mirror of
https://github.com/Qortal/pirate-librustzcash.git
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Add 'pairing/' from commit '09b6e6f9212020f385218e5cf5287e381ccd312b'
git-subtree-dir: pairing git-subtree-mainline:ad16ba6a35git-subtree-split:09b6e6f921
This commit is contained in:
Jack Grigg
908
pairing/src/bls12_381/fq2.rs
Normal file
908
pairing/src/bls12_381/fq2.rs
Normal file
@@ -0,0 +1,908 @@
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use super::fq::{FROBENIUS_COEFF_FQ2_C1, Fq, NEGATIVE_ONE};
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use rand::{Rand, Rng};
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use {Field, SqrtField};
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use std::cmp::Ordering;
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/// An element of Fq2, represented by c0 + c1 * u.
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#[derive(Copy, Clone, Debug, Eq, PartialEq)]
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pub struct Fq2 {
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pub c0: Fq,
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pub c1: Fq,
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}
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impl ::std::fmt::Display for Fq2 {
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fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
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write!(f, "Fq2({} + {} * u)", self.c0, self.c1)
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}
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}
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/// `Fq2` elements are ordered lexicographically.
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impl Ord for Fq2 {
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#[inline(always)]
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fn cmp(&self, other: &Fq2) -> Ordering {
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match self.c1.cmp(&other.c1) {
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Ordering::Greater => Ordering::Greater,
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Ordering::Less => Ordering::Less,
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Ordering::Equal => self.c0.cmp(&other.c0),
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}
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}
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}
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impl PartialOrd for Fq2 {
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#[inline(always)]
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fn partial_cmp(&self, other: &Fq2) -> Option<Ordering> {
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Some(self.cmp(other))
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}
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}
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impl Fq2 {
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/// Multiply this element by the cubic and quadratic nonresidue 1 + u.
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pub fn mul_by_nonresidue(&mut self) {
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let t0 = self.c0;
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self.c0.sub_assign(&self.c1);
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self.c1.add_assign(&t0);
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}
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/// Norm of Fq2 as extension field in i over Fq
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pub fn norm(&self) -> Fq {
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let mut t0 = self.c0;
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let mut t1 = self.c1;
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t0.square();
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t1.square();
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t1.add_assign(&t0);
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t1
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}
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}
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impl Rand for Fq2 {
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fn rand<R: Rng>(rng: &mut R) -> Self {
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Fq2 {
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c0: rng.gen(),
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c1: rng.gen(),
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}
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}
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}
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impl Field for Fq2 {
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fn zero() -> Self {
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Fq2 {
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c0: Fq::zero(),
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c1: Fq::zero(),
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}
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}
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fn one() -> Self {
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Fq2 {
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c0: Fq::one(),
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c1: Fq::zero(),
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}
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}
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fn is_zero(&self) -> bool {
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self.c0.is_zero() && self.c1.is_zero()
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}
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fn square(&mut self) {
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let mut ab = self.c0;
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ab.mul_assign(&self.c1);
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let mut c0c1 = self.c0;
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c0c1.add_assign(&self.c1);
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let mut c0 = self.c1;
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c0.negate();
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c0.add_assign(&self.c0);
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c0.mul_assign(&c0c1);
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c0.sub_assign(&ab);
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self.c1 = ab;
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self.c1.add_assign(&ab);
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c0.add_assign(&ab);
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self.c0 = c0;
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}
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fn double(&mut self) {
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self.c0.double();
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self.c1.double();
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}
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fn negate(&mut self) {
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self.c0.negate();
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self.c1.negate();
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}
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fn add_assign(&mut self, other: &Self) {
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self.c0.add_assign(&other.c0);
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self.c1.add_assign(&other.c1);
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}
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fn sub_assign(&mut self, other: &Self) {
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self.c0.sub_assign(&other.c0);
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self.c1.sub_assign(&other.c1);
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}
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fn mul_assign(&mut self, other: &Self) {
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let mut aa = self.c0;
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aa.mul_assign(&other.c0);
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let mut bb = self.c1;
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bb.mul_assign(&other.c1);
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let mut o = other.c0;
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o.add_assign(&other.c1);
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self.c1.add_assign(&self.c0);
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self.c1.mul_assign(&o);
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self.c1.sub_assign(&aa);
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self.c1.sub_assign(&bb);
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self.c0 = aa;
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self.c0.sub_assign(&bb);
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}
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fn inverse(&self) -> Option<Self> {
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let mut t1 = self.c1;
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t1.square();
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let mut t0 = self.c0;
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t0.square();
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t0.add_assign(&t1);
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t0.inverse().map(|t| {
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let mut tmp = Fq2 {
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c0: self.c0,
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c1: self.c1,
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};
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tmp.c0.mul_assign(&t);
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tmp.c1.mul_assign(&t);
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tmp.c1.negate();
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tmp
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})
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}
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fn frobenius_map(&mut self, power: usize) {
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self.c1.mul_assign(&FROBENIUS_COEFF_FQ2_C1[power % 2]);
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}
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}
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impl SqrtField for Fq2 {
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fn legendre(&self) -> ::LegendreSymbol {
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self.norm().legendre()
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}
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fn sqrt(&self) -> Option<Self> {
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// Algorithm 9, https://eprint.iacr.org/2012/685.pdf
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if self.is_zero() {
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Some(Self::zero())
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} else {
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// a1 = self^((q - 3) / 4)
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let mut a1 = self.pow([
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0xee7fbfffffffeaaa,
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0x7aaffffac54ffff,
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0xd9cc34a83dac3d89,
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0xd91dd2e13ce144af,
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0x92c6e9ed90d2eb35,
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0x680447a8e5ff9a6,
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]);
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let mut alpha = a1;
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alpha.square();
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alpha.mul_assign(self);
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let mut a0 = alpha;
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a0.frobenius_map(1);
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a0.mul_assign(&alpha);
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let neg1 = Fq2 {
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c0: NEGATIVE_ONE,
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c1: Fq::zero(),
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};
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if a0 == neg1 {
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None
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} else {
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a1.mul_assign(self);
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if alpha == neg1 {
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a1.mul_assign(&Fq2 {
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c0: Fq::zero(),
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c1: Fq::one(),
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});
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} else {
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alpha.add_assign(&Fq2::one());
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// alpha = alpha^((q - 1) / 2)
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alpha = alpha.pow([
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0xdcff7fffffffd555,
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0xf55ffff58a9ffff,
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0xb39869507b587b12,
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0xb23ba5c279c2895f,
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0x258dd3db21a5d66b,
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0xd0088f51cbff34d,
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]);
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a1.mul_assign(&alpha);
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}
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Some(a1)
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}
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}
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}
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}
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#[test]
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fn test_fq2_ordering() {
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let mut a = Fq2 {
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c0: Fq::zero(),
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c1: Fq::zero(),
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};
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let mut b = a.clone();
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assert!(a.cmp(&b) == Ordering::Equal);
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b.c0.add_assign(&Fq::one());
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assert!(a.cmp(&b) == Ordering::Less);
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a.c0.add_assign(&Fq::one());
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assert!(a.cmp(&b) == Ordering::Equal);
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b.c1.add_assign(&Fq::one());
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assert!(a.cmp(&b) == Ordering::Less);
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a.c0.add_assign(&Fq::one());
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assert!(a.cmp(&b) == Ordering::Less);
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a.c1.add_assign(&Fq::one());
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assert!(a.cmp(&b) == Ordering::Greater);
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b.c0.add_assign(&Fq::one());
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assert!(a.cmp(&b) == Ordering::Equal);
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}
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#[test]
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fn test_fq2_basics() {
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assert_eq!(
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Fq2 {
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c0: Fq::zero(),
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c1: Fq::zero(),
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},
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Fq2::zero()
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);
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assert_eq!(
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Fq2 {
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c0: Fq::one(),
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c1: Fq::zero(),
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},
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Fq2::one()
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);
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assert!(Fq2::zero().is_zero());
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assert!(!Fq2::one().is_zero());
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assert!(!Fq2 {
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c0: Fq::zero(),
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c1: Fq::one(),
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}.is_zero());
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}
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#[test]
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fn test_fq2_squaring() {
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use super::fq::FqRepr;
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use PrimeField;
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let mut a = Fq2 {
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c0: Fq::one(),
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c1: Fq::one(),
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}; // u + 1
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a.square();
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assert_eq!(
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a,
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Fq2 {
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c0: Fq::zero(),
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c1: Fq::from_repr(FqRepr::from(2)).unwrap(),
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}
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); // 2u
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let mut a = Fq2 {
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c0: Fq::zero(),
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c1: Fq::one(),
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}; // u
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a.square();
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assert_eq!(a, {
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let mut neg1 = Fq::one();
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neg1.negate();
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Fq2 {
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c0: neg1,
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c1: Fq::zero(),
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}
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}); // -1
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let mut a = Fq2 {
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c0: Fq::from_repr(FqRepr([
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0x9c2c6309bbf8b598,
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0x4eef5c946536f602,
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0x90e34aab6fb6a6bd,
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||||
0xf7f295a94e58ae7c,
|
||||
0x41b76dcc1c3fbe5e,
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||||
0x7080c5fa1d8e042,
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])).unwrap(),
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c1: Fq::from_repr(FqRepr([
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0x38f473b3c870a4ab,
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||||
0x6ad3291177c8c7e5,
|
||||
0xdac5a4c911a4353e,
|
||||
0xbfb99020604137a0,
|
||||
0xfc58a7b7be815407,
|
||||
0x10d1615e75250a21,
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])).unwrap(),
|
||||
};
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a.square();
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assert_eq!(
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a,
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Fq2 {
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c0: Fq::from_repr(FqRepr([
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||||
0xf262c28c538bcf68,
|
||||
0xb9f2a66eae1073ba,
|
||||
0xdc46ab8fad67ae0,
|
||||
0xcb674157618da176,
|
||||
0x4cf17b5893c3d327,
|
||||
0x7eac81369c43361
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0xc1579cf58e980cf8,
|
||||
0xa23eb7e12dd54d98,
|
||||
0xe75138bce4cec7aa,
|
||||
0x38d0d7275a9689e1,
|
||||
0x739c983042779a65,
|
||||
0x1542a61c8a8db994
|
||||
])).unwrap(),
|
||||
}
|
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);
|
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}
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|
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#[test]
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||||
fn test_fq2_mul() {
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||||
use super::fq::FqRepr;
|
||||
use PrimeField;
|
||||
|
||||
let mut a = Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x85c9f989e1461f03,
|
||||
0xa2e33c333449a1d6,
|
||||
0x41e461154a7354a3,
|
||||
0x9ee53e7e84d7532e,
|
||||
0x1c202d8ed97afb45,
|
||||
0x51d3f9253e2516f,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0xa7348a8b511aedcf,
|
||||
0x143c215d8176b319,
|
||||
0x4cc48081c09b8903,
|
||||
0x9533e4a9a5158be,
|
||||
0x7a5e1ecb676d65f9,
|
||||
0x180c3ee46656b008,
|
||||
])).unwrap(),
|
||||
};
|
||||
a.mul_assign(&Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0xe21f9169805f537e,
|
||||
0xfc87e62e179c285d,
|
||||
0x27ece175be07a531,
|
||||
0xcd460f9f0c23e430,
|
||||
0x6c9110292bfa409,
|
||||
0x2c93a72eb8af83e,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x4b1c3f936d8992d4,
|
||||
0x1d2a72916dba4c8a,
|
||||
0x8871c508658d1e5f,
|
||||
0x57a06d3135a752ae,
|
||||
0x634cd3c6c565096d,
|
||||
0x19e17334d4e93558,
|
||||
])).unwrap(),
|
||||
});
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x95b5127e6360c7e4,
|
||||
0xde29c31a19a6937e,
|
||||
0xf61a96dacf5a39bc,
|
||||
0x5511fe4d84ee5f78,
|
||||
0x5310a202d92f9963,
|
||||
0x1751afbe166e5399
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x84af0e1bd630117a,
|
||||
0x6c63cd4da2c2aa7,
|
||||
0x5ba6e5430e883d40,
|
||||
0xc975106579c275ee,
|
||||
0x33a9ac82ce4c5083,
|
||||
0x1ef1a36c201589d
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq2_inverse() {
|
||||
use super::fq::FqRepr;
|
||||
use PrimeField;
|
||||
|
||||
assert!(Fq2::zero().inverse().is_none());
|
||||
|
||||
let a = Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x85c9f989e1461f03,
|
||||
0xa2e33c333449a1d6,
|
||||
0x41e461154a7354a3,
|
||||
0x9ee53e7e84d7532e,
|
||||
0x1c202d8ed97afb45,
|
||||
0x51d3f9253e2516f,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0xa7348a8b511aedcf,
|
||||
0x143c215d8176b319,
|
||||
0x4cc48081c09b8903,
|
||||
0x9533e4a9a5158be,
|
||||
0x7a5e1ecb676d65f9,
|
||||
0x180c3ee46656b008,
|
||||
])).unwrap(),
|
||||
};
|
||||
let a = a.inverse().unwrap();
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x70300f9bcb9e594,
|
||||
0xe5ecda5fdafddbb2,
|
||||
0x64bef617d2915a8f,
|
||||
0xdfba703293941c30,
|
||||
0xa6c3d8f9586f2636,
|
||||
0x1351ef01941b70c4
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x8c39fd76a8312cb4,
|
||||
0x15d7b6b95defbff0,
|
||||
0x947143f89faedee9,
|
||||
0xcbf651a0f367afb2,
|
||||
0xdf4e54f0d3ef15a6,
|
||||
0x103bdf241afb0019
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq2_addition() {
|
||||
use super::fq::FqRepr;
|
||||
use PrimeField;
|
||||
|
||||
let mut a = Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x2d0078036923ffc7,
|
||||
0x11e59ea221a3b6d2,
|
||||
0x8b1a52e0a90f59ed,
|
||||
0xb966ce3bc2108b13,
|
||||
0xccc649c4b9532bf3,
|
||||
0xf8d295b2ded9dc,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x977df6efcdaee0db,
|
||||
0x946ae52d684fa7ed,
|
||||
0xbe203411c66fb3a5,
|
||||
0xb3f8afc0ee248cad,
|
||||
0x4e464dea5bcfd41e,
|
||||
0x12d1137b8a6a837,
|
||||
])).unwrap(),
|
||||
};
|
||||
a.add_assign(&Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x619a02d78dc70ef2,
|
||||
0xb93adfc9119e33e8,
|
||||
0x4bf0b99a9f0dca12,
|
||||
0x3b88899a42a6318f,
|
||||
0x986a4a62fa82a49d,
|
||||
0x13ce433fa26027f5,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x66323bf80b58b9b9,
|
||||
0xa1379b6facf6e596,
|
||||
0x402aef1fb797e32f,
|
||||
0x2236f55246d0d44d,
|
||||
0x4c8c1800eb104566,
|
||||
0x11d6e20e986c2085,
|
||||
])).unwrap(),
|
||||
});
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x8e9a7adaf6eb0eb9,
|
||||
0xcb207e6b3341eaba,
|
||||
0xd70b0c7b481d23ff,
|
||||
0xf4ef57d604b6bca2,
|
||||
0x65309427b3d5d090,
|
||||
0x14c715d5553f01d2
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0xfdb032e7d9079a94,
|
||||
0x35a2809d15468d83,
|
||||
0xfe4b23317e0796d5,
|
||||
0xd62fa51334f560fa,
|
||||
0x9ad265eb46e01984,
|
||||
0x1303f3465112c8bc
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq2_subtraction() {
|
||||
use super::fq::FqRepr;
|
||||
use PrimeField;
|
||||
|
||||
let mut a = Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x2d0078036923ffc7,
|
||||
0x11e59ea221a3b6d2,
|
||||
0x8b1a52e0a90f59ed,
|
||||
0xb966ce3bc2108b13,
|
||||
0xccc649c4b9532bf3,
|
||||
0xf8d295b2ded9dc,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x977df6efcdaee0db,
|
||||
0x946ae52d684fa7ed,
|
||||
0xbe203411c66fb3a5,
|
||||
0xb3f8afc0ee248cad,
|
||||
0x4e464dea5bcfd41e,
|
||||
0x12d1137b8a6a837,
|
||||
])).unwrap(),
|
||||
};
|
||||
a.sub_assign(&Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x619a02d78dc70ef2,
|
||||
0xb93adfc9119e33e8,
|
||||
0x4bf0b99a9f0dca12,
|
||||
0x3b88899a42a6318f,
|
||||
0x986a4a62fa82a49d,
|
||||
0x13ce433fa26027f5,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x66323bf80b58b9b9,
|
||||
0xa1379b6facf6e596,
|
||||
0x402aef1fb797e32f,
|
||||
0x2236f55246d0d44d,
|
||||
0x4c8c1800eb104566,
|
||||
0x11d6e20e986c2085,
|
||||
])).unwrap(),
|
||||
});
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x8565752bdb5c9b80,
|
||||
0x7756bed7c15982e9,
|
||||
0xa65a6be700b285fe,
|
||||
0xe255902672ef6c43,
|
||||
0x7f77a718021c342d,
|
||||
0x72ba14049fe9881
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0xeb4abaf7c255d1cd,
|
||||
0x11df49bc6cacc256,
|
||||
0xe52617930588c69a,
|
||||
0xf63905f39ad8cb1f,
|
||||
0x4cd5dd9fb40b3b8f,
|
||||
0x957411359ba6e4c
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq2_negation() {
|
||||
use super::fq::FqRepr;
|
||||
use PrimeField;
|
||||
|
||||
let mut a = Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x2d0078036923ffc7,
|
||||
0x11e59ea221a3b6d2,
|
||||
0x8b1a52e0a90f59ed,
|
||||
0xb966ce3bc2108b13,
|
||||
0xccc649c4b9532bf3,
|
||||
0xf8d295b2ded9dc,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x977df6efcdaee0db,
|
||||
0x946ae52d684fa7ed,
|
||||
0xbe203411c66fb3a5,
|
||||
0xb3f8afc0ee248cad,
|
||||
0x4e464dea5bcfd41e,
|
||||
0x12d1137b8a6a837,
|
||||
])).unwrap(),
|
||||
};
|
||||
a.negate();
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x8cfe87fc96dbaae4,
|
||||
0xcc6615c8fb0492d,
|
||||
0xdc167fc04da19c37,
|
||||
0xab107d49317487ab,
|
||||
0x7e555df189f880e3,
|
||||
0x19083f5486a10cbd
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x228109103250c9d0,
|
||||
0x8a411ad149045812,
|
||||
0xa9109e8f3041427e,
|
||||
0xb07e9bc405608611,
|
||||
0xfcd559cbe77bd8b8,
|
||||
0x18d400b280d93e62
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq2_doubling() {
|
||||
use super::fq::FqRepr;
|
||||
use PrimeField;
|
||||
|
||||
let mut a = Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x2d0078036923ffc7,
|
||||
0x11e59ea221a3b6d2,
|
||||
0x8b1a52e0a90f59ed,
|
||||
0xb966ce3bc2108b13,
|
||||
0xccc649c4b9532bf3,
|
||||
0xf8d295b2ded9dc,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x977df6efcdaee0db,
|
||||
0x946ae52d684fa7ed,
|
||||
0xbe203411c66fb3a5,
|
||||
0xb3f8afc0ee248cad,
|
||||
0x4e464dea5bcfd41e,
|
||||
0x12d1137b8a6a837,
|
||||
])).unwrap(),
|
||||
};
|
||||
a.double();
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x5a00f006d247ff8e,
|
||||
0x23cb3d4443476da4,
|
||||
0x1634a5c1521eb3da,
|
||||
0x72cd9c7784211627,
|
||||
0x998c938972a657e7,
|
||||
0x1f1a52b65bdb3b9
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x2efbeddf9b5dc1b6,
|
||||
0x28d5ca5ad09f4fdb,
|
||||
0x7c4068238cdf674b,
|
||||
0x67f15f81dc49195b,
|
||||
0x9c8c9bd4b79fa83d,
|
||||
0x25a226f714d506e
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq2_frobenius_map() {
|
||||
use super::fq::FqRepr;
|
||||
use PrimeField;
|
||||
|
||||
let mut a = Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x2d0078036923ffc7,
|
||||
0x11e59ea221a3b6d2,
|
||||
0x8b1a52e0a90f59ed,
|
||||
0xb966ce3bc2108b13,
|
||||
0xccc649c4b9532bf3,
|
||||
0xf8d295b2ded9dc,
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x977df6efcdaee0db,
|
||||
0x946ae52d684fa7ed,
|
||||
0xbe203411c66fb3a5,
|
||||
0xb3f8afc0ee248cad,
|
||||
0x4e464dea5bcfd41e,
|
||||
0x12d1137b8a6a837,
|
||||
])).unwrap(),
|
||||
};
|
||||
a.frobenius_map(0);
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x2d0078036923ffc7,
|
||||
0x11e59ea221a3b6d2,
|
||||
0x8b1a52e0a90f59ed,
|
||||
0xb966ce3bc2108b13,
|
||||
0xccc649c4b9532bf3,
|
||||
0xf8d295b2ded9dc
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x977df6efcdaee0db,
|
||||
0x946ae52d684fa7ed,
|
||||
0xbe203411c66fb3a5,
|
||||
0xb3f8afc0ee248cad,
|
||||
0x4e464dea5bcfd41e,
|
||||
0x12d1137b8a6a837
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
a.frobenius_map(1);
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x2d0078036923ffc7,
|
||||
0x11e59ea221a3b6d2,
|
||||
0x8b1a52e0a90f59ed,
|
||||
0xb966ce3bc2108b13,
|
||||
0xccc649c4b9532bf3,
|
||||
0xf8d295b2ded9dc
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x228109103250c9d0,
|
||||
0x8a411ad149045812,
|
||||
0xa9109e8f3041427e,
|
||||
0xb07e9bc405608611,
|
||||
0xfcd559cbe77bd8b8,
|
||||
0x18d400b280d93e62
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
a.frobenius_map(1);
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x2d0078036923ffc7,
|
||||
0x11e59ea221a3b6d2,
|
||||
0x8b1a52e0a90f59ed,
|
||||
0xb966ce3bc2108b13,
|
||||
0xccc649c4b9532bf3,
|
||||
0xf8d295b2ded9dc
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x977df6efcdaee0db,
|
||||
0x946ae52d684fa7ed,
|
||||
0xbe203411c66fb3a5,
|
||||
0xb3f8afc0ee248cad,
|
||||
0x4e464dea5bcfd41e,
|
||||
0x12d1137b8a6a837
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
a.frobenius_map(2);
|
||||
assert_eq!(
|
||||
a,
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x2d0078036923ffc7,
|
||||
0x11e59ea221a3b6d2,
|
||||
0x8b1a52e0a90f59ed,
|
||||
0xb966ce3bc2108b13,
|
||||
0xccc649c4b9532bf3,
|
||||
0xf8d295b2ded9dc
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0x977df6efcdaee0db,
|
||||
0x946ae52d684fa7ed,
|
||||
0xbe203411c66fb3a5,
|
||||
0xb3f8afc0ee248cad,
|
||||
0x4e464dea5bcfd41e,
|
||||
0x12d1137b8a6a837
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq2_sqrt() {
|
||||
use super::fq::FqRepr;
|
||||
use PrimeField;
|
||||
|
||||
assert_eq!(
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x476b4c309720e227,
|
||||
0x34c2d04faffdab6,
|
||||
0xa57e6fc1bab51fd9,
|
||||
0xdb4a116b5bf74aa1,
|
||||
0x1e58b2159dfe10e2,
|
||||
0x7ca7da1f13606ac
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0xfa8de88b7516d2c3,
|
||||
0x371a75ed14f41629,
|
||||
0x4cec2dca577a3eb6,
|
||||
0x212611bca4e99121,
|
||||
0x8ee5394d77afb3d,
|
||||
0xec92336650e49d5
|
||||
])).unwrap(),
|
||||
}.sqrt()
|
||||
.unwrap(),
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0x40b299b2704258c5,
|
||||
0x6ef7de92e8c68b63,
|
||||
0x6d2ddbe552203e82,
|
||||
0x8d7f1f723d02c1d3,
|
||||
0x881b3e01b611c070,
|
||||
0x10f6963bbad2ebc5
|
||||
])).unwrap(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0xc099534fc209e752,
|
||||
0x7670594665676447,
|
||||
0x28a20faed211efe7,
|
||||
0x6b852aeaf2afcb1b,
|
||||
0xa4c93b08105d71a9,
|
||||
0x8d7cfff94216330
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
|
||||
assert_eq!(
|
||||
Fq2 {
|
||||
c0: Fq::from_repr(FqRepr([
|
||||
0xb9f78429d1517a6b,
|
||||
0x1eabfffeb153ffff,
|
||||
0x6730d2a0f6b0f624,
|
||||
0x64774b84f38512bf,
|
||||
0x4b1ba7b6434bacd7,
|
||||
0x1a0111ea397fe69a
|
||||
])).unwrap(),
|
||||
c1: Fq::zero(),
|
||||
}.sqrt()
|
||||
.unwrap(),
|
||||
Fq2 {
|
||||
c0: Fq::zero(),
|
||||
c1: Fq::from_repr(FqRepr([
|
||||
0xb9fefffffd4357a3,
|
||||
0x1eabfffeb153ffff,
|
||||
0x6730d2a0f6b0f624,
|
||||
0x64774b84f38512bf,
|
||||
0x4b1ba7b6434bacd7,
|
||||
0x1a0111ea397fe69a
|
||||
])).unwrap(),
|
||||
}
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_fq2_legendre() {
|
||||
use LegendreSymbol::*;
|
||||
|
||||
assert_eq!(Zero, Fq2::zero().legendre());
|
||||
// i^2 = -1
|
||||
let mut m1 = Fq2::one();
|
||||
m1.negate();
|
||||
assert_eq!(QuadraticResidue, m1.legendre());
|
||||
m1.mul_by_nonresidue();
|
||||
assert_eq!(QuadraticNonResidue, m1.legendre());
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
use rand::{SeedableRng, XorShiftRng};
|
||||
|
||||
#[test]
|
||||
fn test_fq2_mul_nonresidue() {
|
||||
let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
||||
|
||||
let nqr = Fq2 {
|
||||
c0: Fq::one(),
|
||||
c1: Fq::one(),
|
||||
};
|
||||
|
||||
for _ in 0..1000 {
|
||||
let mut a = Fq2::rand(&mut rng);
|
||||
let mut b = a;
|
||||
a.mul_by_nonresidue();
|
||||
b.mul_assign(&nqr);
|
||||
|
||||
assert_eq!(a, b);
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn fq2_field_tests() {
|
||||
use PrimeField;
|
||||
|
||||
::tests::field::random_field_tests::<Fq2>();
|
||||
::tests::field::random_sqrt_tests::<Fq2>();
|
||||
::tests::field::random_frobenius_tests::<Fq2, _>(super::fq::Fq::char(), 13);
|
||||
}
|
||||
Reference in New Issue
Block a user