mirror of
https://github.com/Qortal/pirate-librustzcash.git
synced 2025-02-15 19:25:47 +00:00
636 lines
19 KiB
Rust
636 lines
19 KiB
Rust
use crate::fp::*;
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use crate::fp2::*;
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use crate::fp6::*;
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use core::fmt;
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use core::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
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use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
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/// This represents an element $c_0 + c_1 w$ of $\mathbb{F}_{p^12} = \mathbb{F}_{p^6} / w^2 - v$.
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pub struct Fp12 {
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pub c0: Fp6,
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pub c1: Fp6,
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}
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impl From<Fp> for Fp12 {
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fn from(f: Fp) -> Fp12 {
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Fp12 {
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c0: Fp6::from(f),
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c1: Fp6::zero(),
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}
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}
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}
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impl From<Fp2> for Fp12 {
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fn from(f: Fp2) -> Fp12 {
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Fp12 {
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c0: Fp6::from(f),
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c1: Fp6::zero(),
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}
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}
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}
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impl From<Fp6> for Fp12 {
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fn from(f: Fp6) -> Fp12 {
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Fp12 {
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c0: f,
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c1: Fp6::zero(),
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}
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}
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}
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impl PartialEq for Fp12 {
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fn eq(&self, other: &Fp12) -> bool {
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self.ct_eq(other).into()
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}
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}
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impl Copy for Fp12 {}
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impl Clone for Fp12 {
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#[inline]
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fn clone(&self) -> Self {
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*self
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}
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}
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impl Default for Fp12 {
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fn default() -> Self {
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Fp12::zero()
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}
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}
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impl fmt::Debug for Fp12 {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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write!(f, "{:?} + ({:?})*w", self.c0, self.c1)
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}
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}
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impl ConditionallySelectable for Fp12 {
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#[inline(always)]
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fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
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Fp12 {
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c0: Fp6::conditional_select(&a.c0, &b.c0, choice),
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c1: Fp6::conditional_select(&a.c1, &b.c1, choice),
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}
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}
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}
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impl ConstantTimeEq for Fp12 {
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#[inline(always)]
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fn ct_eq(&self, other: &Self) -> Choice {
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self.c0.ct_eq(&other.c0) & self.c1.ct_eq(&other.c1)
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}
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}
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impl Fp12 {
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#[inline]
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pub fn zero() -> Self {
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Fp12 {
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c0: Fp6::zero(),
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c1: Fp6::zero(),
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}
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}
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#[inline]
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pub fn one() -> Self {
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Fp12 {
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c0: Fp6::one(),
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c1: Fp6::zero(),
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}
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}
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pub fn mul_by_014(&self, c0: &Fp2, c1: &Fp2, c4: &Fp2) -> Fp12 {
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let aa = self.c0.mul_by_01(c0, c1);
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let bb = self.c1.mul_by_1(c4);
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let o = c1 + c4;
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let c1 = self.c1 + self.c0;
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let c1 = c1.mul_by_01(c0, &o);
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let c1 = c1 - aa - bb;
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let c0 = bb;
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let c0 = c0.mul_by_nonresidue();
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let c0 = c0 + aa;
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Fp12 { c0, c1 }
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}
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#[inline(always)]
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pub fn is_zero(&self) -> Choice {
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self.c0.is_zero() & self.c1.is_zero()
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}
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#[inline(always)]
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pub fn conjugate(&self) -> Self {
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Fp12 {
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c0: self.c0,
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c1: -self.c1,
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}
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}
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/// Raises this element to p.
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#[inline(always)]
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pub fn frobenius_map(&self) -> Self {
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let c0 = self.c0.frobenius_map();
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let c1 = self.c1.frobenius_map();
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// c1 = c1 * (u + 1)^((p - 1) / 6)
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let c1 = c1
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* Fp6::from(Fp2 {
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c0: Fp::from_raw_unchecked([
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0x0708_9552_b319_d465,
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0xc669_5f92_b50a_8313,
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0x97e8_3ccc_d117_228f,
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0xa35b_aeca_b2dc_29ee,
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0x1ce3_93ea_5daa_ce4d,
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0x08f2_220f_b0fb_66eb,
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]),
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c1: Fp::from_raw_unchecked([
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0xb2f6_6aad_4ce5_d646,
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0x5842_a06b_fc49_7cec,
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0xcf48_95d4_2599_d394,
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0xc11b_9cba_40a8_e8d0,
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0x2e38_13cb_e5a0_de89,
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0x110e_efda_8884_7faf,
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]),
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});
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Fp12 { c0, c1 }
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}
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#[inline]
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pub fn square(&self) -> Self {
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let ab = self.c0 * self.c1;
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let c0c1 = self.c0 + self.c1;
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let c0 = self.c1.mul_by_nonresidue();
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let c0 = c0 + self.c0;
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let c0 = c0 * c0c1;
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let c0 = c0 - ab;
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let c1 = ab + ab;
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let c0 = c0 - ab.mul_by_nonresidue();
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Fp12 { c0, c1 }
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}
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pub fn invert(&self) -> CtOption<Self> {
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(self.c0.square() - self.c1.square().mul_by_nonresidue())
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.invert()
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.map(|t| Fp12 {
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c0: self.c0 * t,
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c1: self.c1 * -t,
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})
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}
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}
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impl<'a, 'b> Mul<&'b Fp12> for &'a Fp12 {
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type Output = Fp12;
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#[inline]
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fn mul(self, other: &'b Fp12) -> Self::Output {
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let aa = self.c0 * other.c0;
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let bb = self.c1 * other.c1;
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let o = other.c0 + other.c1;
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let c1 = self.c1 + self.c0;
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let c1 = c1 * o;
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let c1 = c1 - aa;
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let c1 = c1 - bb;
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let c0 = bb.mul_by_nonresidue();
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let c0 = c0 + aa;
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Fp12 { c0, c1 }
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}
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}
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impl<'a, 'b> Add<&'b Fp12> for &'a Fp12 {
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type Output = Fp12;
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#[inline]
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fn add(self, rhs: &'b Fp12) -> Self::Output {
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Fp12 {
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c0: self.c0 + rhs.c0,
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c1: self.c1 + rhs.c1,
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}
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}
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}
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impl<'a> Neg for &'a Fp12 {
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type Output = Fp12;
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#[inline]
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fn neg(self) -> Self::Output {
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Fp12 {
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c0: -self.c0,
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c1: -self.c1,
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}
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}
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}
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impl Neg for Fp12 {
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type Output = Fp12;
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#[inline]
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fn neg(self) -> Self::Output {
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-&self
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}
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}
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impl<'a, 'b> Sub<&'b Fp12> for &'a Fp12 {
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type Output = Fp12;
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#[inline]
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fn sub(self, rhs: &'b Fp12) -> Self::Output {
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Fp12 {
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c0: self.c0 - rhs.c0,
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c1: self.c1 - rhs.c1,
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}
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}
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}
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impl_binops_additive!(Fp12, Fp12);
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impl_binops_multiplicative!(Fp12, Fp12);
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#[test]
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fn test_arithmetic() {
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use crate::fp::*;
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use crate::fp2::*;
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let a = Fp12 {
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c0: Fp6 {
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c0: Fp2 {
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c0: Fp::from_raw_unchecked([
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0x47f9_cb98_b1b8_2d58,
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0x5fe9_11eb_a3aa_1d9d,
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0x96bf_1b5f_4dd8_1db3,
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0x8100_d27c_c925_9f5b,
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0xafa2_0b96_7464_0eab,
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0x09bb_cea7_d8d9_497d,
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]),
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c1: Fp::from_raw_unchecked([
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0x0303_cb98_b166_2daa,
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0xd931_10aa_0a62_1d5a,
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0xbfa9_820c_5be4_a468,
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0x0ba3_643e_cb05_a348,
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0xdc35_34bb_1f1c_25a6,
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0x06c3_05bb_19c0_e1c1,
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]),
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},
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c1: Fp2 {
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c0: Fp::from_raw_unchecked([
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0x46f9_cb98_b162_d858,
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0x0be9_109c_f7aa_1d57,
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0xc791_bc55_fece_41d2,
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0xf84c_5770_4e38_5ec2,
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0xcb49_c1d9_c010_e60f,
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0x0acd_b8e1_58bf_e3c8,
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]),
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c1: Fp::from_raw_unchecked([
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0x8aef_cb98_b15f_8306,
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0x3ea1_108f_e4f2_1d54,
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0xcf79_f69f_a1b7_df3b,
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0xe4f5_4aa1_d16b_1a3c,
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0xba5e_4ef8_6105_a679,
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0x0ed8_6c07_97be_e5cf,
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]),
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},
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c2: Fp2 {
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c0: Fp::from_raw_unchecked([
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0xcee5_cb98_b15c_2db4,
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0x7159_1082_d23a_1d51,
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0xd762_30e9_44a1_7ca4,
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0xd19e_3dd3_549d_d5b6,
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0xa972_dc17_01fa_66e3,
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0x12e3_1f2d_d6bd_e7d6,
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]),
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c1: Fp::from_raw_unchecked([
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0xad2a_cb98_b173_2d9d,
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0x2cfd_10dd_0696_1d64,
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0x0739_6b86_c6ef_24e8,
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0xbd76_e2fd_b1bf_c820,
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0x6afe_a7f6_de94_d0d5,
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0x1099_4b0c_5744_c040,
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]),
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},
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},
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c1: Fp6 {
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c0: Fp2 {
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c0: Fp::from_raw_unchecked([
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0x47f9_cb98_b1b8_2d58,
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0x5fe9_11eb_a3aa_1d9d,
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0x96bf_1b5f_4dd8_1db3,
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0x8100_d27c_c925_9f5b,
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0xafa2_0b96_7464_0eab,
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0x09bb_cea7_d8d9_497d,
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]),
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c1: Fp::from_raw_unchecked([
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0x0303_cb98_b166_2daa,
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0xd931_10aa_0a62_1d5a,
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0xbfa9_820c_5be4_a468,
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0x0ba3_643e_cb05_a348,
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0xdc35_34bb_1f1c_25a6,
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0x06c3_05bb_19c0_e1c1,
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]),
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},
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c1: Fp2 {
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c0: Fp::from_raw_unchecked([
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0x46f9_cb98_b162_d858,
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0x0be9_109c_f7aa_1d57,
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0xc791_bc55_fece_41d2,
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0xf84c_5770_4e38_5ec2,
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0xcb49_c1d9_c010_e60f,
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0x0acd_b8e1_58bf_e3c8,
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]),
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c1: Fp::from_raw_unchecked([
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0x8aef_cb98_b15f_8306,
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0x3ea1_108f_e4f2_1d54,
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0xcf79_f69f_a1b7_df3b,
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0xe4f5_4aa1_d16b_1a3c,
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0xba5e_4ef8_6105_a679,
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0x0ed8_6c07_97be_e5cf,
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]),
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},
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c2: Fp2 {
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c0: Fp::from_raw_unchecked([
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0xcee5_cb98_b15c_2db4,
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0x7159_1082_d23a_1d51,
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0xd762_30e9_44a1_7ca4,
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0xd19e_3dd3_549d_d5b6,
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0xa972_dc17_01fa_66e3,
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0x12e3_1f2d_d6bd_e7d6,
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]),
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c1: Fp::from_raw_unchecked([
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0xad2a_cb98_b173_2d9d,
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0x2cfd_10dd_0696_1d64,
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0x0739_6b86_c6ef_24e8,
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0xbd76_e2fd_b1bf_c820,
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0x6afe_a7f6_de94_d0d5,
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0x1099_4b0c_5744_c040,
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]),
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},
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},
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};
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let b = Fp12 {
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c0: Fp6 {
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c0: Fp2 {
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c0: Fp::from_raw_unchecked([
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0x47f9_cb98_b1b8_2d58,
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0x5fe9_11eb_a3aa_1d9d,
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0x96bf_1b5f_4dd8_1db3,
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0x8100_d272_c925_9f5b,
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0xafa2_0b96_7464_0eab,
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0x09bb_cea7_d8d9_497d,
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]),
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c1: Fp::from_raw_unchecked([
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0x0303_cb98_b166_2daa,
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0xd931_10aa_0a62_1d5a,
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0xbfa9_820c_5be4_a468,
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0x0ba3_643e_cb05_a348,
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0xdc35_34bb_1f1c_25a6,
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0x06c3_05bb_19c0_e1c1,
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]),
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},
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c1: Fp2 {
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c0: Fp::from_raw_unchecked([
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0x46f9_cb98_b162_d858,
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0x0be9_109c_f7aa_1d57,
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0xc791_bc55_fece_41d2,
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0xf84c_5770_4e38_5ec2,
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0xcb49_c1d9_c010_e60f,
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0x0acd_b8e1_58bf_e348,
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]),
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c1: Fp::from_raw_unchecked([
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0x8aef_cb98_b15f_8306,
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0x3ea1_108f_e4f2_1d54,
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0xcf79_f69f_a1b7_df3b,
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0xe4f5_4aa1_d16b_1a3c,
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0xba5e_4ef8_6105_a679,
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0x0ed8_6c07_97be_e5cf,
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]),
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},
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c2: Fp2 {
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c0: Fp::from_raw_unchecked([
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0xcee5_cb98_b15c_2db4,
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0x7159_1082_d23a_1d51,
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0xd762_30e9_44a1_7ca4,
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0xd19e_3dd3_549d_d5b6,
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0xa972_dc17_01fa_66e3,
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0x12e3_1f2d_d6bd_e7d6,
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]),
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c1: Fp::from_raw_unchecked([
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0xad2a_cb98_b173_2d9d,
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0x2cfd_10dd_0696_1d64,
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0x0739_6b86_c6ef_24e8,
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0xbd76_e2fd_b1bf_c820,
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0x6afe_a7f6_de94_d0d5,
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0x1099_4b0c_5744_c040,
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]),
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},
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},
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c1: Fp6 {
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c0: Fp2 {
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c0: Fp::from_raw_unchecked([
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0x47f9_cb98_b1b8_2d58,
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0x5fe9_11eb_a3aa_1d9d,
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0x96bf_1b5f_4dd2_1db3,
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0x8100_d27c_c925_9f5b,
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0xafa2_0b96_7464_0eab,
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0x09bb_cea7_d8d9_497d,
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]),
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c1: Fp::from_raw_unchecked([
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0x0303_cb98_b166_2daa,
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0xd931_10aa_0a62_1d5a,
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0xbfa9_820c_5be4_a468,
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0x0ba3_643e_cb05_a348,
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0xdc35_34bb_1f1c_25a6,
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0x06c3_05bb_19c0_e1c1,
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]),
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},
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c1: Fp2 {
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c0: Fp::from_raw_unchecked([
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0x46f9_cb98_b162_d858,
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0x0be9_109c_f7aa_1d57,
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0xc791_bc55_fece_41d2,
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0xf84c_5770_4e38_5ec2,
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0xcb49_c1d9_c010_e60f,
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0x0acd_b8e1_58bf_e3c8,
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]),
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c1: Fp::from_raw_unchecked([
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0x8aef_cb98_b15f_8306,
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0x3ea1_108f_e4f2_1d54,
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0xcf79_f69f_a117_df3b,
|
|
0xe4f5_4aa1_d16b_1a3c,
|
|
0xba5e_4ef8_6105_a679,
|
|
0x0ed8_6c07_97be_e5cf,
|
|
]),
|
|
},
|
|
c2: Fp2 {
|
|
c0: Fp::from_raw_unchecked([
|
|
0xcee5_cb98_b15c_2db4,
|
|
0x7159_1082_d23a_1d51,
|
|
0xd762_30e9_44a1_7ca4,
|
|
0xd19e_3dd3_549d_d5b6,
|
|
0xa972_dc17_01fa_66e3,
|
|
0x12e3_1f2d_d6bd_e7d6,
|
|
]),
|
|
c1: Fp::from_raw_unchecked([
|
|
0xad2a_cb98_b173_2d9d,
|
|
0x2cfd_10dd_0696_1d64,
|
|
0x0739_6b86_c6ef_24e8,
|
|
0xbd76_e2fd_b1bf_c820,
|
|
0x6afe_a7f6_de94_d0d5,
|
|
0x1099_4b0c_5744_c040,
|
|
]),
|
|
},
|
|
},
|
|
};
|
|
|
|
let c = Fp12 {
|
|
c0: Fp6 {
|
|
c0: Fp2 {
|
|
c0: Fp::from_raw_unchecked([
|
|
0x47f9_cb98_71b8_2d58,
|
|
0x5fe9_11eb_a3aa_1d9d,
|
|
0x96bf_1b5f_4dd8_1db3,
|
|
0x8100_d27c_c925_9f5b,
|
|
0xafa2_0b96_7464_0eab,
|
|
0x09bb_cea7_d8d9_497d,
|
|
]),
|
|
c1: Fp::from_raw_unchecked([
|
|
0x0303_cb98_b166_2daa,
|
|
0xd931_10aa_0a62_1d5a,
|
|
0xbfa9_820c_5be4_a468,
|
|
0x0ba3_643e_cb05_a348,
|
|
0xdc35_34bb_1f1c_25a6,
|
|
0x06c3_05bb_19c0_e1c1,
|
|
]),
|
|
},
|
|
c1: Fp2 {
|
|
c0: Fp::from_raw_unchecked([
|
|
0x46f9_cb98_b162_d858,
|
|
0x0be9_109c_f7aa_1d57,
|
|
0x7791_bc55_fece_41d2,
|
|
0xf84c_5770_4e38_5ec2,
|
|
0xcb49_c1d9_c010_e60f,
|
|
0x0acd_b8e1_58bf_e3c8,
|
|
]),
|
|
c1: Fp::from_raw_unchecked([
|
|
0x8aef_cb98_b15f_8306,
|
|
0x3ea1_108f_e4f2_1d54,
|
|
0xcf79_f69f_a1b7_df3b,
|
|
0xe4f5_4aa1_d16b_133c,
|
|
0xba5e_4ef8_6105_a679,
|
|
0x0ed8_6c07_97be_e5cf,
|
|
]),
|
|
},
|
|
c2: Fp2 {
|
|
c0: Fp::from_raw_unchecked([
|
|
0xcee5_cb98_b15c_2db4,
|
|
0x7159_1082_d23a_1d51,
|
|
0xd762_40e9_44a1_7ca4,
|
|
0xd19e_3dd3_549d_d5b6,
|
|
0xa972_dc17_01fa_66e3,
|
|
0x12e3_1f2d_d6bd_e7d6,
|
|
]),
|
|
c1: Fp::from_raw_unchecked([
|
|
0xad2a_cb98_b173_2d9d,
|
|
0x2cfd_10dd_0696_1d64,
|
|
0x0739_6b86_c6ef_24e8,
|
|
0xbd76_e2fd_b1bf_c820,
|
|
0x6afe_a7f6_de94_d0d5,
|
|
0x1099_4b0c_1744_c040,
|
|
]),
|
|
},
|
|
},
|
|
c1: Fp6 {
|
|
c0: Fp2 {
|
|
c0: Fp::from_raw_unchecked([
|
|
0x47f9_cb98_b1b8_2d58,
|
|
0x5fe9_11eb_a3aa_1d9d,
|
|
0x96bf_1b5f_4dd8_1db3,
|
|
0x8100_d27c_c925_9f5b,
|
|
0xafa2_0b96_7464_0eab,
|
|
0x09bb_cea7_d8d9_497d,
|
|
]),
|
|
c1: Fp::from_raw_unchecked([
|
|
0x0303_cb98_b166_2daa,
|
|
0xd931_10aa_0a62_1d5a,
|
|
0xbfa9_820c_5be4_a468,
|
|
0x0ba3_643e_cb05_a348,
|
|
0xdc35_34bb_1f1c_25a6,
|
|
0x06c3_05bb_19c0_e1c1,
|
|
]),
|
|
},
|
|
c1: Fp2 {
|
|
c0: Fp::from_raw_unchecked([
|
|
0x46f9_cb98_b162_d858,
|
|
0x0be9_109c_f7aa_1d57,
|
|
0xc791_bc55_fece_41d2,
|
|
0xf84c_5770_4e38_5ec2,
|
|
0xcb49_c1d3_c010_e60f,
|
|
0x0acd_b8e1_58bf_e3c8,
|
|
]),
|
|
c1: Fp::from_raw_unchecked([
|
|
0x8aef_cb98_b15f_8306,
|
|
0x3ea1_108f_e4f2_1d54,
|
|
0xcf79_f69f_a1b7_df3b,
|
|
0xe4f5_4aa1_d16b_1a3c,
|
|
0xba5e_4ef8_6105_a679,
|
|
0x0ed8_6c07_97be_e5cf,
|
|
]),
|
|
},
|
|
c2: Fp2 {
|
|
c0: Fp::from_raw_unchecked([
|
|
0xcee5_cb98_b15c_2db4,
|
|
0x7159_1082_d23a_1d51,
|
|
0xd762_30e9_44a1_7ca4,
|
|
0xd19e_3dd3_549d_d5b6,
|
|
0xa972_dc17_01fa_66e3,
|
|
0x12e3_1f2d_d6bd_e7d6,
|
|
]),
|
|
c1: Fp::from_raw_unchecked([
|
|
0xad2a_cb98_b173_2d9d,
|
|
0x2cfd_10dd_0696_1d64,
|
|
0x0739_6b86_c6ef_24e8,
|
|
0xbd76_e2fd_b1bf_c820,
|
|
0x6afe_a7f6_de94_d0d5,
|
|
0x1099_4b0c_5744_1040,
|
|
]),
|
|
},
|
|
},
|
|
};
|
|
|
|
// because a and b and c are similar to each other and
|
|
// I was lazy, this is just some arbitrary way to make
|
|
// them a little more different
|
|
let a = a.square().invert().unwrap().square() + c;
|
|
let b = b.square().invert().unwrap().square() + a;
|
|
let c = c.square().invert().unwrap().square() + b;
|
|
|
|
assert_eq!(a.square(), a * a);
|
|
assert_eq!(b.square(), b * b);
|
|
assert_eq!(c.square(), c * c);
|
|
|
|
assert_eq!((a + b) * c.square(), (c * c * a) + (c * c * b));
|
|
|
|
assert_eq!(
|
|
a.invert().unwrap() * b.invert().unwrap(),
|
|
(a * b).invert().unwrap()
|
|
);
|
|
assert_eq!(a.invert().unwrap() * a, Fp12::one());
|
|
|
|
assert!(a != a.frobenius_map());
|
|
assert_eq!(
|
|
a,
|
|
a.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
.frobenius_map()
|
|
);
|
|
}
|