Use macros to instantiate finite fields.
This commit is contained in:
Sean Bowe
parent
a8c01aba09
commit
3ebd527167
16
src/arith.rs
16
src/arith.rs
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@ -7,7 +7,8 @@ use byteorder::{ByteOrder, BigEndian};
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/// 256-bit, stack allocated biginteger for use in prime field
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/// arithmetic.
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#[derive(Copy, Clone, Debug, PartialEq, Eq)]
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pub struct U256([u64; 4]);
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#[repr(C)]
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pub struct U256(pub [u64; 4]);
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impl Encodable for U256 {
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fn encode<S: Encoder>(&self, s: &mut S) -> Result<(), S::Error> {
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@ -40,7 +41,7 @@ impl Decodable for U256 {
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n[1] = BigEndian::read_u64(&buf[16..]);
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n[0] = BigEndian::read_u64(&buf[24..]);
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Ok(n.into())
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Ok(U256(n))
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}
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}
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@ -66,22 +67,15 @@ impl PartialOrd for U256 {
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}
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}
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impl From<[u64; 4]> for U256 {
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#[inline]
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fn from(a: [u64; 4]) -> U256 {
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U256(a)
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}
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}
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impl U256 {
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#[inline]
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pub fn zero() -> U256 {
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[0, 0, 0, 0].into()
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U256([0, 0, 0, 0])
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}
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#[inline]
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pub fn one() -> U256 {
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[1, 0, 0, 0].into()
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U256([1, 0, 0, 0])
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}
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/// Produce a random number (mod `modulo`)
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350
src/fields/fp.rs
350
src/fields/fp.rs
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@ -1,238 +1,174 @@
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use rand::Rng;
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use std::ops::{Add, Sub, Mul, Neg};
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use std::fmt;
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use std::marker::PhantomData;
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use super::FieldElement;
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use rustc_serialize::{Encodable, Encoder, Decodable, Decoder};
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use arith::U256;
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pub trait FpParams {
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fn name() -> &'static str;
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fn modulus() -> U256;
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fn inv() -> u64;
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fn rsquared() -> U256;
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fn rcubed() -> U256;
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fn one() -> U256;
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}
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macro_rules! field_impl {
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($name:ident, $modulus:expr, $rsquared:expr, $rcubed:expr, $one:expr, $inv:expr) => {
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#[derive(Copy, Clone, PartialEq, Eq, Debug)]
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#[repr(C)]
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pub struct $name(U256);
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#[repr(C)]
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pub struct Fp<P: FpParams>(U256, PhantomData<P>);
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impl<P: FpParams> Copy for Fp<P> { }
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impl<P: FpParams> Clone for Fp<P> {
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fn clone(&self) -> Self { *self }
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}
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impl<P: FpParams> PartialEq for Fp<P> {
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fn eq(&self, other: &Self) -> bool {
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self.0 == other.0
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}
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}
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impl<P: FpParams> Eq for Fp<P> { }
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impl<P: FpParams> fmt::Debug for Fp<P> {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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write!(f, "{}({:?})", P::name(), self.0)
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}
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}
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impl<P: FpParams> From<Fp<P>> for U256 {
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fn from(mut a: Fp<P>) -> Self {
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a.0.mul(&U256::one(), &P::modulus(), P::inv());
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impl From<$name> for U256 {
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#[inline]
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fn from(mut a: $name) -> Self {
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a.0.mul(&U256::one(), &U256($modulus), $inv);
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a.0
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}
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}
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a.0
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}
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}
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impl Encodable for $name {
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fn encode<S: Encoder>(&self, s: &mut S) -> Result<(), S::Error> {
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let normalized = U256::from(*self);
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#[inline]
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pub fn const_fp<P: FpParams, I: Into<U256>>(i: I) -> Fp<P> {
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Fp(i.into(), PhantomData)
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}
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normalized.encode(s)
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}
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}
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impl<P: FpParams> Encodable for Fp<P> {
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fn encode<S: Encoder>(&self, s: &mut S) -> Result<(), S::Error> {
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let normalized = U256::from(*self);
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impl Decodable for $name {
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fn decode<S: Decoder>(s: &mut S) -> Result<$name, S::Error> {
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$name::new(try!(U256::decode(s))).ok_or_else(|| s.error("integer is not less than modulus"))
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}
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}
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normalized.encode(s)
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}
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}
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impl $name {
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pub fn from_str(s: &str) -> Option<Self> {
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let ints: Vec<_> = {
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let mut acc = Self::zero();
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(0..11).map(|_| {let tmp = acc; acc = acc + Self::one(); tmp}).collect()
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};
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impl<P: FpParams> Decodable for Fp<P> {
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fn decode<S: Decoder>(s: &mut S) -> Result<Fp<P>, S::Error> {
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Fp::new(try!(U256::decode(s))).ok_or_else(|| s.error("integer is not less than modulus"))
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}
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}
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let mut res = Self::zero();
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for c in s.chars() {
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match c.to_digit(10) {
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Some(d) => {
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res = res * ints[10];
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res = res + ints[d as usize];
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},
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None => {
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return None;
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}
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}
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}
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impl<P: FpParams> Fp<P> {
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pub fn from_str(s: &str) -> Option<Self> {
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let ints: Vec<_> = {
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let mut acc = Self::zero();
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(0..11).map(|_| {let tmp = acc; acc = acc + Self::one(); tmp}).collect()
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};
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Some(res)
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}
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let mut res = Self::zero();
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for c in s.chars() {
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match c.to_digit(10) {
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Some(d) => {
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res = res * ints[10];
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res = res + ints[d as usize];
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},
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None => {
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return None;
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/// Converts a U256 to an Fp so long as it's below the modulus.
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pub fn new(mut a: U256) -> Option<Self> {
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if a < U256($modulus) {
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a.mul(&U256($rsquared), &U256($modulus), $inv);
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Some($name(a))
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} else {
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None
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}
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}
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}
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Some(res)
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}
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}
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impl FieldElement for $name {
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#[inline]
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fn zero() -> Self {
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$name(U256([0, 0, 0, 0]))
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}
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impl<P: FpParams> Fp<P> {
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/// Converts a U256 to an Fp so long as it's below the modulus.
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pub fn new(mut a: U256) -> Option<Self> {
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if a < P::modulus() {
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a.mul(&P::rsquared(), &P::modulus(), P::inv());
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#[inline]
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fn one() -> Self {
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$name(U256($one))
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}
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fn random<R: Rng>(rng: &mut R) -> Self {
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$name(U256::random(rng, &U256($modulus)))
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}
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Some(Fp(a, PhantomData))
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} else {
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None
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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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fn inverse(mut 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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self.0.invert(&U256($modulus));
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self.0.mul(&U256($rcubed), &U256($modulus), $inv);
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Some(self)
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}
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}
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}
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impl Add for $name {
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type Output = $name;
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#[inline]
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fn add(mut self, other: $name) -> $name {
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self.0.add(&other.0, &U256($modulus));
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self
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}
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}
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impl Sub for $name {
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type Output = $name;
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#[inline]
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fn sub(mut self, other: $name) -> $name {
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self.0.sub(&other.0, &U256($modulus));
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self
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}
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}
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impl Mul for $name {
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type Output = $name;
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#[inline]
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fn mul(mut self, other: $name) -> $name {
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self.0.mul(&other.0, &U256($modulus), $inv);
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self
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}
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}
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impl Neg for $name {
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type Output = $name;
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#[inline]
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fn neg(mut self) -> $name {
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self.0.neg(&U256($modulus));
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self
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}
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}
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}
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}
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impl<P: FpParams> FieldElement for Fp<P> {
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fn zero() -> Self {
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const_fp(U256::zero())
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}
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field_impl!(
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Fr,
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[0x43e1f593f0000001, 0x2833e84879b97091, 0xb85045b68181585d, 0x30644e72e131a029],
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[0x1bb8e645ae216da7, 0x53fe3ab1e35c59e3, 0x8c49833d53bb8085, 0x0216d0b17f4e44a5],
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[0x5e94d8e1b4bf0040, 0x2a489cbe1cfbb6b8, 0x893cc664a19fcfed, 0x0cf8594b7fcc657c],
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[0xac96341c4ffffffb, 0x36fc76959f60cd29, 0x666ea36f7879462e, 0xe0a77c19a07df2f],
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0xc2e1f593efffffff
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);
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fn one() -> Self {
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const_fp(P::one())
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}
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fn random<R: Rng>(rng: &mut R) -> Self {
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const_fp(U256::random(rng, &P::modulus()))
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}
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field_impl!(
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Fq,
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[0x3c208c16d87cfd47, 0x97816a916871ca8d, 0xb85045b68181585d, 0x30644e72e131a029],
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[0xf32cfc5b538afa89, 0xb5e71911d44501fb, 0x47ab1eff0a417ff6, 0x06d89f71cab8351f],
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[0xb1cd6dafda1530df, 0x62f210e6a7283db6, 0xef7f0b0c0ada0afb, 0x20fd6e902d592544],
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[0xd35d438dc58f0d9d, 0xa78eb28f5c70b3d, 0x666ea36f7879462c, 0xe0a77c19a07df2f],
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0x87d20782e4866389
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);
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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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fn inverse(mut 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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self.0.invert(&P::modulus());
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self.0.mul(&P::rcubed(), &P::modulus(), P::inv());
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Some(self)
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}
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}
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}
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impl<P: FpParams> Add for Fp<P> {
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type Output = Fp<P>;
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fn add(mut self, other: Fp<P>) -> Fp<P> {
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self.0.add(&other.0, &P::modulus());
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self
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}
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}
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impl<P: FpParams> Sub for Fp<P> {
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type Output = Fp<P>;
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fn sub(mut self, other: Fp<P>) -> Fp<P> {
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self.0.sub(&other.0, &P::modulus());
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self
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}
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}
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impl<P: FpParams> Mul for Fp<P> {
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type Output = Fp<P>;
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fn mul(mut self, other: Fp<P>) -> Fp<P> {
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self.0.mul(&other.0, &P::modulus(), P::inv());
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self
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}
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}
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impl<P: FpParams> Neg for Fp<P> {
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type Output = Fp<P>;
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fn neg(mut self) -> Fp<P> {
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self.0.neg(&P::modulus());
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self
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}
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}
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pub struct FrParams;
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pub type Fr = Fp<FrParams>;
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impl FpParams for FrParams {
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fn name() -> &'static str { "Fr" }
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#[inline]
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fn modulus() -> U256 {
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// 21888242871839275222246405745257275088548364400416034343698204186575808495617
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[0x43e1f593f0000001, 0x2833e84879b97091, 0xb85045b68181585d, 0x30644e72e131a029].into()
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}
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#[inline]
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fn inv() -> u64 {
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0xc2e1f593efffffff
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}
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#[inline]
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fn rsquared() -> U256 {
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// 944936681149208446651664254269745548490766851729442924617792859073125903783
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[0x1bb8e645ae216da7, 0x53fe3ab1e35c59e3, 0x8c49833d53bb8085, 0x0216d0b17f4e44a5].into()
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}
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#[inline]
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fn rcubed() -> U256 {
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// 5866548545943845227489894872040244720403868105578784105281690076696998248512
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[0x5e94d8e1b4bf0040, 0x2a489cbe1cfbb6b8, 0x893cc664a19fcfed, 0x0cf8594b7fcc657c].into()
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}
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#[inline]
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fn one() -> U256 {
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[0xac96341c4ffffffb, 0x36fc76959f60cd29, 0x666ea36f7879462e, 0xe0a77c19a07df2f].into()
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}
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}
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pub struct FqParams;
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pub type Fq = Fp<FqParams>;
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impl FpParams for FqParams {
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fn name() -> &'static str { "Fq" }
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#[inline]
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fn modulus() -> U256 {
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// 21888242871839275222246405745257275088696311157297823662689037894645226208583
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[0x3c208c16d87cfd47, 0x97816a916871ca8d, 0xb85045b68181585d, 0x30644e72e131a029].into()
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}
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#[inline]
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fn inv() -> u64 {
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0x87d20782e4866389
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}
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#[inline]
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fn rsquared() -> U256 {
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// 3096616502983703923843567936837374451735540968419076528771170197431451843209
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[0xf32cfc5b538afa89, 0xb5e71911d44501fb, 0x47ab1eff0a417ff6, 0x06d89f71cab8351f].into()
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}
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#[inline]
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fn rcubed() -> U256 {
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// 14921786541159648185948152738563080959093619838510245177710943249661917737183
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[0xb1cd6dafda1530df, 0x62f210e6a7283db6, 0xef7f0b0c0ada0afb, 0x20fd6e902d592544].into()
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}
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#[inline]
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fn one() -> U256 {
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[0xd35d438dc58f0d9d, 0xa78eb28f5c70b3d, 0x666ea36f7879462c, 0xe0a77c19a07df2f].into()
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}
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#[inline]
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pub fn const_fq(i: [u64; 4]) -> Fq {
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Fq(U256(i))
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}
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#[test]
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@ -1,4 +1,4 @@
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use fields::{FieldElement, Fq2, Fq, Fq6, const_fp};
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use fields::{FieldElement, Fq2, Fq, Fq6, const_fq};
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use std::ops::{Add, Sub, Mul, Neg};
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use rand::Rng;
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@ -8,16 +8,16 @@ fn frobenius_coeffs_c1(power: usize) -> Fq2 {
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match power % 12 {
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0 => Fq2::one(),
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1 => Fq2::new(
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const_fp([12653890742059813127, 14585784200204367754, 1278438861261381767, 212598772761311868]),
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const_fp([11683091849979440498, 14992204589386555739, 15866167890766973222, 1200023580730561873])
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const_fq([12653890742059813127, 14585784200204367754, 1278438861261381767, 212598772761311868]),
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const_fq([11683091849979440498, 14992204589386555739, 15866167890766973222, 1200023580730561873])
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),
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2 => Fq2::new(
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const_fp([14595462726357228530, 17349508522658994025, 1017833795229664280, 299787779797702374]),
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const_fq([14595462726357228530, 17349508522658994025, 1017833795229664280, 299787779797702374]),
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Fq::zero()
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),
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3 => Fq2::new(
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const_fp([3914496794763385213, 790120733010914719, 7322192392869644725, 581366264293887267]),
|
||||
const_fp([12817045492518885689, 4440270538777280383, 11178533038884588256, 2767537931541304486])
|
||||
const_fq([3914496794763385213, 790120733010914719, 7322192392869644725, 581366264293887267]),
|
||||
const_fq([12817045492518885689, 4440270538777280383, 11178533038884588256, 2767537931541304486])
|
||||
),
|
||||
_ => unimplemented!()
|
||||
}
|
||||
|
|
@ -96,7 +96,7 @@ impl Fq12 {
|
|||
|
||||
pub fn exp_by_neg_z(&self) -> Fq12 {
|
||||
self.cyclotomic_pow(
|
||||
U256::from([4965661367192848881, 0, 0, 0])
|
||||
U256([4965661367192848881, 0, 0, 0])
|
||||
).unitary_inverse()
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
use fields::{FieldElement, const_fp, Fq};
|
||||
use fields::{FieldElement, const_fq, Fq};
|
||||
use std::ops::{Add, Sub, Mul, Neg};
|
||||
use rand::Rng;
|
||||
|
||||
|
|
@ -8,14 +8,14 @@ use rustc_serialize::{Encodable, Encoder, Decodable, Decoder};
|
|||
fn fq_non_residue() -> Fq {
|
||||
// (q - 1) is a quadratic nonresidue in Fq
|
||||
// 21888242871839275222246405745257275088696311157297823662689037894645226208582
|
||||
const_fp([0x68c3488912edefaa, 0x8d087f6872aabf4f, 0x51e1a24709081231, 0x2259d6b14729c0fa])
|
||||
const_fq([0x68c3488912edefaa, 0x8d087f6872aabf4f, 0x51e1a24709081231, 0x2259d6b14729c0fa])
|
||||
}
|
||||
|
||||
#[inline]
|
||||
pub fn fq2_nonresidue() -> Fq2 {
|
||||
Fq2::new(
|
||||
const_fp([0xf60647ce410d7ff7, 0x2f3d6f4dd31bd011, 0x2943337e3940c6d1, 0x1d9598e8a7e39857]),
|
||||
const_fp([0xd35d438dc58f0d9d, 0x0a78eb28f5c70b3d, 0x666ea36f7879462c, 0x0e0a77c19a07df2f])
|
||||
const_fq([0xf60647ce410d7ff7, 0x2f3d6f4dd31bd011, 0x2943337e3940c6d1, 0x1d9598e8a7e39857]),
|
||||
const_fq([0xd35d438dc58f0d9d, 0x0a78eb28f5c70b3d, 0x666ea36f7879462c, 0x0e0a77c19a07df2f])
|
||||
)
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
use fields::{FieldElement, Fq, Fq2, const_fp};
|
||||
use fields::{FieldElement, Fq, Fq2, const_fq};
|
||||
use std::ops::{Add, Sub, Mul, Neg};
|
||||
use rand::Rng;
|
||||
|
||||
|
|
@ -6,16 +6,16 @@ fn frobenius_coeffs_c1(n: usize) -> Fq2 {
|
|||
match n % 6 {
|
||||
0 => Fq2::one(),
|
||||
1 => Fq2::new(
|
||||
const_fp([13075984984163199792, 3782902503040509012, 8791150885551868305, 1825854335138010348]),
|
||||
const_fp([7963664994991228759, 12257807996192067905, 13179524609921305146, 2767831111890561987])
|
||||
const_fq([13075984984163199792, 3782902503040509012, 8791150885551868305, 1825854335138010348]),
|
||||
const_fq([7963664994991228759, 12257807996192067905, 13179524609921305146, 2767831111890561987])
|
||||
),
|
||||
2 => Fq2::new(
|
||||
const_fp([3697675806616062876, 9065277094688085689, 6918009208039626314, 2775033306905974752]),
|
||||
const_fq([3697675806616062876, 9065277094688085689, 6918009208039626314, 2775033306905974752]),
|
||||
Fq::zero()
|
||||
),
|
||||
3 => Fq2::new(
|
||||
const_fp([14532872967180610477, 12903226530429559474, 1868623743233345524, 2316889217940299650]),
|
||||
const_fp([12447993766991532972, 4121872836076202828, 7630813605053367399, 740282956577754197])
|
||||
const_fq([14532872967180610477, 12903226530429559474, 1868623743233345524, 2316889217940299650]),
|
||||
const_fq([12447993766991532972, 4121872836076202828, 7630813605053367399, 740282956577754197])
|
||||
),
|
||||
_ => unimplemented!()
|
||||
}
|
||||
|
|
@ -24,16 +24,16 @@ fn frobenius_coeffs_c2(n: usize) -> Fq2 {
|
|||
match n % 6 {
|
||||
0 => Fq2::one(),
|
||||
1 => Fq2::new(
|
||||
const_fp([8314163329781907090, 11942187022798819835, 11282677263046157209, 1576150870752482284]),
|
||||
const_fp([6763840483288992073, 7118829427391486816, 4016233444936635065, 2630958277570195709])
|
||||
const_fq([8314163329781907090, 11942187022798819835, 11282677263046157209, 1576150870752482284]),
|
||||
const_fq([6763840483288992073, 7118829427391486816, 4016233444936635065, 2630958277570195709])
|
||||
),
|
||||
2 => Fq2::new(
|
||||
const_fp([8183898218631979349, 12014359695528440611, 12263358156045030468, 3187210487005268291]),
|
||||
const_fq([8183898218631979349, 12014359695528440611, 12263358156045030468, 3187210487005268291]),
|
||||
Fq::zero()
|
||||
),
|
||||
3 => Fq2::new(
|
||||
const_fp([4938922280314430175, 13823286637238282975, 15589480384090068090, 481952561930628184]),
|
||||
const_fp([3105754162722846417, 11647802298615474591, 13057042392041828081, 1660844386505564338])
|
||||
const_fq([4938922280314430175, 13823286637238282975, 15589480384090068090, 481952561930628184]),
|
||||
const_fq([3105754162722846417, 11647802298615474591, 13057042392041828081, 1660844386505564338])
|
||||
),
|
||||
_ => unimplemented!()
|
||||
}
|
||||
|
|
|
|||
|
|
@ -8,7 +8,7 @@ use rand::Rng;
|
|||
use std::ops::{Add, Sub, Mul, Neg};
|
||||
use std::fmt::Debug;
|
||||
|
||||
pub use self::fp::{Fq,Fr,const_fp};
|
||||
pub use self::fp::{Fq,Fr,const_fq};
|
||||
pub use self::fq2::{Fq2, fq2_nonresidue};
|
||||
pub use self::fq6::Fq6;
|
||||
pub use self::fq12::Fq12;
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
use std::ops::{Add,Sub,Neg,Mul};
|
||||
use fields::{FieldElement, Fq, Fq2, Fq12, Fr, const_fp, fq2_nonresidue};
|
||||
use fields::{FieldElement, Fq, Fq2, Fq12, Fr, const_fq, fq2_nonresidue};
|
||||
use arith::U256;
|
||||
use std::fmt;
|
||||
use rand::Rng;
|
||||
|
|
@ -334,13 +334,13 @@ impl GroupParams for G1Params {
|
|||
fn one() -> G<Self> {
|
||||
G {
|
||||
x: Fq::one(),
|
||||
y: const_fp([0xa6ba871b8b1e1b3a, 0x14f1d651eb8e167b, 0xccdd46def0f28c58, 0x1c14ef83340fbe5e]),
|
||||
y: const_fq([0xa6ba871b8b1e1b3a, 0x14f1d651eb8e167b, 0xccdd46def0f28c58, 0x1c14ef83340fbe5e]),
|
||||
z: Fq::one()
|
||||
}
|
||||
}
|
||||
|
||||
fn coeff_b() -> Fq {
|
||||
const_fp([0x7a17caa950ad28d7, 0x1f6ac17ae15521b9, 0x334bea4e696bd284, 0x2a1f6744ce179d8e])
|
||||
const_fq([0x7a17caa950ad28d7, 0x1f6ac17ae15521b9, 0x334bea4e696bd284, 0x2a1f6744ce179d8e])
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -356,12 +356,12 @@ impl GroupParams for G2Params {
|
|||
fn one() -> G<Self> {
|
||||
G {
|
||||
x: Fq2::new(
|
||||
const_fp([0x8e83b5d102bc2026, 0xdceb1935497b0172, 0xfbb8264797811adf, 0x19573841af96503b]),
|
||||
const_fp([0xafb4737da84c6140, 0x6043dd5a5802d8c4, 0x09e950fc52a02f86, 0x14fef0833aea7b6b])
|
||||
const_fq([0x8e83b5d102bc2026, 0xdceb1935497b0172, 0xfbb8264797811adf, 0x19573841af96503b]),
|
||||
const_fq([0xafb4737da84c6140, 0x6043dd5a5802d8c4, 0x09e950fc52a02f86, 0x14fef0833aea7b6b])
|
||||
),
|
||||
y: Fq2::new(
|
||||
const_fp([0x619dfa9d886be9f6, 0xfe7fd297f59e9b78, 0xff9e1a62231b7dfe, 0x28fd7eebae9e4206]),
|
||||
const_fp([0x64095b56c71856ee, 0xdc57f922327d3cbb, 0x55f935be33351076, 0x0da4a0e693fd6482])
|
||||
const_fq([0x619dfa9d886be9f6, 0xfe7fd297f59e9b78, 0xff9e1a62231b7dfe, 0x28fd7eebae9e4206]),
|
||||
const_fq([0x64095b56c71856ee, 0xdc57f922327d3cbb, 0x55f935be33351076, 0x0da4a0e693fd6482])
|
||||
),
|
||||
z: Fq2::one()
|
||||
}
|
||||
|
|
@ -369,8 +369,8 @@ impl GroupParams for G2Params {
|
|||
|
||||
fn coeff_b() -> Fq2 {
|
||||
Fq2::new(
|
||||
const_fp([0x3bf938e377b802a8, 0x020b1b273633535d, 0x26b7edf049755260, 0x2514c6324384a86d]),
|
||||
const_fp([0x38e7ecccd1dcff67, 0x65f0b37d93ce0d3e, 0xd749d0dd22ac00aa, 0x0141b9ce4a688d4d])
|
||||
const_fq([0x3bf938e377b802a8, 0x020b1b273633535d, 0x26b7edf049755260, 0x2514c6324384a86d]),
|
||||
const_fq([0x38e7ecccd1dcff67, 0x65f0b37d93ce0d3e, 0xd749d0dd22ac00aa, 0x0141b9ce4a688d4d])
|
||||
)
|
||||
}
|
||||
}
|
||||
|
|
@ -421,27 +421,27 @@ fn twist() -> Fq2 {
|
|||
|
||||
#[inline]
|
||||
fn two_inv() -> Fq {
|
||||
const_fp([9781510331150239090, 15059239858463337189, 10331104244869713732, 2249375503248834476])
|
||||
const_fq([9781510331150239090, 15059239858463337189, 10331104244869713732, 2249375503248834476])
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn ate_loop_count() -> U256 {
|
||||
[0x9d797039be763ba8, 0x0000000000000001, 0x0000000000000000, 0x0000000000000000].into()
|
||||
U256([0x9d797039be763ba8, 0x0000000000000001, 0x0000000000000000, 0x0000000000000000])
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn twist_mul_by_q_x() -> Fq2 {
|
||||
Fq2::new(
|
||||
const_fp([13075984984163199792, 3782902503040509012, 8791150885551868305, 1825854335138010348]),
|
||||
const_fp([7963664994991228759, 12257807996192067905, 13179524609921305146, 2767831111890561987])
|
||||
const_fq([13075984984163199792, 3782902503040509012, 8791150885551868305, 1825854335138010348]),
|
||||
const_fq([7963664994991228759, 12257807996192067905, 13179524609921305146, 2767831111890561987])
|
||||
)
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn twist_mul_by_q_y() -> Fq2 {
|
||||
Fq2::new(
|
||||
const_fp([16482010305593259561, 13488546290961988299, 3578621962720924518, 2681173117283399901]),
|
||||
const_fp([11661927080404088775, 553939530661941723, 7860678177968807019, 3208568454732775116])
|
||||
const_fq([16482010305593259561, 13488546290961988299, 3578621962720924518, 2681173117283399901]),
|
||||
const_fq([11661927080404088775, 553939530661941723, 7860678177968807019, 3208568454732775116])
|
||||
)
|
||||
}
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue