Replace implementations of Fq and Fr with derives
This commit is contained in:
Jack Grigg
parent
d9d711ebb7
commit
a9d8079c2a
@ -1,6 +1,6 @@
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use rand::{Rand, SeedableRng, XorShiftRng};
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use ff::{Field, PrimeField, PrimeFieldRepr, SqrtField};
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use ff::{Field, PrimeField, PrimeFieldRepr};
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use pairing::bls12_381::*;
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#[bench]
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@ -1,69 +1,5 @@
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use super::fq2::Fq2;
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use std::cmp::Ordering;
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use {Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr, SqrtField};
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// q = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
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const MODULUS: FqRepr = FqRepr([
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0xb9feffffffffaaab,
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0x1eabfffeb153ffff,
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0x6730d2a0f6b0f624,
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0x64774b84f38512bf,
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0x4b1ba7b6434bacd7,
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0x1a0111ea397fe69a,
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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 = 381;
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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 = 3;
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// R = 2**384 % q
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const R: FqRepr = FqRepr([
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0x760900000002fffd,
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0xebf4000bc40c0002,
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0x5f48985753c758ba,
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0x77ce585370525745,
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0x5c071a97a256ec6d,
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0x15f65ec3fa80e493,
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]);
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// R2 = R^2 % q
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const R2: FqRepr = FqRepr([
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0xf4df1f341c341746,
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0xa76e6a609d104f1,
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0x8de5476c4c95b6d5,
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0x67eb88a9939d83c0,
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0x9a793e85b519952d,
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0x11988fe592cae3aa,
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]);
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// INV = -(q^{-1} mod 2^64) mod 2^64
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const INV: u64 = 0x89f3fffcfffcfffd;
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// GENERATOR = 2 (multiplicative generator of q-1 order, that is also quadratic nonresidue)
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const GENERATOR: FqRepr = FqRepr([
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0x321300000006554f,
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0xb93c0018d6c40005,
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0x57605e0db0ddbb51,
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0x8b256521ed1f9bcb,
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0x6cf28d7901622c03,
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0x11ebab9dbb81e28c,
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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: FqRepr = FqRepr([
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0x43f5fffffffcaaae,
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0x32b7fff2ed47fffd,
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0x7e83a49a2e99d69,
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0xeca8f3318332bb7a,
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0xef148d1ea0f4c069,
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0x40ab3263eff0206,
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]);
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use {Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr};
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// B coefficient of BLS12-381 curve, 4.
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pub const B_COEFF: Fq = Fq(FqRepr([
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@ -507,667 +443,11 @@ pub const NEGATIVE_ONE: Fq = Fq(FqRepr([
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0x40ab3263eff0206,
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]));
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#[derive(Copy, Clone, PartialEq, Eq, Default, Debug)]
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pub struct FqRepr(pub [u64; 6]);
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impl ::rand::Rand for FqRepr {
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#[inline(always)]
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fn rand<R: ::rand::Rng>(rng: &mut R) -> Self {
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FqRepr(rng.gen())
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}
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}
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impl ::std::fmt::Display for FqRepr {
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fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
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try!(write!(f, "0x"));
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for i in self.0.iter().rev() {
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try!(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 FqRepr {
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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 FqRepr {
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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 FqRepr {
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#[inline(always)]
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fn from(val: u64) -> FqRepr {
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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 FqRepr {
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#[inline(always)]
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fn cmp(&self, other: &FqRepr) -> 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 Ordering::Less;
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} else if a > b {
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return Ordering::Greater;
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}
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}
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Ordering::Equal
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}
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}
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impl PartialOrd for FqRepr {
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#[inline(always)]
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fn partial_cmp(&self, other: &FqRepr) -> Option<Ordering> {
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Some(self.cmp(other))
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}
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}
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impl PrimeFieldRepr for FqRepr {
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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 * 6 {
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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 * 6 {
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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 = (6 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: &FqRepr) {
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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 = ::ff::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: &FqRepr) {
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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 = ::ff::sbb(*a, *b, &mut borrow);
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}
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}
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}
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#[derive(Copy, Clone, PartialEq, Eq, Debug)]
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#[derive(PrimeField)]
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#[PrimeFieldModulus = "4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787"]
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#[PrimeFieldGenerator = "2"]
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pub struct Fq(FqRepr);
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/// `Fq` elements are ordered lexicographically.
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impl Ord for Fq {
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#[inline(always)]
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fn cmp(&self, other: &Fq) -> Ordering {
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self.into_repr().cmp(&other.into_repr())
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}
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}
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impl PartialOrd for Fq {
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#[inline(always)]
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fn partial_cmp(&self, other: &Fq) -> Option<Ordering> {
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Some(self.cmp(other))
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}
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}
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impl ::std::fmt::Display for Fq {
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fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
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write!(f, "Fq({})", self.into_repr())
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}
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}
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impl ::rand::Rand for Fq {
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fn rand<R: ::rand::Rng>(rng: &mut R) -> Self {
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loop {
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let mut tmp = Fq(FqRepr::rand(rng));
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// Mask away the unused bits at the beginning.
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tmp.0.as_mut()[5] &= 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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}
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impl From<Fq> for FqRepr {
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fn from(e: Fq) -> FqRepr {
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e.into_repr()
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}
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}
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impl PrimeField for Fq {
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type Repr = FqRepr;
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fn from_repr(r: FqRepr) -> Result<Fq, PrimeFieldDecodingError> {
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let mut r = Fq(r);
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if r.is_valid() {
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r.mul_assign(&Fq(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) -> FqRepr {
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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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(self.0).0[4],
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(self.0).0[5],
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0,
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0,
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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() -> FqRepr {
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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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Fq(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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Fq(ROOT_OF_UNITY)
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}
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}
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impl Field for Fq {
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#[inline]
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fn zero() -> Self {
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Fq(FqRepr::from(0))
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}
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#[inline]
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fn one() -> Self {
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Fq(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 add_assign(&mut self, other: &Fq) {
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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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#[inline]
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fn double(&mut self) {
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// This cannot exceed the backing capacity.
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self.0.mul2();
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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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#[inline]
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fn sub_assign(&mut self, other: &Fq) {
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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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#[inline]
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fn negate(&mut 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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}
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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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let one = FqRepr::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 = Fq(R2); // Avoids unnecessary reduction step.
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let mut c = Self::zero();
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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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while v.is_even() {
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v.div2();
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if c.0.is_even() {
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c.0.div2();
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} else {
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c.0.add_nocarry(&MODULUS);
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c.0.div2();
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}
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}
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if v < u {
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u.sub_noborrow(&v);
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b.sub_assign(&c);
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} else {
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v.sub_noborrow(&u);
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c.sub_assign(&b);
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}
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}
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if u == one {
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Some(b)
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} else {
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Some(c)
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}
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}
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}
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#[inline(always)]
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fn frobenius_map(&mut self, _: usize) {
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// This has no effect in a prime field.
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}
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#[inline]
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fn mul_assign(&mut self, other: &Fq) {
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let mut carry = 0;
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let r0 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[0], &mut carry);
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let r1 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[1], &mut carry);
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let r2 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[2], &mut carry);
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let r3 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[3], &mut carry);
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let r4 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[4], &mut carry);
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let r5 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[5], &mut carry);
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let r6 = carry;
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let mut carry = 0;
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let r1 = ::ff::mac_with_carry(r1, (self.0).0[1], (other.0).0[0], &mut carry);
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let r2 = ::ff::mac_with_carry(r2, (self.0).0[1], (other.0).0[1], &mut carry);
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let r3 = ::ff::mac_with_carry(r3, (self.0).0[1], (other.0).0[2], &mut carry);
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let r4 = ::ff::mac_with_carry(r4, (self.0).0[1], (other.0).0[3], &mut carry);
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let r5 = ::ff::mac_with_carry(r5, (self.0).0[1], (other.0).0[4], &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[1], (other.0).0[5], &mut carry);
|
||||
let r7 = carry;
|
||||
let mut carry = 0;
|
||||
let r2 = ::ff::mac_with_carry(r2, (self.0).0[2], (other.0).0[0], &mut carry);
|
||||
let r3 = ::ff::mac_with_carry(r3, (self.0).0[2], (other.0).0[1], &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[2], (other.0).0[2], &mut carry);
|
||||
let r5 = ::ff::mac_with_carry(r5, (self.0).0[2], (other.0).0[3], &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[2], (other.0).0[4], &mut carry);
|
||||
let r7 = ::ff::mac_with_carry(r7, (self.0).0[2], (other.0).0[5], &mut carry);
|
||||
let r8 = carry;
|
||||
let mut carry = 0;
|
||||
let r3 = ::ff::mac_with_carry(r3, (self.0).0[3], (other.0).0[0], &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[3], (other.0).0[1], &mut carry);
|
||||
let r5 = ::ff::mac_with_carry(r5, (self.0).0[3], (other.0).0[2], &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[3], (other.0).0[3], &mut carry);
|
||||
let r7 = ::ff::mac_with_carry(r7, (self.0).0[3], (other.0).0[4], &mut carry);
|
||||
let r8 = ::ff::mac_with_carry(r8, (self.0).0[3], (other.0).0[5], &mut carry);
|
||||
let r9 = carry;
|
||||
let mut carry = 0;
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[4], (other.0).0[0], &mut carry);
|
||||
let r5 = ::ff::mac_with_carry(r5, (self.0).0[4], (other.0).0[1], &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[4], (other.0).0[2], &mut carry);
|
||||
let r7 = ::ff::mac_with_carry(r7, (self.0).0[4], (other.0).0[3], &mut carry);
|
||||
let r8 = ::ff::mac_with_carry(r8, (self.0).0[4], (other.0).0[4], &mut carry);
|
||||
let r9 = ::ff::mac_with_carry(r9, (self.0).0[4], (other.0).0[5], &mut carry);
|
||||
let r10 = carry;
|
||||
let mut carry = 0;
|
||||
let r5 = ::ff::mac_with_carry(r5, (self.0).0[5], (other.0).0[0], &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[5], (other.0).0[1], &mut carry);
|
||||
let r7 = ::ff::mac_with_carry(r7, (self.0).0[5], (other.0).0[2], &mut carry);
|
||||
let r8 = ::ff::mac_with_carry(r8, (self.0).0[5], (other.0).0[3], &mut carry);
|
||||
let r9 = ::ff::mac_with_carry(r9, (self.0).0[5], (other.0).0[4], &mut carry);
|
||||
let r10 = ::ff::mac_with_carry(r10, (self.0).0[5], (other.0).0[5], &mut carry);
|
||||
let r11 = carry;
|
||||
self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11);
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn square(&mut self) {
|
||||
let mut carry = 0;
|
||||
let r1 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[1], &mut carry);
|
||||
let r2 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[2], &mut carry);
|
||||
let r3 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[3], &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[4], &mut carry);
|
||||
let r5 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[5], &mut carry);
|
||||
let r6 = carry;
|
||||
let mut carry = 0;
|
||||
let r3 = ::ff::mac_with_carry(r3, (self.0).0[1], (self.0).0[2], &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[1], (self.0).0[3], &mut carry);
|
||||
let r5 = ::ff::mac_with_carry(r5, (self.0).0[1], (self.0).0[4], &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[1], (self.0).0[5], &mut carry);
|
||||
let r7 = carry;
|
||||
let mut carry = 0;
|
||||
let r5 = ::ff::mac_with_carry(r5, (self.0).0[2], (self.0).0[3], &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[2], (self.0).0[4], &mut carry);
|
||||
let r7 = ::ff::mac_with_carry(r7, (self.0).0[2], (self.0).0[5], &mut carry);
|
||||
let r8 = carry;
|
||||
let mut carry = 0;
|
||||
let r7 = ::ff::mac_with_carry(r7, (self.0).0[3], (self.0).0[4], &mut carry);
|
||||
let r8 = ::ff::mac_with_carry(r8, (self.0).0[3], (self.0).0[5], &mut carry);
|
||||
let r9 = carry;
|
||||
let mut carry = 0;
|
||||
let r9 = ::ff::mac_with_carry(r9, (self.0).0[4], (self.0).0[5], &mut carry);
|
||||
let r10 = carry;
|
||||
|
||||
let r11 = r10 >> 63;
|
||||
let r10 = (r10 << 1) | (r9 >> 63);
|
||||
let r9 = (r9 << 1) | (r8 >> 63);
|
||||
let r8 = (r8 << 1) | (r7 >> 63);
|
||||
let r7 = (r7 << 1) | (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 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[0], &mut carry);
|
||||
let r1 = ::ff::adc(r1, 0, &mut carry);
|
||||
let r2 = ::ff::mac_with_carry(r2, (self.0).0[1], (self.0).0[1], &mut carry);
|
||||
let r3 = ::ff::adc(r3, 0, &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[2], (self.0).0[2], &mut carry);
|
||||
let r5 = ::ff::adc(r5, 0, &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[3], (self.0).0[3], &mut carry);
|
||||
let r7 = ::ff::adc(r7, 0, &mut carry);
|
||||
let r8 = ::ff::mac_with_carry(r8, (self.0).0[4], (self.0).0[4], &mut carry);
|
||||
let r9 = ::ff::adc(r9, 0, &mut carry);
|
||||
let r10 = ::ff::mac_with_carry(r10, (self.0).0[5], (self.0).0[5], &mut carry);
|
||||
let r11 = ::ff::adc(r11, 0, &mut carry);
|
||||
self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11);
|
||||
}
|
||||
}
|
||||
|
||||
impl Fq {
|
||||
/// 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,
|
||||
mut r8: u64,
|
||||
mut r9: u64,
|
||||
mut r10: u64,
|
||||
mut r11: 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;
|
||||
::ff::mac_with_carry(r0, k, MODULUS.0[0], &mut carry);
|
||||
r1 = ::ff::mac_with_carry(r1, k, MODULUS.0[1], &mut carry);
|
||||
r2 = ::ff::mac_with_carry(r2, k, MODULUS.0[2], &mut carry);
|
||||
r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[3], &mut carry);
|
||||
r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[4], &mut carry);
|
||||
r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[5], &mut carry);
|
||||
r6 = ::ff::adc(r6, 0, &mut carry);
|
||||
let carry2 = carry;
|
||||
let k = r1.wrapping_mul(INV);
|
||||
let mut carry = 0;
|
||||
::ff::mac_with_carry(r1, k, MODULUS.0[0], &mut carry);
|
||||
r2 = ::ff::mac_with_carry(r2, k, MODULUS.0[1], &mut carry);
|
||||
r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[2], &mut carry);
|
||||
r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[3], &mut carry);
|
||||
r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[4], &mut carry);
|
||||
r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[5], &mut carry);
|
||||
r7 = ::ff::adc(r7, carry2, &mut carry);
|
||||
let carry2 = carry;
|
||||
let k = r2.wrapping_mul(INV);
|
||||
let mut carry = 0;
|
||||
::ff::mac_with_carry(r2, k, MODULUS.0[0], &mut carry);
|
||||
r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[1], &mut carry);
|
||||
r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[2], &mut carry);
|
||||
r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[3], &mut carry);
|
||||
r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[4], &mut carry);
|
||||
r7 = ::ff::mac_with_carry(r7, k, MODULUS.0[5], &mut carry);
|
||||
r8 = ::ff::adc(r8, carry2, &mut carry);
|
||||
let carry2 = carry;
|
||||
let k = r3.wrapping_mul(INV);
|
||||
let mut carry = 0;
|
||||
::ff::mac_with_carry(r3, k, MODULUS.0[0], &mut carry);
|
||||
r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[1], &mut carry);
|
||||
r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[2], &mut carry);
|
||||
r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[3], &mut carry);
|
||||
r7 = ::ff::mac_with_carry(r7, k, MODULUS.0[4], &mut carry);
|
||||
r8 = ::ff::mac_with_carry(r8, k, MODULUS.0[5], &mut carry);
|
||||
r9 = ::ff::adc(r9, carry2, &mut carry);
|
||||
let carry2 = carry;
|
||||
let k = r4.wrapping_mul(INV);
|
||||
let mut carry = 0;
|
||||
::ff::mac_with_carry(r4, k, MODULUS.0[0], &mut carry);
|
||||
r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[1], &mut carry);
|
||||
r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[2], &mut carry);
|
||||
r7 = ::ff::mac_with_carry(r7, k, MODULUS.0[3], &mut carry);
|
||||
r8 = ::ff::mac_with_carry(r8, k, MODULUS.0[4], &mut carry);
|
||||
r9 = ::ff::mac_with_carry(r9, k, MODULUS.0[5], &mut carry);
|
||||
r10 = ::ff::adc(r10, carry2, &mut carry);
|
||||
let carry2 = carry;
|
||||
let k = r5.wrapping_mul(INV);
|
||||
let mut carry = 0;
|
||||
::ff::mac_with_carry(r5, k, MODULUS.0[0], &mut carry);
|
||||
r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[1], &mut carry);
|
||||
r7 = ::ff::mac_with_carry(r7, k, MODULUS.0[2], &mut carry);
|
||||
r8 = ::ff::mac_with_carry(r8, k, MODULUS.0[3], &mut carry);
|
||||
r9 = ::ff::mac_with_carry(r9, k, MODULUS.0[4], &mut carry);
|
||||
r10 = ::ff::mac_with_carry(r10, k, MODULUS.0[5], &mut carry);
|
||||
r11 = ::ff::adc(r11, carry2, &mut carry);
|
||||
(self.0).0[0] = r6;
|
||||
(self.0).0[1] = r7;
|
||||
(self.0).0[2] = r8;
|
||||
(self.0).0[3] = r9;
|
||||
(self.0).0[4] = r10;
|
||||
(self.0).0[5] = r11;
|
||||
self.reduce();
|
||||
}
|
||||
}
|
||||
|
||||
impl SqrtField for Fq {
|
||||
fn legendre(&self) -> ::ff::LegendreSymbol {
|
||||
// s = self^((q - 1) // 2)
|
||||
let s = self.pow([
|
||||
0xdcff7fffffffd555,
|
||||
0xf55ffff58a9ffff,
|
||||
0xb39869507b587b12,
|
||||
0xb23ba5c279c2895f,
|
||||
0x258dd3db21a5d66b,
|
||||
0xd0088f51cbff34d,
|
||||
]);
|
||||
if s == Fq::zero() {
|
||||
::ff::LegendreSymbol::Zero
|
||||
} else if s == Fq::one() {
|
||||
::ff::LegendreSymbol::QuadraticResidue
|
||||
} else {
|
||||
::ff::LegendreSymbol::QuadraticNonResidue
|
||||
}
|
||||
}
|
||||
|
||||
fn sqrt(&self) -> Option<Self> {
|
||||
// Shank's algorithm for q mod 4 = 3
|
||||
// https://eprint.iacr.org/2012/685.pdf (page 9, algorithm 2)
|
||||
|
||||
// a1 = self^((q - 3) // 4)
|
||||
let mut a1 = self.pow([
|
||||
0xee7fbfffffffeaaa,
|
||||
0x7aaffffac54ffff,
|
||||
0xd9cc34a83dac3d89,
|
||||
0xd91dd2e13ce144af,
|
||||
0x92c6e9ed90d2eb35,
|
||||
0x680447a8e5ff9a6,
|
||||
]);
|
||||
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_b_coeff() {
|
||||
assert_eq!(Fq::from_repr(FqRepr::from(4)).unwrap(), B_COEFF);
|
||||
@ -1897,6 +1177,8 @@ use rand::{Rand, SeedableRng, XorShiftRng};
|
||||
|
||||
#[test]
|
||||
fn test_fq_repr_ordering() {
|
||||
use std::cmp::Ordering;
|
||||
|
||||
fn assert_equality(a: FqRepr, b: FqRepr) {
|
||||
assert_eq!(a, b);
|
||||
assert!(a.cmp(&b) == Ordering::Equal);
|
||||
@ -2743,6 +2025,8 @@ fn test_fq_pow() {
|
||||
|
||||
#[test]
|
||||
fn test_fq_sqrt() {
|
||||
use ff::SqrtField;
|
||||
|
||||
let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
||||
|
||||
assert_eq!(Fq::zero().sqrt().unwrap(), Fq::zero());
|
||||
@ -2876,6 +2160,8 @@ fn test_fq_num_bits() {
|
||||
|
||||
#[test]
|
||||
fn test_fq_root_of_unity() {
|
||||
use ff::SqrtField;
|
||||
|
||||
assert_eq!(Fq::S, 1);
|
||||
assert_eq!(
|
||||
Fq::multiplicative_generator(),
|
||||
@ -2923,6 +2209,7 @@ fn fq_repr_tests() {
|
||||
#[test]
|
||||
fn test_fq_legendre() {
|
||||
use ff::LegendreSymbol::*;
|
||||
use ff::SqrtField;
|
||||
|
||||
assert_eq!(QuadraticResidue, Fq::one().legendre());
|
||||
assert_eq!(Zero, Fq::zero().legendre());
|
||||
|
||||
@ -1,646 +1,10 @@
|
||||
use ff::{Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr, SqrtField};
|
||||
use ff::{Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr};
|
||||
|
||||
// r = 52435875175126190479447740508185965837690552500527637822603658699938581184513
|
||||
const MODULUS: FrRepr = FrRepr([
|
||||
0xffffffff00000001,
|
||||
0x53bda402fffe5bfe,
|
||||
0x3339d80809a1d805,
|
||||
0x73eda753299d7d48,
|
||||
]);
|
||||
|
||||
// The number of bits needed to represent the modulus.
|
||||
const MODULUS_BITS: u32 = 255;
|
||||
|
||||
// The number of bits that must be shaved from the beginning of
|
||||
// the representation when randomly sampling.
|
||||
const REPR_SHAVE_BITS: u32 = 1;
|
||||
|
||||
// R = 2**256 % r
|
||||
const R: FrRepr = FrRepr([
|
||||
0x1fffffffe,
|
||||
0x5884b7fa00034802,
|
||||
0x998c4fefecbc4ff5,
|
||||
0x1824b159acc5056f,
|
||||
]);
|
||||
|
||||
// R2 = R^2 % r
|
||||
const R2: FrRepr = FrRepr([
|
||||
0xc999e990f3f29c6d,
|
||||
0x2b6cedcb87925c23,
|
||||
0x5d314967254398f,
|
||||
0x748d9d99f59ff11,
|
||||
]);
|
||||
|
||||
// INV = -(r^{-1} mod 2^64) mod 2^64
|
||||
const INV: u64 = 0xfffffffeffffffff;
|
||||
|
||||
// GENERATOR = 7 (multiplicative generator of r-1 order, that is also quadratic nonresidue)
|
||||
const GENERATOR: FrRepr = FrRepr([
|
||||
0xefffffff1,
|
||||
0x17e363d300189c0f,
|
||||
0xff9c57876f8457b0,
|
||||
0x351332208fc5a8c4,
|
||||
]);
|
||||
|
||||
// 2^s * t = MODULUS - 1 with t odd
|
||||
const S: u32 = 32;
|
||||
|
||||
// 2^s root of unity computed by GENERATOR^t
|
||||
const ROOT_OF_UNITY: FrRepr = FrRepr([
|
||||
0xb9b58d8c5f0e466a,
|
||||
0x5b1b4c801819d7ec,
|
||||
0xaf53ae352a31e64,
|
||||
0x5bf3adda19e9b27b,
|
||||
]);
|
||||
|
||||
#[derive(Copy, Clone, PartialEq, Eq, Default, Debug)]
|
||||
pub struct FrRepr(pub [u64; 4]);
|
||||
|
||||
impl ::rand::Rand for FrRepr {
|
||||
#[inline(always)]
|
||||
fn rand<R: ::rand::Rng>(rng: &mut R) -> Self {
|
||||
FrRepr(rng.gen())
|
||||
}
|
||||
}
|
||||
|
||||
impl ::std::fmt::Display for FrRepr {
|
||||
fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
|
||||
try!(write!(f, "0x"));
|
||||
for i in self.0.iter().rev() {
|
||||
try!(write!(f, "{:016x}", *i));
|
||||
}
|
||||
|
||||
Ok(())
|
||||
}
|
||||
}
|
||||
|
||||
impl AsRef<[u64]> for FrRepr {
|
||||
#[inline(always)]
|
||||
fn as_ref(&self) -> &[u64] {
|
||||
&self.0
|
||||
}
|
||||
}
|
||||
|
||||
impl AsMut<[u64]> for FrRepr {
|
||||
#[inline(always)]
|
||||
fn as_mut(&mut self) -> &mut [u64] {
|
||||
&mut self.0
|
||||
}
|
||||
}
|
||||
|
||||
impl From<u64> for FrRepr {
|
||||
#[inline(always)]
|
||||
fn from(val: u64) -> FrRepr {
|
||||
let mut repr = Self::default();
|
||||
repr.0[0] = val;
|
||||
repr
|
||||
}
|
||||
}
|
||||
|
||||
impl Ord for FrRepr {
|
||||
#[inline(always)]
|
||||
fn cmp(&self, other: &FrRepr) -> ::std::cmp::Ordering {
|
||||
for (a, b) in self.0.iter().rev().zip(other.0.iter().rev()) {
|
||||
if a < b {
|
||||
return ::std::cmp::Ordering::Less;
|
||||
} else if a > b {
|
||||
return ::std::cmp::Ordering::Greater;
|
||||
}
|
||||
}
|
||||
|
||||
::std::cmp::Ordering::Equal
|
||||
}
|
||||
}
|
||||
|
||||
impl PartialOrd for FrRepr {
|
||||
#[inline(always)]
|
||||
fn partial_cmp(&self, other: &FrRepr) -> Option<::std::cmp::Ordering> {
|
||||
Some(self.cmp(other))
|
||||
}
|
||||
}
|
||||
|
||||
impl PrimeFieldRepr for FrRepr {
|
||||
#[inline(always)]
|
||||
fn is_odd(&self) -> bool {
|
||||
self.0[0] & 1 == 1
|
||||
}
|
||||
|
||||
#[inline(always)]
|
||||
fn is_even(&self) -> bool {
|
||||
!self.is_odd()
|
||||
}
|
||||
|
||||
#[inline(always)]
|
||||
fn is_zero(&self) -> bool {
|
||||
self.0.iter().all(|&e| e == 0)
|
||||
}
|
||||
|
||||
#[inline(always)]
|
||||
fn shr(&mut self, mut n: u32) {
|
||||
if n >= 64 * 4 {
|
||||
*self = Self::from(0);
|
||||
return;
|
||||
}
|
||||
|
||||
while n >= 64 {
|
||||
let mut t = 0;
|
||||
for i in self.0.iter_mut().rev() {
|
||||
::std::mem::swap(&mut t, i);
|
||||
}
|
||||
n -= 64;
|
||||
}
|
||||
|
||||
if n > 0 {
|
||||
let mut t = 0;
|
||||
for i in self.0.iter_mut().rev() {
|
||||
let t2 = *i << (64 - n);
|
||||
*i >>= n;
|
||||
*i |= t;
|
||||
t = t2;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[inline(always)]
|
||||
fn div2(&mut self) {
|
||||
let mut t = 0;
|
||||
for i in self.0.iter_mut().rev() {
|
||||
let t2 = *i << 63;
|
||||
*i >>= 1;
|
||||
*i |= t;
|
||||
t = t2;
|
||||
}
|
||||
}
|
||||
|
||||
#[inline(always)]
|
||||
fn mul2(&mut self) {
|
||||
let mut last = 0;
|
||||
for i in &mut self.0 {
|
||||
let tmp = *i >> 63;
|
||||
*i <<= 1;
|
||||
*i |= last;
|
||||
last = tmp;
|
||||
}
|
||||
}
|
||||
|
||||
#[inline(always)]
|
||||
fn shl(&mut self, mut n: u32) {
|
||||
if n >= 64 * 4 {
|
||||
*self = Self::from(0);
|
||||
return;
|
||||
}
|
||||
|
||||
while n >= 64 {
|
||||
let mut t = 0;
|
||||
for i in &mut self.0 {
|
||||
::std::mem::swap(&mut t, i);
|
||||
}
|
||||
n -= 64;
|
||||
}
|
||||
|
||||
if n > 0 {
|
||||
let mut t = 0;
|
||||
for i in &mut self.0 {
|
||||
let t2 = *i >> (64 - n);
|
||||
*i <<= n;
|
||||
*i |= t;
|
||||
t = t2;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[inline(always)]
|
||||
fn num_bits(&self) -> u32 {
|
||||
let mut ret = (4 as u32) * 64;
|
||||
for i in self.0.iter().rev() {
|
||||
let leading = i.leading_zeros();
|
||||
ret -= leading;
|
||||
if leading != 64 {
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
ret
|
||||
}
|
||||
|
||||
#[inline(always)]
|
||||
fn add_nocarry(&mut self, other: &FrRepr) {
|
||||
let mut carry = 0;
|
||||
|
||||
for (a, b) in self.0.iter_mut().zip(other.0.iter()) {
|
||||
*a = ::ff::adc(*a, *b, &mut carry);
|
||||
}
|
||||
}
|
||||
|
||||
#[inline(always)]
|
||||
fn sub_noborrow(&mut self, other: &FrRepr) {
|
||||
let mut borrow = 0;
|
||||
|
||||
for (a, b) in self.0.iter_mut().zip(other.0.iter()) {
|
||||
*a = ::ff::sbb(*a, *b, &mut borrow);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[derive(Copy, Clone, PartialEq, Eq, Debug)]
|
||||
#[derive(PrimeField)]
|
||||
#[PrimeFieldModulus = "52435875175126190479447740508185965837690552500527637822603658699938581184513"]
|
||||
#[PrimeFieldGenerator = "7"]
|
||||
pub struct Fr(FrRepr);
|
||||
|
||||
impl ::std::fmt::Display for Fr {
|
||||
fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
|
||||
write!(f, "Fr({})", self.into_repr())
|
||||
}
|
||||
}
|
||||
|
||||
impl ::rand::Rand for Fr {
|
||||
fn rand<R: ::rand::Rng>(rng: &mut R) -> Self {
|
||||
loop {
|
||||
let mut tmp = Fr(FrRepr::rand(rng));
|
||||
|
||||
// Mask away the unused bits at the beginning.
|
||||
tmp.0.as_mut()[3] &= 0xffffffffffffffff >> REPR_SHAVE_BITS;
|
||||
|
||||
if tmp.is_valid() {
|
||||
return tmp;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl From<Fr> for FrRepr {
|
||||
fn from(e: Fr) -> FrRepr {
|
||||
e.into_repr()
|
||||
}
|
||||
}
|
||||
|
||||
impl PrimeField for Fr {
|
||||
type Repr = FrRepr;
|
||||
|
||||
fn from_repr(r: FrRepr) -> Result<Fr, PrimeFieldDecodingError> {
|
||||
let mut r = Fr(r);
|
||||
if r.is_valid() {
|
||||
r.mul_assign(&Fr(R2));
|
||||
|
||||
Ok(r)
|
||||
} else {
|
||||
Err(PrimeFieldDecodingError::NotInField(format!("{}", r.0)))
|
||||
}
|
||||
}
|
||||
|
||||
fn into_repr(&self) -> FrRepr {
|
||||
let mut r = *self;
|
||||
r.mont_reduce(
|
||||
(self.0).0[0],
|
||||
(self.0).0[1],
|
||||
(self.0).0[2],
|
||||
(self.0).0[3],
|
||||
0,
|
||||
0,
|
||||
0,
|
||||
0,
|
||||
);
|
||||
r.0
|
||||
}
|
||||
|
||||
fn char() -> FrRepr {
|
||||
MODULUS
|
||||
}
|
||||
|
||||
const NUM_BITS: u32 = MODULUS_BITS;
|
||||
|
||||
const CAPACITY: u32 = Self::NUM_BITS - 1;
|
||||
|
||||
fn multiplicative_generator() -> Self {
|
||||
Fr(GENERATOR)
|
||||
}
|
||||
|
||||
const S: u32 = S;
|
||||
|
||||
fn root_of_unity() -> Self {
|
||||
Fr(ROOT_OF_UNITY)
|
||||
}
|
||||
}
|
||||
|
||||
impl Field for Fr {
|
||||
#[inline]
|
||||
fn zero() -> Self {
|
||||
Fr(FrRepr::from(0))
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn one() -> Self {
|
||||
Fr(R)
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn is_zero(&self) -> bool {
|
||||
self.0.is_zero()
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn add_assign(&mut self, other: &Fr) {
|
||||
// This cannot exceed the backing capacity.
|
||||
self.0.add_nocarry(&other.0);
|
||||
|
||||
// However, it may need to be reduced.
|
||||
self.reduce();
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn double(&mut self) {
|
||||
// This cannot exceed the backing capacity.
|
||||
self.0.mul2();
|
||||
|
||||
// However, it may need to be reduced.
|
||||
self.reduce();
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn sub_assign(&mut self, other: &Fr) {
|
||||
// If `other` is larger than `self`, we'll need to add the modulus to self first.
|
||||
if other.0 > self.0 {
|
||||
self.0.add_nocarry(&MODULUS);
|
||||
}
|
||||
|
||||
self.0.sub_noborrow(&other.0);
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn negate(&mut self) {
|
||||
if !self.is_zero() {
|
||||
let mut tmp = MODULUS;
|
||||
tmp.sub_noborrow(&self.0);
|
||||
self.0 = tmp;
|
||||
}
|
||||
}
|
||||
|
||||
fn inverse(&self) -> Option<Self> {
|
||||
if self.is_zero() {
|
||||
None
|
||||
} else {
|
||||
// Guajardo Kumar Paar Pelzl
|
||||
// Efficient Software-Implementation of Finite Fields with Applications to Cryptography
|
||||
// Algorithm 16 (BEA for Inversion in Fp)
|
||||
|
||||
let one = FrRepr::from(1);
|
||||
|
||||
let mut u = self.0;
|
||||
let mut v = MODULUS;
|
||||
let mut b = Fr(R2); // Avoids unnecessary reduction step.
|
||||
let mut c = Self::zero();
|
||||
|
||||
while u != one && v != one {
|
||||
while u.is_even() {
|
||||
u.div2();
|
||||
|
||||
if b.0.is_even() {
|
||||
b.0.div2();
|
||||
} else {
|
||||
b.0.add_nocarry(&MODULUS);
|
||||
b.0.div2();
|
||||
}
|
||||
}
|
||||
|
||||
while v.is_even() {
|
||||
v.div2();
|
||||
|
||||
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 mul_assign(&mut self, other: &Fr) {
|
||||
let mut carry = 0;
|
||||
let r0 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[0], &mut carry);
|
||||
let r1 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[1], &mut carry);
|
||||
let r2 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[2], &mut carry);
|
||||
let r3 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[3], &mut carry);
|
||||
let r4 = carry;
|
||||
let mut carry = 0;
|
||||
let r1 = ::ff::mac_with_carry(r1, (self.0).0[1], (other.0).0[0], &mut carry);
|
||||
let r2 = ::ff::mac_with_carry(r2, (self.0).0[1], (other.0).0[1], &mut carry);
|
||||
let r3 = ::ff::mac_with_carry(r3, (self.0).0[1], (other.0).0[2], &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[1], (other.0).0[3], &mut carry);
|
||||
let r5 = carry;
|
||||
let mut carry = 0;
|
||||
let r2 = ::ff::mac_with_carry(r2, (self.0).0[2], (other.0).0[0], &mut carry);
|
||||
let r3 = ::ff::mac_with_carry(r3, (self.0).0[2], (other.0).0[1], &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[2], (other.0).0[2], &mut carry);
|
||||
let r5 = ::ff::mac_with_carry(r5, (self.0).0[2], (other.0).0[3], &mut carry);
|
||||
let r6 = carry;
|
||||
let mut carry = 0;
|
||||
let r3 = ::ff::mac_with_carry(r3, (self.0).0[3], (other.0).0[0], &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[3], (other.0).0[1], &mut carry);
|
||||
let r5 = ::ff::mac_with_carry(r5, (self.0).0[3], (other.0).0[2], &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[3], (other.0).0[3], &mut carry);
|
||||
let r7 = carry;
|
||||
self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7);
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn square(&mut self) {
|
||||
let mut carry = 0;
|
||||
let r1 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[1], &mut carry);
|
||||
let r2 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[2], &mut carry);
|
||||
let r3 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[3], &mut carry);
|
||||
let r4 = carry;
|
||||
let mut carry = 0;
|
||||
let r3 = ::ff::mac_with_carry(r3, (self.0).0[1], (self.0).0[2], &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[1], (self.0).0[3], &mut carry);
|
||||
let r5 = carry;
|
||||
let mut carry = 0;
|
||||
let r5 = ::ff::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 = ::ff::mac_with_carry(0, (self.0).0[0], (self.0).0[0], &mut carry);
|
||||
let r1 = ::ff::adc(r1, 0, &mut carry);
|
||||
let r2 = ::ff::mac_with_carry(r2, (self.0).0[1], (self.0).0[1], &mut carry);
|
||||
let r3 = ::ff::adc(r3, 0, &mut carry);
|
||||
let r4 = ::ff::mac_with_carry(r4, (self.0).0[2], (self.0).0[2], &mut carry);
|
||||
let r5 = ::ff::adc(r5, 0, &mut carry);
|
||||
let r6 = ::ff::mac_with_carry(r6, (self.0).0[3], (self.0).0[3], &mut carry);
|
||||
let r7 = ::ff::adc(r7, 0, &mut carry);
|
||||
self.mont_reduce(r0, r1, r2, r3, r4, r5, r6, r7);
|
||||
}
|
||||
}
|
||||
|
||||
impl Fr {
|
||||
/// 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;
|
||||
::ff::mac_with_carry(r0, k, MODULUS.0[0], &mut carry);
|
||||
r1 = ::ff::mac_with_carry(r1, k, MODULUS.0[1], &mut carry);
|
||||
r2 = ::ff::mac_with_carry(r2, k, MODULUS.0[2], &mut carry);
|
||||
r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[3], &mut carry);
|
||||
r4 = ::ff::adc(r4, 0, &mut carry);
|
||||
let carry2 = carry;
|
||||
let k = r1.wrapping_mul(INV);
|
||||
let mut carry = 0;
|
||||
::ff::mac_with_carry(r1, k, MODULUS.0[0], &mut carry);
|
||||
r2 = ::ff::mac_with_carry(r2, k, MODULUS.0[1], &mut carry);
|
||||
r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[2], &mut carry);
|
||||
r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[3], &mut carry);
|
||||
r5 = ::ff::adc(r5, carry2, &mut carry);
|
||||
let carry2 = carry;
|
||||
let k = r2.wrapping_mul(INV);
|
||||
let mut carry = 0;
|
||||
::ff::mac_with_carry(r2, k, MODULUS.0[0], &mut carry);
|
||||
r3 = ::ff::mac_with_carry(r3, k, MODULUS.0[1], &mut carry);
|
||||
r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[2], &mut carry);
|
||||
r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[3], &mut carry);
|
||||
r6 = ::ff::adc(r6, carry2, &mut carry);
|
||||
let carry2 = carry;
|
||||
let k = r3.wrapping_mul(INV);
|
||||
let mut carry = 0;
|
||||
::ff::mac_with_carry(r3, k, MODULUS.0[0], &mut carry);
|
||||
r4 = ::ff::mac_with_carry(r4, k, MODULUS.0[1], &mut carry);
|
||||
r5 = ::ff::mac_with_carry(r5, k, MODULUS.0[2], &mut carry);
|
||||
r6 = ::ff::mac_with_carry(r6, k, MODULUS.0[3], &mut carry);
|
||||
r7 = ::ff::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();
|
||||
}
|
||||
}
|
||||
|
||||
impl SqrtField for Fr {
|
||||
fn legendre(&self) -> ::ff::LegendreSymbol {
|
||||
// s = self^((r - 1) // 2)
|
||||
let s = self.pow([
|
||||
0x7fffffff80000000,
|
||||
0xa9ded2017fff2dff,
|
||||
0x199cec0404d0ec02,
|
||||
0x39f6d3a994cebea4,
|
||||
]);
|
||||
if s == Self::zero() {
|
||||
::ff::LegendreSymbol::Zero
|
||||
} else if s == Self::one() {
|
||||
::ff::LegendreSymbol::QuadraticResidue
|
||||
} else {
|
||||
::ff::LegendreSymbol::QuadraticNonResidue
|
||||
}
|
||||
}
|
||||
|
||||
fn sqrt(&self) -> Option<Self> {
|
||||
// Tonelli-Shank's algorithm for q mod 16 = 1
|
||||
// https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
|
||||
match self.legendre() {
|
||||
::ff::LegendreSymbol::Zero => Some(*self),
|
||||
::ff::LegendreSymbol::QuadraticNonResidue => None,
|
||||
::ff::LegendreSymbol::QuadraticResidue => {
|
||||
let mut c = Fr(ROOT_OF_UNITY);
|
||||
// r = self^((t + 1) // 2)
|
||||
let mut r = self.pow([
|
||||
0x7fff2dff80000000,
|
||||
0x4d0ec02a9ded201,
|
||||
0x94cebea4199cec04,
|
||||
0x39f6d3a9,
|
||||
]);
|
||||
// t = self^t
|
||||
let mut t = self.pow([
|
||||
0xfffe5bfeffffffff,
|
||||
0x9a1d80553bda402,
|
||||
0x299d7d483339d808,
|
||||
0x73eda753,
|
||||
]);
|
||||
let mut m = S;
|
||||
|
||||
while t != Self::one() {
|
||||
let mut i = 1;
|
||||
{
|
||||
let mut t2i = t;
|
||||
t2i.square();
|
||||
loop {
|
||||
if t2i == Self::one() {
|
||||
break;
|
||||
}
|
||||
t2i.square();
|
||||
i += 1;
|
||||
}
|
||||
}
|
||||
|
||||
for _ in 0..(m - i - 1) {
|
||||
c.square();
|
||||
}
|
||||
r.mul_assign(&c);
|
||||
c.square();
|
||||
t.mul_assign(&c);
|
||||
m = i;
|
||||
}
|
||||
|
||||
Some(r)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
use rand::{Rand, SeedableRng, XorShiftRng};
|
||||
|
||||
@ -909,6 +273,7 @@ fn test_fr_repr_sub_noborrow() {
|
||||
#[test]
|
||||
fn test_fr_legendre() {
|
||||
use ff::LegendreSymbol::*;
|
||||
use ff::SqrtField;
|
||||
|
||||
assert_eq!(QuadraticResidue, Fr::one().legendre());
|
||||
assert_eq!(Zero, Fr::zero().legendre());
|
||||
@ -1418,6 +783,8 @@ fn test_fr_pow() {
|
||||
|
||||
#[test]
|
||||
fn test_fr_sqrt() {
|
||||
use ff::SqrtField;
|
||||
|
||||
let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
||||
|
||||
assert_eq!(Fr::zero().sqrt().unwrap(), Fr::zero());
|
||||
@ -1583,6 +950,8 @@ fn test_fr_num_bits() {
|
||||
|
||||
#[test]
|
||||
fn test_fr_root_of_unity() {
|
||||
use ff::SqrtField;
|
||||
|
||||
assert_eq!(Fr::S, 32);
|
||||
assert_eq!(
|
||||
Fr::multiplicative_generator(),
|
||||
|
||||
@ -14,6 +14,7 @@
|
||||
#![deny(missing_debug_implementations)]
|
||||
|
||||
extern crate byteorder;
|
||||
#[macro_use]
|
||||
extern crate ff;
|
||||
extern crate rand;
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user