS.0[1], &mut carry);
|
|
r4 = mac_with_carry(r4, k, MODULUS.0[2], &mut carry);
|
|
r5 = mac_with_carry(r5, k, MODULUS.0[3], &mut carry);
|
|
r6 = adc(r6, carry2, &mut carry);
|
|
let carry2 = carry;
|
|
let k = r3.wrapping_mul(INV);
|
|
let mut carry = 0;
|
|
mac_with_carry(r3, k, MODULUS.0[0], &mut carry);
|
|
r4 = mac_with_carry(r4, k, MODULUS.0[1], &mut carry);
|
|
r5 = mac_with_carry(r5, k, MODULUS.0[2], &mut carry);
|
|
r6 = mac_with_carry(r6, k, MODULUS.0[3], &mut carry);
|
|
r7 = adc(r7, carry2, &mut carry);
|
|
(self.0).0[0] = r4;
|
|
(self.0).0[1] = r5;
|
|
(self.0).0[2] = r6;
|
|
(self.0).0[3] = r7;
|
|
self.reduce();
|
|
}
|
|
|
|
fn mul_bits<S: AsRef<[u64]>>(&self, bits: BitIterator<S>) -> Self {
|
|
let mut res = Self::zero();
|
|
for bit in bits {
|
|
res = res.double();
|
|
|
|
if bit {
|
|
res.add_assign(self)
|
|
}
|
|
}
|
|
res
|
|
}
|
|
}
|
|
|
|
impl ToUniform for Fs {
|
|
/// Convert a little endian byte string into a uniform
|
|
/// field element. The number is reduced mod s. The caller
|
|
/// is responsible for ensuring the input is 64 bytes of
|
|
/// Random Oracle output.
|
|
fn to_uniform(digest: &[u8]) -> Self {
|
|
assert_eq!(digest.len(), 64);
|
|
let mut repr: [u64; 8] = [0; 8];
|
|
LittleEndian::read_u64_into(digest, &mut repr);
|
|
Self::one().mul_bits(BitIterator::new(repr))
|
|
}
|
|
}
|
|
|
|
impl SqrtField for Fs {
|
|
fn legendre(&self) -> LegendreSymbol {
|
|
// s = self^((s - 1) // 2)
|
|
let s = self.pow([
|
|
0x684b872f6b7b965b,
|
|
0x53341049e6640841,
|
|
0x83339d80809a1d80,
|
|
0x73eda753299d7d4,
|
|
]);
|
|
if s == Self::zero() {
|
|
Zero
|
|
} else if s == Self::one() {
|
|
QuadraticResidue
|
|
} else {
|
|
QuadraticNonResidue
|
|
}
|
|
}
|
|
|
|
fn sqrt(&self) -> Option<Self> {
|
|
// Shank's algorithm for s mod 4 = 3
|
|
// https://eprint.iacr.org/2012/685.pdf (page 9, algorithm 2)
|
|
|
|
// a1 = self^((s - 3) // 4)
|
|
let mut a1 = self.pow([
|
|
0xb425c397b5bdcb2d,
|
|
0x299a0824f3320420,
|
|
0x4199cec0404d0ec0,
|
|
0x39f6d3a994cebea,
|
|
]);
|
|
let mut a0 = a1;
|
|
a0.square();
|
|
a0.mul_assign(self);
|
|
|
|
if a0 == NEGATIVE_ONE {
|
|
None
|
|
} else {
|
|
a1.mul_assign(self);
|
|
Some(a1)
|
|
}
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_neg_one() {
|
|
let o = Fs::one().neg();
|
|
|
|
assert_eq!(NEGATIVE_ONE, o);
|
|
}
|
|
|
|
#[cfg(test)]
|
|
use rand_core::SeedableRng;
|
|
#[cfg(test)]
|
|
use rand_xorshift::XorShiftRng;
|
|
|
|
#[test]
|
|
fn test_fs_repr_ordering() {
|
|
fn assert_equality(a: FsRepr, b: FsRepr) {
|
|
assert_eq!(a, b);
|
|
assert!(a.cmp(&b) == ::std::cmp::Ordering::Equal);
|
|
}
|
|
|
|
fn assert_lt(a: FsRepr, b: FsRepr) {
|
|
assert!(a < b);
|
|
assert!(b > a);
|
|
}
|
|
|
|
assert_equality(
|
|
FsRepr([9999, 9999, 9999, 9999]),
|
|
FsRepr([9999, 9999, 9999, 9999]),
|
|
);
|
|
assert_equality(
|
|
FsRepr([9999, 9998, 9999, 9999]),
|
|
FsRepr([9999, 9998, 9999, 9999]),
|
|
);
|
|
assert_equality(
|
|
FsRepr([9999, 9999, 9999, 9997]),
|
|
FsRepr([9999, 9999, 9999, 9997]),
|
|
);
|
|
assert_lt(
|
|
FsRepr([9999, 9997, 9999, 9998]),
|
|
FsRepr([9999, 9997, 9999, 9999]),
|
|
);
|
|
assert_lt(
|
|
FsRepr([9999, 9997, 9998, 9999]),
|
|
FsRepr([9999, 9997, 9999, 9999]),
|
|
);
|
|
assert_lt(
|
|
FsRepr([9, 9999, 9999, 9997]),
|
|
FsRepr([9999, 9999, 9999, 9997]),
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_repr_from() {
|
|
assert_eq!(FsRepr::from(100), FsRepr([100, 0, 0, 0]));
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_repr_is_odd() {
|
|
assert!(!FsRepr::from(0).is_odd());
|
|
assert!(FsRepr::from(0).is_even());
|
|
assert!(FsRepr::from(1).is_odd());
|
|
assert!(!FsRepr::from(1).is_even());
|
|
assert!(!FsRepr::from(324834872).is_odd());
|
|
assert!(FsRepr::from(324834872).is_even());
|
|
assert!(FsRepr::from(324834873).is_odd());
|
|
assert!(!FsRepr::from(324834873).is_even());
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_repr_is_zero() {
|
|
assert!(FsRepr::from(0).is_zero());
|
|
assert!(!FsRepr::from(1).is_zero());
|
|
assert!(!FsRepr([0, 0, 1, 0]).is_zero());
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_repr_div2() {
|
|
let mut a = FsRepr([
|
|
0xbd2920b19c972321,
|
|
0x174ed0466a3be37e,
|
|
0xd468d5e3b551f0b5,
|
|
0xcb67c072733beefc,
|
|
]);
|
|
a.div2();
|
|
assert_eq!(
|
|
a,
|
|
FsRepr([
|
|
0x5e949058ce4b9190,
|
|
0x8ba76823351df1bf,
|
|
0x6a346af1daa8f85a,
|
|
0x65b3e039399df77e
|
|
])
|
|
);
|
|
for _ in 0..10 {
|
|
a.div2();
|
|
}
|
|
assert_eq!(
|
|
a,
|
|
FsRepr([
|
|
0x6fd7a524163392e4,
|
|
0x16a2e9da08cd477c,
|
|
0xdf9a8d1abc76aa3e,
|
|
0x196cf80e4e677d
|
|
])
|
|
);
|
|
for _ in 0..200 {
|
|
a.div2();
|
|
}
|
|
assert_eq!(a, FsRepr([0x196cf80e4e67, 0x0, 0x0, 0x0]));
|
|
for _ in 0..40 {
|
|
a.div2();
|
|
}
|
|
assert_eq!(a, FsRepr([0x19, 0x0, 0x0, 0x0]));
|
|
for _ in 0..4 {
|
|
a.div2();
|
|
}
|
|
assert_eq!(a, FsRepr([0x1, 0x0, 0x0, 0x0]));
|
|
a.div2();
|
|
assert!(a.is_zero());
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_repr_shr() {
|
|
let mut a = FsRepr([
|
|
0xb33fbaec482a283f,
|
|
0x997de0d3a88cb3df,
|
|
0x9af62d2a9a0e5525,
|
|
0x36003ab08de70da1,
|
|
]);
|
|
a.shr(0);
|
|
assert_eq!(
|
|
a,
|
|
FsRepr([
|
|
0xb33fbaec482a283f,
|
|
0x997de0d3a88cb3df,
|
|
0x9af62d2a9a0e5525,
|
|
0x36003ab08de70da1
|
|
])
|
|
);
|
|
a.shr(1);
|
|
assert_eq!(
|
|
a,
|
|
FsRepr([
|
|
0xd99fdd762415141f,
|
|
0xccbef069d44659ef,
|
|
0xcd7b16954d072a92,
|
|
0x1b001d5846f386d0
|
|
])
|
|
);
|
|
a.shr(50);
|
|
assert_eq!(
|
|
a,
|
|
FsRepr([
|
|
0xbc1a7511967bf667,
|
|
0xc5a55341caa4b32f,
|
|
0x75611bce1b4335e,
|
|
0x6c0
|
|
])
|
|
);
|
|
a.shr(130);
|
|
assert_eq!(a, FsRepr([0x1d5846f386d0cd7, 0x1b0, 0x0, 0x0]));
|
|
a.shr(64);
|
|
assert_eq!(a, FsRepr([0x1b0, 0x0, 0x0, 0x0]));
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_repr_mul2() {
|
|
let mut a = FsRepr::from(23712937547);
|
|
a.mul2();
|
|
assert_eq!(a, FsRepr([0xb0acd6c96, 0x0, 0x0, 0x0]));
|
|
for _ in 0..60 {
|
|
a.mul2();
|
|
}
|
|
assert_eq!(a, FsRepr([0x6000000000000000, 0xb0acd6c9, 0x0, 0x0]));
|
|
for _ in 0..128 {
|
|
a.mul2();
|
|
}
|
|
assert_eq!(a, FsRepr([0x0, 0x0, 0x6000000000000000, 0xb0acd6c9]));
|
|
for _ in 0..60 {
|
|
a.mul2();
|
|
}
|
|
assert_eq!(a, FsRepr([0x0, 0x0, 0x0, 0x9600000000000000]));
|
|
for _ in 0..7 {
|
|
a.mul2();
|
|
}
|
|
assert!(a.is_zero());
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_repr_num_bits() {
|
|
let mut a = FsRepr::from(0);
|
|
assert_eq!(0, a.num_bits());
|
|
a = FsRepr::from(1);
|
|
for i in 1..257 {
|
|
assert_eq!(i, a.num_bits());
|
|
a.mul2();
|
|
}
|
|
assert_eq!(0, a.num_bits());
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_repr_sub_noborrow() {
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
let mut t = FsRepr([
|
|
0x8e62a7e85264e2c3,
|
|
0xb23d34c1941d3ca,
|
|
0x5976930b7502dd15,
|
|
0x600f3fb517bf5495,
|
|
]);
|
|
t.sub_noborrow(&FsRepr([
|
|
0xd64f669809cbc6a4,
|
|
0xfa76cb9d90cf7637,
|
|
0xfefb0df9038d43b3,
|
|
0x298a30c744b31acf,
|
|
]));
|
|
assert!(
|
|
t == FsRepr([
|
|
0xb813415048991c1f,
|
|
0x10ad07ae88725d92,
|
|
0x5a7b851271759961,
|
|
0x36850eedd30c39c5
|
|
])
|
|
);
|
|
|
|
for _ in 0..1000 {
|
|
let mut a = Fs::random(&mut rng).into_repr();
|
|
a.0[3] >>= 30;
|
|
let mut b = a;
|
|
for _ in 0..10 {
|
|
b.mul2();
|
|
}
|
|
let mut c = b;
|
|
for _ in 0..10 {
|
|
c.mul2();
|
|
}
|
|
|
|
assert!(a < b);
|
|
assert!(b < c);
|
|
|
|
let mut csub_ba = c;
|
|
csub_ba.sub_noborrow(&b);
|
|
csub_ba.sub_noborrow(&a);
|
|
|
|
let mut csub_ab = c;
|
|
csub_ab.sub_noborrow(&a);
|
|
csub_ab.sub_noborrow(&b);
|
|
|
|
assert_eq!(csub_ab, csub_ba);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_legendre() {
|
|
assert_eq!(QuadraticResidue, Fs::one().legendre());
|
|
assert_eq!(Zero, Fs::zero().legendre());
|
|
|
|
let e = FsRepr([
|
|
0x8385eec23df1f88e,
|
|
0x9a01fb412b2dba16,
|
|
0x4c928edcdd6c22f,
|
|
0x9f2df7ef69ecef9,
|
|
]);
|
|
assert_eq!(QuadraticResidue, Fs::from_repr(e).unwrap().legendre());
|
|
let e = FsRepr([
|
|
0xe8ed9f299da78568,
|
|
0x35efdebc88b2209,
|
|
0xc82125cb1f916dbe,
|
|
0x6813d2b38c39bd0,
|
|
]);
|
|
assert_eq!(QuadraticNonResidue, Fs::from_repr(e).unwrap().legendre());
|
|
}
|
|
|
|
#[test]
|
|
fn test_fr_repr_add_nocarry() {
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
let mut t = FsRepr([
|
|
0xd64f669809cbc6a4,
|
|
0xfa76cb9d90cf7637,
|
|
0xfefb0df9038d43b3,
|
|
0x298a30c744b31acf,
|
|
]);
|
|
t.add_nocarry(&FsRepr([
|
|
0x8e62a7e85264e2c3,
|
|
0xb23d34c1941d3ca,
|
|
0x5976930b7502dd15,
|
|
0x600f3fb517bf5495,
|
|
]));
|
|
assert_eq!(
|
|
t,
|
|
FsRepr([
|
|
0x64b20e805c30a967,
|
|
0x59a9ee9aa114a02,
|
|
0x5871a104789020c9,
|
|
0x8999707c5c726f65
|
|
])
|
|
);
|
|
|
|
// Test for the associativity of addition.
|
|
for _ in 0..1000 {
|
|
let mut a = Fs::random(&mut rng).into_repr();
|
|
let mut b = Fs::random(&mut rng).into_repr();
|
|
let mut c = Fs::random(&mut rng).into_repr();
|
|
|
|
// Unset the first few bits, so that overflow won't occur.
|
|
a.0[3] >>= 3;
|
|
b.0[3] >>= 3;
|
|
c.0[3] >>= 3;
|
|
|
|
let mut abc = a;
|
|
abc.add_nocarry(&b);
|
|
abc.add_nocarry(&c);
|
|
|
|
let mut acb = a;
|
|
acb.add_nocarry(&c);
|
|
acb.add_nocarry(&b);
|
|
|
|
let mut bac = b;
|
|
bac.add_nocarry(&a);
|
|
bac.add_nocarry(&c);
|
|
|
|
let mut bca = b;
|
|
bca.add_nocarry(&c);
|
|
bca.add_nocarry(&a);
|
|
|
|
let mut cab = c;
|
|
cab.add_nocarry(&a);
|
|
cab.add_nocarry(&b);
|
|
|
|
let mut cba = c;
|
|
cba.add_nocarry(&b);
|
|
cba.add_nocarry(&a);
|
|
|
|
assert_eq!(abc, acb);
|
|
assert_eq!(abc, bac);
|
|
assert_eq!(abc, bca);
|
|
assert_eq!(abc, cab);
|
|
assert_eq!(abc, cba);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_is_valid() {
|
|
let mut a = Fs(MODULUS);
|
|
assert!(!a.is_valid());
|
|
a.0.sub_noborrow(&FsRepr::from(1));
|
|
assert!(a.is_valid());
|
|
assert!(Fs(FsRepr::from(0)).is_valid());
|
|
assert!(Fs(FsRepr([
|
|
0xd0970e5ed6f72cb6,
|
|
0xa6682093ccc81082,
|
|
0x6673b0101343b00,
|
|
0xe7db4ea6533afa9
|
|
]))
|
|
.is_valid());
|
|
assert!(!Fs(FsRepr([
|
|
0xffffffffffffffff,
|
|
0xffffffffffffffff,
|
|
0xffffffffffffffff,
|
|
0xffffffffffffffff
|
|
]))
|
|
.is_valid());
|
|
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
for _ in 0..1000 {
|
|
let a = Fs::random(&mut rng);
|
|
assert!(a.is_valid());
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_add_assign() {
|
|
{
|
|
// Random number
|
|
let mut tmp = Fs::from_str(
|
|
"4577408157467272683998459759522778614363623736323078995109579213719612604198",
|
|
)
|
|
.unwrap();
|
|
assert!(tmp.is_valid());
|
|
// Test that adding zero has no effect.
|
|
tmp.add_assign(&Fs(FsRepr::from(0)));
|
|
assert_eq!(
|
|
tmp,
|
|
Fs(FsRepr([
|
|
0x8e6bfff4722d6e67,
|
|
0x5643da5c892044f9,
|
|
0x9465f4b281921a69,
|
|
0x25f752d3edd7162
|
|
]))
|
|
);
|
|
// Add one and test for the result.
|
|
tmp.add_assign(&Fs(FsRepr::from(1)));
|
|
assert_eq!(
|
|
tmp,
|
|
Fs(FsRepr([
|
|
0x8e6bfff4722d6e68,
|
|
0x5643da5c892044f9,
|
|
0x9465f4b281921a69,
|
|
0x25f752d3edd7162
|
|
]))
|
|
);
|
|
// Add another random number that exercises the reduction.
|
|
tmp.add_assign(&Fs(FsRepr([
|
|
0xb634d07bc42d4a70,
|
|
0xf724f0c008411f5f,
|
|
0x456d4053d865af34,
|
|
0x24ce814e8c63027,
|
|
])));
|
|
assert_eq!(
|
|
tmp,
|
|
Fs(FsRepr([
|
|
0x44a0d070365ab8d8,
|
|
0x4d68cb1c91616459,
|
|
0xd9d3350659f7c99e,
|
|
0x4ac5d4227a3a189
|
|
]))
|
|
);
|
|
// Add one to (s - 1) and test for the result.
|
|
tmp = Fs(FsRepr([
|
|
0xd0970e5ed6f72cb6,
|
|
0xa6682093ccc81082,
|
|
0x6673b0101343b00,
|
|
0xe7db4ea6533afa9,
|
|
]));
|
|
tmp.add_assign(&Fs(FsRepr::from(1)));
|
|
assert!(tmp.0.is_zero());
|
|
// Add a random number to another one such that the result is s - 1
|
|
tmp = Fs(FsRepr([
|
|
0xa11fda5950ce3636,
|
|
0x922e0dbccfe0ca0e,
|
|
0xacebb6e215b82d4a,
|
|
0x97ffb8cdc3aee93,
|
|
]));
|
|
tmp.add_assign(&Fs(FsRepr([
|
|
0x2f7734058628f680,
|
|
0x143a12d6fce74674,
|
|
0x597b841eeb7c0db6,
|
|
0x4fdb95d88f8c115,
|
|
])));
|
|
assert_eq!(
|
|
tmp,
|
|
Fs(FsRepr([
|
|
0xd0970e5ed6f72cb6,
|
|
0xa6682093ccc81082,
|
|
0x6673b0101343b00,
|
|
0xe7db4ea6533afa9
|
|
]))
|
|
);
|
|
// Add one to the result and test for it.
|
|
tmp.add_assign(&Fs(FsRepr::from(1)));
|
|
assert!(tmp.0.is_zero());
|
|
}
|
|
|
|
// Test associativity
|
|
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
for _ in 0..1000 {
|
|
// Generate a, b, c and ensure (a + b) + c == a + (b + c).
|
|
let a = Fs::random(&mut rng);
|
|
let b = Fs::random(&mut rng);
|
|
let c = Fs::random(&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!(tmp1.is_valid());
|
|
assert!(tmp2.is_valid());
|
|
assert_eq!(tmp1, tmp2);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_sub_assign() {
|
|
{
|
|
// Test arbitrary subtraction that tests reduction.
|
|
let mut tmp = Fs(FsRepr([
|
|
0xb384d9f6877afd99,
|
|
0x4442513958e1a1c1,
|
|
0x352c4b8a95eccc3f,
|
|
0x2db62dee4b0f2,
|
|
]));
|
|
tmp.sub_assign(&Fs(FsRepr([
|
|
0xec5bd2d13ed6b05a,
|
|
0x2adc0ab3a39b5fa,
|
|
0x82d3360a493e637e,
|
|
0x53ccff4a64d6679,
|
|
])));
|
|
assert_eq!(
|
|
tmp,
|
|
Fs(FsRepr([
|
|
0x97c015841f9b79f6,
|
|
0xe7fcb121eb6ffc49,
|
|
0xb8c050814de2a3c1,
|
|
0x943c0589dcafa21
|
|
]))
|
|
);
|
|
|
|
// Test the opposite subtraction which doesn't test reduction.
|
|
tmp = Fs(FsRepr([
|
|
0xec5bd2d13ed6b05a,
|
|
0x2adc0ab3a39b5fa,
|
|
0x82d3360a493e637e,
|
|
0x53ccff4a64d6679,
|
|
]));
|
|
tmp.sub_assign(&Fs(FsRepr([
|
|
0xb384d9f6877afd99,
|
|
0x4442513958e1a1c1,
|
|
0x352c4b8a95eccc3f,
|
|
0x2db62dee4b0f2,
|
|
])));
|
|
assert_eq!(
|
|
tmp,
|
|
Fs(FsRepr([
|
|
0x38d6f8dab75bb2c1,
|
|
0xbe6b6f71e1581439,
|
|
0x4da6ea7fb351973e,
|
|
0x539f491c768b587
|
|
]))
|
|
);
|
|
|
|
// Test for sensible results with zero
|
|
tmp = Fs(FsRepr::from(0));
|
|
tmp.sub_assign(&Fs(FsRepr::from(0)));
|
|
assert!(tmp.is_zero());
|
|
|
|
tmp = Fs(FsRepr([
|
|
0x361e16aef5cce835,
|
|
0x55bbde2536e274c1,
|
|
0x4dc77a63fd15ee75,
|
|
0x1e14bb37c14f230,
|
|
]));
|
|
tmp.sub_assign(&Fs(FsRepr::from(0)));
|
|
assert_eq!(
|
|
tmp,
|
|
Fs(FsRepr([
|
|
0x361e16aef5cce835,
|
|
0x55bbde2536e274c1,
|
|
0x4dc77a63fd15ee75,
|
|
0x1e14bb37c14f230
|
|
]))
|
|
);
|
|
}
|
|
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
for _ in 0..1000 {
|
|
// Ensure that (a - b) + (b - a) = 0.
|
|
let a = Fs::random(&mut rng);
|
|
let b = Fs::random(&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_fs_mul_assign() {
|
|
let mut tmp = Fs(FsRepr([
|
|
0xb433b01287f71744,
|
|
0x4eafb86728c4d108,
|
|
0xfdd52c14b9dfbe65,
|
|
0x2ff1f3434821118,
|
|
]));
|
|
tmp.mul_assign(&Fs(FsRepr([
|
|
0xdae00fc63c9fa90f,
|
|
0x5a5ed89b96ce21ce,
|
|
0x913cd26101bd6f58,
|
|
0x3f0822831697fe9,
|
|
])));
|
|
assert!(
|
|
tmp == Fs(FsRepr([
|
|
0xb68ecb61d54d2992,
|
|
0x5ff95874defce6a6,
|
|
0x3590eb053894657d,
|
|
0x53823a118515933
|
|
]))
|
|
);
|
|
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
for _ in 0..1000000 {
|
|
// Ensure that (a * b) * c = a * (b * c)
|
|
let a = Fs::random(&mut rng);
|
|
let b = Fs::random(&mut rng);
|
|
let c = Fs::random(&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 = Fs::random(&mut rng);
|
|
let mut a = Fs::random(&mut rng);
|
|
let mut b = Fs::random(&mut rng);
|
|
let mut c = Fs::random(&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_fr_squaring() {
|
|
let mut a = Fs(FsRepr([
|
|
0xffffffffffffffff,
|
|
0xffffffffffffffff,
|
|
0xffffffffffffffff,
|
|
0xe7db4ea6533afa8,
|
|
]));
|
|
assert!(a.is_valid());
|
|
a.square();
|
|
assert_eq!(
|
|
a,
|
|
Fs::from_repr(FsRepr([
|
|
0x12c7f55cbc52fbaa,
|
|
0xdedc98a0b5e6ce9e,
|
|
0xad2892726a5396a,
|
|
0x9fe82af8fee77b3
|
|
]))
|
|
.unwrap()
|
|
);
|
|
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
for _ in 0..1000000 {
|
|
// Ensure that (a * a) = a^2
|
|
let a = Fs::random(&mut rng);
|
|
|
|
let mut tmp = a;
|
|
tmp.square();
|
|
|
|
let mut tmp2 = a;
|
|
tmp2.mul_assign(&a);
|
|
|
|
assert_eq!(tmp, tmp2);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_inverse() {
|
|
assert!(Fs::zero().inverse().is_none());
|
|
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
let one = Fs::one();
|
|
|
|
for _ in 0..1000 {
|
|
// Ensure that a * a^-1 = 1
|
|
let mut a = Fs::random(&mut rng);
|
|
let ainv = a.inverse().unwrap();
|
|
a.mul_assign(&ainv);
|
|
assert_eq!(a, one);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_double() {
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
for _ in 0..1000 {
|
|
// Ensure doubling a is equivalent to adding a to itself.
|
|
let a = Fs::random(&mut rng);
|
|
assert_eq!(a.double(), a + a);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_neg() {
|
|
{
|
|
let a = Fs::zero().neg();
|
|
|
|
assert!(a.is_zero());
|
|
}
|
|
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
for _ in 0..1000 {
|
|
// Ensure (a - (-a)) = 0.
|
|
let mut a = Fs::random(&mut rng);
|
|
let b = a.neg();
|
|
a.add_assign(&b);
|
|
|
|
assert!(a.is_zero());
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_pow() {
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
for i in 0..1000 {
|
|
// Exponentiate by various small numbers and ensure it consists with repeated
|
|
// multiplication.
|
|
let a = Fs::random(&mut rng);
|
|
let target = a.pow(&[i]);
|
|
let mut c = Fs::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 = Fs::random(&mut rng);
|
|
|
|
assert_eq!(a, a.pow(Fs::char()));
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_sqrt() {
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
assert_eq!(Fs::zero().sqrt().unwrap(), Fs::zero());
|
|
|
|
for _ in 0..1000 {
|
|
// Ensure sqrt(a^2) = a or -a
|
|
let a = Fs::random(&mut rng);
|
|
let nega = a.neg();
|
|
let mut b = a;
|
|
b.square();
|
|
|
|
let b = b.sqrt().unwrap();
|
|
|
|
assert!(a == b || nega == b);
|
|
}
|
|
|
|
for _ in 0..1000 {
|
|
// Ensure sqrt(a)^2 = a for random a
|
|
let a = Fs::random(&mut rng);
|
|
|
|
if let Some(mut tmp) = a.sqrt() {
|
|
tmp.square();
|
|
|
|
assert_eq!(a, tmp);
|
|
}
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_from_into_repr() {
|
|
// r + 1 should not be in the field
|
|
assert!(Fs::from_repr(FsRepr([
|
|
0xd0970e5ed6f72cb8,
|
|
0xa6682093ccc81082,
|
|
0x6673b0101343b00,
|
|
0xe7db4ea6533afa9
|
|
]))
|
|
.is_err());
|
|
|
|
// r should not be in the field
|
|
assert!(Fs::from_repr(Fs::char()).is_err());
|
|
|
|
// Multiply some arbitrary representations to see if the result is as expected.
|
|
let a = FsRepr([
|
|
0x5f2d0c05d0337b71,
|
|
0xa1df2b0f8a20479,
|
|
0xad73785e71bb863,
|
|
0x504a00480c9acec,
|
|
]);
|
|
let mut a_fs = Fs::from_repr(a).unwrap();
|
|
let b = FsRepr([
|
|
0x66356ff51e477562,
|
|
0x60a92ab55cf7603,
|
|
0x8e4273c7364dd192,
|
|
0x36df8844a344dc5,
|
|
]);
|
|
let b_fs = Fs::from_repr(b).unwrap();
|
|
let c = FsRepr([
|
|
0x7eef61708f4f2868,
|
|
0x747a7e6cf52946fb,
|
|
0x83dd75d7c9120017,
|
|
0x762f5177f0f3df7,
|
|
]);
|
|
a_fs.mul_assign(&b_fs);
|
|
assert_eq!(a_fs.into_repr(), c);
|
|
|
|
// Zero should be in the field.
|
|
assert!(Fs::from_repr(FsRepr::from(0)).unwrap().is_zero());
|
|
|
|
let mut rng = XorShiftRng::from_seed([
|
|
0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
|
|
0xe5,
|
|
]);
|
|
|
|
for _ in 0..1000 {
|
|
// Try to turn Fs elements into representations and back again, and compare.
|
|
let a = Fs::random(&mut rng);
|
|
let a_repr = a.into_repr();
|
|
let b_repr = FsRepr::from(a);
|
|
assert_eq!(a_repr, b_repr);
|
|
let a_again = Fs::from_repr(a_repr).unwrap();
|
|
|
|
assert_eq!(a, a_again);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_repr_display() {
|
|
assert_eq!(
|
|
format!(
|
|
"{}",
|
|
FsRepr([
|
|
0xa296db59787359df,
|
|
0x8d3e33077430d318,
|
|
0xd1abf5c606102eb7,
|
|
0xcbc33ee28108f0
|
|
])
|
|
),
|
|
"0x00cbc33ee28108f0d1abf5c606102eb78d3e33077430d318a296db59787359df".to_string()
|
|
);
|
|
assert_eq!(
|
|
format!(
|
|
"{}",
|
|
FsRepr([
|
|
0x14cb03535054a620,
|
|
0x312aa2bf2d1dff52,
|
|
0x970fe98746ab9361,
|
|
0xc1e18acf82711e6
|
|
])
|
|
),
|
|
"0x0c1e18acf82711e6970fe98746ab9361312aa2bf2d1dff5214cb03535054a620".to_string()
|
|
);
|
|
assert_eq!(
|
|
format!(
|
|
"{}",
|
|
FsRepr([
|
|
0xffffffffffffffff,
|
|
0xffffffffffffffff,
|
|
0xffffffffffffffff,
|
|
0xffffffffffffffff
|
|
])
|
|
),
|
|
"0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff".to_string()
|
|
);
|
|
assert_eq!(
|
|
format!("{}", FsRepr([0, 0, 0, 0])),
|
|
"0x0000000000000000000000000000000000000000000000000000000000000000".to_string()
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_display() {
|
|
assert_eq!(
|
|
format!(
|
|
"{}",
|
|
Fs::from_repr(FsRepr([
|
|
0x5528efb9998a01a3,
|
|
0x5bd2add5cb357089,
|
|
0xc061fa6adb491f98,
|
|
0x70db9d143db03d9
|
|
]))
|
|
.unwrap()
|
|
),
|
|
"Fs(0x070db9d143db03d9c061fa6adb491f985bd2add5cb3570895528efb9998a01a3)".to_string()
|
|
);
|
|
assert_eq!(
|
|
format!(
|
|
"{}",
|
|
Fs::from_repr(FsRepr([
|
|
0xd674745e2717999e,
|
|
0xbeb1f52d3e96f338,
|
|
0x9c7ae147549482b9,
|
|
0x999706024530d22
|
|
]))
|
|
.unwrap()
|
|
),
|
|
"Fs(0x0999706024530d229c7ae147549482b9beb1f52d3e96f338d674745e2717999e)".to_string()
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_num_bits() {
|
|
assert_eq!(Fs::NUM_BITS, 252);
|
|
assert_eq!(Fs::CAPACITY, 251);
|
|
}
|
|
|
|
#[test]
|
|
fn test_fs_root_of_unity() {
|
|
assert_eq!(Fs::S, 1);
|
|
assert_eq!(
|
|
Fs::multiplicative_generator(),
|
|
Fs::from_repr(FsRepr::from(6)).unwrap()
|
|
);
|
|
assert_eq!(
|
|
Fs::multiplicative_generator().pow([
|
|
0x684b872f6b7b965b,
|
|
0x53341049e6640841,
|
|
0x83339d80809a1d80,
|
|
0x73eda753299d7d4
|
|
]),
|
|
Fs::root_of_unity()
|
|
);
|
|
assert_eq!(Fs::root_of_unity().pow([1 << Fs::S]), Fs::one());
|
|
assert!(Fs::multiplicative_generator().sqrt().is_none());
|
|
}
|