zec
/
librustzcash
mirror of https://github.com/zcash/librustzcash.git
1
0
Fork 0
Code Issues Projects Releases Wiki Activity

Replace implementations of Fq and Fr with derives

This commit is contained in:
Jack Grigg 2018-07-02 06:57:05 +01:00
parent d9d711ebb7
commit a9d8079c2a
No known key found for this signature in database
GPG Key ID: 1B8D649257DB0829
4 changed files with 22 additions and 1365 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
benches/bls12_381/fr.rs
View File

@ -1,6 +1,6 @@
use rand::{Rand, SeedableRng, XorShiftRng};
use ff::{Field, PrimeField, PrimeFieldRepr, SqrtField};
use ff::{Field, PrimeField, PrimeFieldRepr};
use pairing::bls12_381::*;
#[bench]

735
src/bls12_381/fq.rs
View File

@ -1,69 +1,5 @@
use super::fq2::Fq2;
use std::cmp::Ordering;
use {Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr, SqrtField};
// q = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
const MODULUS: FqRepr = FqRepr([
0xb9feffffffffaaab,
0x1eabfffeb153ffff,
0x6730d2a0f6b0f624,
0x64774b84f38512bf,
0x4b1ba7b6434bacd7,
0x1a0111ea397fe69a,
]);
// The number of bits needed to represent the modulus.
const MODULUS_BITS: u32 = 381;
// The number of bits that must be shaved from the beginning of
// the representation when randomly sampling.
const REPR_SHAVE_BITS: u32 = 3;
// R = 2**384 % q
const R: FqRepr = FqRepr([
0x760900000002fffd,
0xebf4000bc40c0002,
0x5f48985753c758ba,
0x77ce585370525745,
0x5c071a97a256ec6d,
0x15f65ec3fa80e493,
]);
// R2 = R^2 % q
const R2: FqRepr = FqRepr([
0xf4df1f341c341746,
0xa76e6a609d104f1,
0x8de5476c4c95b6d5,
0x67eb88a9939d83c0,
0x9a793e85b519952d,
0x11988fe592cae3aa,
]);
// INV = -(q^{-1} mod 2^64) mod 2^64
const INV: u64 = 0x89f3fffcfffcfffd;
// GENERATOR = 2 (multiplicative generator of q-1 order, that is also quadratic nonresidue)
const GENERATOR: FqRepr = FqRepr([
0x321300000006554f,
0xb93c0018d6c40005,
0x57605e0db0ddbb51,
0x8b256521ed1f9bcb,
0x6cf28d7901622c03,
0x11ebab9dbb81e28c,
]);
// 2^s * t = MODULUS - 1 with t odd
const S: u32 = 1;
// 2^s root of unity computed by GENERATOR^t
const ROOT_OF_UNITY: FqRepr = FqRepr([
0x43f5fffffffcaaae,
0x32b7fff2ed47fffd,
0x7e83a49a2e99d69,
0xeca8f3318332bb7a,
0xef148d1ea0f4c069,
0x40ab3263eff0206,
]);
use {Field, PrimeField, PrimeFieldDecodingError, PrimeFieldRepr};
// B coefficient of BLS12-381 curve, 4.
pub const B_COEFF: Fq = Fq(FqRepr([
@ -507,667 +443,11 @@ pub const NEGATIVE_ONE: Fq = Fq(FqRepr([
0x40ab3263eff0206,
]));
#[derive(Copy, Clone, PartialEq, Eq, Default, Debug)]
pub struct FqRepr(pub [u64; 6]);
impl ::rand::Rand for FqRepr {
#[inline(always)]
fn rand<R: ::rand::Rng>(rng: &mut R) -> Self {
FqRepr(rng.gen())
}
}
impl ::std::fmt::Display for FqRepr {
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 FqRepr {
#[inline(always)]
fn as_ref(&self) -> &[u64] {
&self.0
}
}
impl AsMut<[u64]> for FqRepr {
#[inline(always)]
fn as_mut(&mut self) -> &mut [u64] {
&mut self.0
}
}
impl From<u64> for FqRepr {
#[inline(always)]
fn from(val: u64) -> FqRepr {
let mut repr = Self::default();
repr.0[0] = val;
repr
}
}
impl Ord for FqRepr {
#[inline(always)]
fn cmp(&self, other: &FqRepr) -> Ordering {
for (a, b) in self.0.iter().rev().zip(other.0.iter().rev()) {
if a < b {
return Ordering::Less;
} else if a > b {
return Ordering::Greater;
}
}
Ordering::Equal
}
}
impl PartialOrd for FqRepr {
#[inline(always)]
fn partial_cmp(&self, other: &FqRepr) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl PrimeFieldRepr for FqRepr {
#[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 * 6 {
*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 * 6 {
*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 = (6 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: &FqRepr) {
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: &FqRepr) {
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 = "4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787"]
#[PrimeFieldGenerator = "2"]
pub struct Fq(FqRepr);
/// `Fq` elements are ordered lexicographically.
impl Ord for Fq {
#[inline(always)]
fn cmp(&self, other: &Fq) -> Ordering {
self.into_repr().cmp(&other.into_repr())
}
}
impl PartialOrd for Fq {
#[inline(always)]
fn partial_cmp(&self, other: &Fq) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl ::std::fmt::Display for Fq {
fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
write!(f, "Fq({})", self.into_repr())
}
}
impl ::rand::Rand for Fq {
fn rand<R: ::rand::Rng>(rng: &mut R) -> Self {
loop {
let mut tmp = Fq(FqRepr::rand(rng));
// Mask away the unused bits at the beginning.
tmp.0.as_mut()[5] &= 0xffffffffffffffff >> REPR_SHAVE_BITS;
if tmp.is_valid() {
return tmp;
}
}
}
}
impl From<Fq> for FqRepr {
fn from(e: Fq) -> FqRepr {
e.into_repr()
}
}
impl PrimeField for Fq {
type Repr = FqRepr;
fn from_repr(r: FqRepr) -> Result<Fq, PrimeFieldDecodingError> {
let mut r = Fq(r);
if r.is_valid() {
r.mul_assign(&Fq(R2));
Ok(r)
} else {
Err(PrimeFieldDecodingError::NotInField(format!("{}", r.0)))
}
}
fn into_repr(&self) -> FqRepr {
let mut r = *self;
r.mont_reduce(
(self.0).0[0],
(self.0).0[1],
(self.0).0[2],
(self.0).0[3],
(self.0).0[4],
(self.0).0[5],
0,
0,
0,
0,
0,
0,
);
r.0
}
fn char() -> FqRepr {
MODULUS
}
const NUM_BITS: u32 = MODULUS_BITS;
const CAPACITY: u32 = Self::NUM_BITS - 1;
fn multiplicative_generator() -> Self {
Fq(GENERATOR)
}
const S: u32 = S;
fn root_of_unity() -> Self {
Fq(ROOT_OF_UNITY)
}
}
impl Field for Fq {
#[inline]
fn zero() -> Self {
Fq(FqRepr::from(0))
}
#[inline]
fn one() -> Self {
Fq(R)
}
#[inline]
fn is_zero(&self) -> bool {
self.0.is_zero()
}
#[inline]
fn add_assign(&mut self, other: &Fq) {
// 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: &Fq) {
// 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 = FqRepr::from(1);
let mut u = self.0;
let mut v = MODULUS;
let mut b = Fq(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: &Fq) {
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 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[4], &mut carry);
let r5 = ::ff::mac_with_carry(0, (self.0).0[0], (other.0).0[5], &mut carry);
let r6 = 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 = ::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());

649
src/bls12_381/fr.rs
View File

@ -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(),

1
src/lib.rs
View File

@ -14,6 +14,7 @@
#![deny(missing_debug_implementations)]
extern crate byteorder;
#[macro_use]
extern crate ff;
extern crate rand;