mirror of
https://github.com/logos-storage/plonky2.git
synced 2026-01-10 01:33:07 +00:00
skeleton
This commit is contained in:
Dmitry Vagner
parent
a96418b36c
commit
625bdb680b
@ -1,9 +1,21 @@
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use std::mem::transmute;
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use std::ops::{Add, Div, Mul, Neg, Sub};
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use ethereum_types::U512;
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use rand::distributions::{Distribution, Standard};
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use rand::Rng;
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use ethereum_types::{U512};
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// use rand::distributions::{Distribution, Standard};
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// use rand::Rng;
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pub trait FieldExt:
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Sized
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+ std::ops::Add<Output = Self>
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+ std::ops::Neg<Output = Self>
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+ std::ops::Sub<Output = Self>
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+ std::ops::Mul<Output = Self>
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+ std::ops::Div<Output = Self>
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{
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const ZERO: Self;
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const UNIT: Self;
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fn inv(self) -> Self;
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}
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pub const BLS_BASE: U512 = U512([
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0xb9feffffffffaaab,
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@ -29,14 +41,14 @@ impl Fp {
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}
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}
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impl Distribution<Fp> for Standard {
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp {
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let xs = rng.gen::<[u64; 8]>();
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Fp {
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val: U512(xs) % BLS_BASE,
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}
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}
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}
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// impl Distribution<Fp> for Standard {
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// fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp {
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// let xs = rng.gen::<[u64; 8]>();
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// Fp {
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// val: U512(xs) % BLS_BASE,
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// }
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// }
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// }
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impl Add for Fp {
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type Output = Self;
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@ -113,8 +125,10 @@ impl Mul for Fp {
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}
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}
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impl Fp {
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pub fn inv(self) -> Fp {
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impl FieldExt for Fp {
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const ZERO: Self = Fp { val: U512::zero() };
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const UNIT: Self = Fp { val: U512::one() };
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fn inv(self) -> Fp {
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exp_fp(self, BLS_BASE - 2)
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}
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}
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@ -128,9 +142,6 @@ impl Div for Fp {
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}
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}
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pub const ZERO_FP: Fp = Fp { val: U512::zero() };
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pub const UNIT_FP: Fp = Fp { val: U512::one() };
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fn exp_fp(x: Fp, e: U512) -> Fp {
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let mut current = x;
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let mut product = Fp { val: U512::one() };
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@ -147,29 +158,20 @@ fn exp_fp(x: Fp, e: U512) -> Fp {
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/// The degree 2 field extension Fp2 is given by adjoining i, the square root of -1, to Fp
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/// The arithmetic in this extension is standard complex arithmetic
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#[derive(Debug, Copy, Clone, PartialEq)]
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pub struct Fp2 {
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pub re: Fp,
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pub im: Fp,
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pub struct Fp2<T> where T: FieldExt {
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pub re: T,
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pub im: T,
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}
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pub const ZERO_FP2: Fp2 = Fp2 {
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re: ZERO_FP,
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im: ZERO_FP,
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};
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pub const UNIT_FP2: Fp2 = Fp2 {
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re: UNIT_FP,
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im: ZERO_FP,
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};
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// impl<T: Distribution<T>> Distribution<Fp2<T>> for Standard {
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// fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp2<T> {
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// let (re, im) = rng.gen::<(T, T)>();
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// Fp2 { re, im }
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// }
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// }
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impl Distribution<Fp2> for Standard {
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp2 {
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let (re, im) = rng.gen::<(Fp, Fp)>();
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Fp2 { re, im }
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}
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}
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impl Add for Fp2 {
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impl<T: FieldExt> Add for Fp2<T> {
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type Output = Self;
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fn add(self, other: Self) -> Self {
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@ -180,7 +182,7 @@ impl Add for Fp2 {
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}
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}
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impl Neg for Fp2 {
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impl<T: FieldExt> Neg for Fp2<T> {
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type Output = Self;
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fn neg(self) -> Self::Output {
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@ -191,7 +193,7 @@ impl Neg for Fp2 {
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}
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}
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impl Sub for Fp2 {
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impl<T: FieldExt> Sub for Fp2<T> {
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type Output = Self;
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fn sub(self, other: Self) -> Self {
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@ -202,7 +204,9 @@ impl Sub for Fp2 {
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}
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}
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impl Mul for Fp2 {
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impl<T: FieldExt> Mul
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for Fp2<T>
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{
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type Output = Self;
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fn mul(self, other: Self) -> Self {
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@ -213,17 +217,9 @@ impl Mul for Fp2 {
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}
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}
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impl Fp2 {
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// We preemptively define a helper function which multiplies an Fp2 element by 1 + i
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fn i1(self) -> Fp2 {
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Fp2 {
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re: self.re - self.im,
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im: self.re + self.im,
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}
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}
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// This function scalar multiplies an Fp2 by an Fp
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pub fn scale(self, x: Fp) -> Fp2 {
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impl<T: FieldExt> Fp2<T> {
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/// This function scalar multiplies an Fp2 by an Fp
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pub fn scale(self, x: T) -> Self {
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Fp2 {
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re: x * self.re,
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im: x * self.im,
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@ -234,8 +230,8 @@ impl Fp2 {
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/// This also happens to be the frobenius map
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/// z -> z^p
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/// since p == 3 mod 4 and hence
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/// i^p = i^3 = -i
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fn conj(self) -> Fp2 {
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/// i^p = i^(4k) * i^3 = 1*(-i) = -i
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fn conj(self) -> Self {
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Fp2 {
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re: self.re,
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im: -self.im,
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@ -243,19 +239,30 @@ impl Fp2 {
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}
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// Return the magnitude squared of a complex number
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fn norm_sq(self) -> Fp {
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fn norm_sq(self) -> T {
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self.re * self.re + self.im * self.im
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}
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}
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impl<T: FieldExt> FieldExt for Fp2<T> {
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const ZERO: Fp2<T> = Fp2 {
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re: T::ZERO,
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im: T::ZERO,
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};
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const UNIT: Fp2<T> = Fp2 {
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re: T::UNIT,
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im: T::ZERO,
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};
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/// The inverse of z is given by z'/||z||^2 since ||z||^2 = zz'
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pub fn inv(self) -> Fp2 {
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fn inv(self) -> Fp2<T> {
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let norm_sq = self.norm_sq();
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self.conj().scale(norm_sq.inv())
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}
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}
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#[allow(clippy::suspicious_arithmetic_impl)]
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impl Div for Fp2 {
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impl<T: FieldExt> Div for Fp2<T> {
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type Output = Self;
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fn div(self, rhs: Self) -> Self::Output {
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@ -263,35 +270,40 @@ impl Div for Fp2 {
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}
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}
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/// The degree 3 field extension Fp6 over Fp2 is given by adjoining t, where t^3 = 1 + i
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// Fp6 has basis 1, t, t^2 over Fp2
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#[derive(Debug, Copy, Clone, PartialEq)]
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pub struct Fp6 {
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pub t0: Fp2,
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pub t1: Fp2,
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pub t2: Fp2,
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trait Adj {
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fn mul_adj(self) -> Self;
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}
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pub const ZERO_FP6: Fp6 = Fp6 {
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t0: ZERO_FP2,
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t1: ZERO_FP2,
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t2: ZERO_FP2,
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};
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pub const UNIT_FP6: Fp6 = Fp6 {
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t0: UNIT_FP2,
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t1: ZERO_FP2,
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t2: ZERO_FP2,
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};
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impl Distribution<Fp6> for Standard {
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp6 {
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let (t0, t1, t2) = rng.gen::<(Fp2, Fp2, Fp2)>();
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Fp6 { t0, t1, t2 }
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/// Helper function which multiplies by the Fp2 element
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/// whose cube root we will adjoin in the next extension
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impl Adj for Fp2<Fp> {
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fn mul_adj(self) -> Self {
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Fp2 {
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re: self.re - self.im,
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im: self.re + self.im,
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}
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}
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}
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impl Add for Fp6 {
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/// The degree 3 field extension Fp6 over Fp2 is given by adjoining t, where t^3 = 1 + i
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/// Fp6 has basis 1, t, t^2 over Fp2
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#[derive(Debug, Copy, Clone, PartialEq)]
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pub struct Fp6<T> where T: FieldExt {
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pub t0: Fp2<T>,
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pub t1: Fp2<T>,
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pub t2: Fp2<T>,
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}
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// impl<T: Distribution<T>> Distribution<Fp6<T>> for Standard {
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// fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp6<T> {
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// let (t0, t1, t2) = rng.gen::<(Fp2<T>, Fp2<T>, Fp2<T>)>();
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// Fp6 { t0, t1, t2 }
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// }
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// }
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impl<T: FieldExt> Add for Fp6<T> {
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type Output = Self;
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fn add(self, other: Self) -> Self {
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@ -303,7 +315,7 @@ impl Add for Fp6 {
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}
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}
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impl Neg for Fp6 {
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impl<T: FieldExt> Neg for Fp6<T> {
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type Output = Self;
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fn neg(self) -> Self::Output {
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@ -315,7 +327,7 @@ impl Neg for Fp6 {
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}
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}
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impl Sub for Fp6 {
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impl<T: FieldExt> Sub for Fp6<T> {
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type Output = Self;
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fn sub(self, other: Self) -> Self {
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@ -327,38 +339,47 @@ impl Sub for Fp6 {
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}
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}
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impl Mul for Fp6 {
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impl<T: FieldExt> Mul for Fp6<T> {
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type Output = Self;
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fn mul(self, other: Self) -> Self {
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Fp6 {
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t0: self.t0 * other.t0 + (self.t1 * other.t2 + self.t2 * other.t1).i1(),
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t1: self.t0 * other.t1 + self.t1 * other.t0 + (self.t2 * other.t2).i1(),
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t0: self.t0 * other.t0 + (self.t1 * other.t2 + self.t2 * other.t1).mul_adj(),
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t1: self.t0 * other.t1 + self.t1 * other.t0 + (self.t2 * other.t2).mul_adj(),
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t2: self.t0 * other.t2 + self.t1 * other.t1 + self.t2 * other.t0,
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}
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}
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}
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impl Fp6 {
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impl<T: FieldExt> Fp6<T> {
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// This function scalar multiplies an Fp6 by an Fp2
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fn scale(self, x: Fp2) -> Fp6 {
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fn scale(self, x: Fp2<T>) -> Fp6<T> {
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Fp6 {
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t0: x * self.t0,
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t1: x * self.t1,
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t2: x * self.t2,
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}
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}
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}
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impl<T: FieldExt + Adj> Fp6<T> {
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/// This function multiplies an Fp6 element by t, and hence shifts the bases,
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/// where the t^2 coefficient picks up a factor of 1+i as the 1 coefficient of the output
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fn sh(self) -> Fp6 {
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fn sh(self) -> Fp6<T> {
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Fp6 {
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t0: self.t2.i1(),
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t0: self.t2.mul_adj(),
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t1: self.t0,
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t2: self.t1,
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}
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}
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}
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pub trait Frob {
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const FROB_T: Self;
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const FROB_Z: Self;
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}
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impl<T: Frob + FieldExt> Fp6<T> {
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/// The nth frobenius endomorphism of a p^q field is given by mapping
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/// x to x^(p^n)
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/// which sends a + bt + ct^2: Fp6 to
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@ -367,10 +388,10 @@ impl Fp6 {
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/// while the values of
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/// t^(p^n) and t^(2p^n)
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/// are precomputed in the constant arrays FROB_T1 and FROB_T2
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pub fn frob(self, n: usize) -> Fp6 {
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pub fn frob(self, n: usize) -> Fp6<T> {
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let n = n % 6;
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let frob_t1 = FROB_T1[n];
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let frob_t2 = FROB_T2[n];
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let frob_t1 = Self::FROB_T[0][n];
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let frob_t2 = Self::FROB_T[1][n];
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if n % 2 != 0 {
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Fp6 {
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@ -386,6 +407,20 @@ impl Fp6 {
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}
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}
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}
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}
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impl<T: FieldExt + Adj> FieldExt for Fp6<T> {
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const ZERO: Fp6<T> = Fp6 {
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t0: Fp2::<T>::ZERO,
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t1: Fp2::<T>::ZERO,
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t2: Fp2::<T>::ZERO,
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};
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const UNIT: Fp6<T> = Fp6 {
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t0: Fp2::<T>::UNIT,
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t1: Fp2::<T>::ZERO,
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t2: Fp2::<T>::ZERO,
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};
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/// Let x_n = x^(p^n) and note that
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/// x_0 = x^(p^0) = x^1 = x
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@ -402,7 +437,7 @@ impl Fp6 {
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/// phi = ||x_1 * x_3 * x_5||^2
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/// and hence the inverse is given by
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/// ([x_1 * x_3] * x_5) * [x_1 * x_3]_1 / ||[x_1 * x_3] * x_5||^2
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pub fn inv(self) -> Fp6 {
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fn inv(self) -> Fp6<T> {
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let prod_13 = self.frob(1) * self.frob(3);
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let prod_135 = (prod_13 * self.frob(5)).t0;
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let phi = prod_135.norm_sq();
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@ -410,15 +445,10 @@ impl Fp6 {
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let prod_24 = prod_13.frob(1);
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prod_24.scale(prod_odds_over_phi)
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}
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pub fn on_stack(self) -> Vec<U512> {
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let f: [U512; 6] = unsafe { transmute(self) };
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f.into_iter().collect()
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}
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}
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#[allow(clippy::suspicious_arithmetic_impl)]
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impl Div for Fp6 {
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impl<T: FieldExt> Div for Fp6<T> {
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type Output = Self;
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fn div(self, rhs: Self) -> Self::Output {
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@ -426,108 +456,111 @@ impl Div for Fp6 {
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}
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}
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/// The degree 2 field extension Fp12 over Fp6 is given by adjoining z, where z^2 = t.
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/// It thus has basis 1, z over Fp6
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#[derive(Debug, Copy, Clone, PartialEq)]
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pub struct Fp12 {
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pub z0: Fp6,
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pub z1: Fp6,
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}
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// /// The degree 2 field extension Fp12 over Fp6 is given by adjoining z, where z^2 = t.
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// /// It thus has basis 1, z over Fp6
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// #[derive(Debug, Copy, Clone, PartialEq)]
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// pub struct Fp12<T> {
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// pub z0: Fp6<T>,
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// pub z1: Fp6<T>,
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// }
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pub const UNIT_FP12: Fp12 = Fp12 {
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z0: UNIT_FP6,
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z1: ZERO_FP6,
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};
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// impl<T: Unital> Unital for Fp12<T> {
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// const ZERO: Fp12<T> = Fp12 {
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// z0: Fp6::<T>::ZERO,
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// z1: Fp6::<T>::ZERO,
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// };
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impl Distribution<Fp12> for Standard {
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp12 {
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let (z0, z1) = rng.gen::<(Fp6, Fp6)>();
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Fp12 { z0, z1 }
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}
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}
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// const UNIT: Fp12<T> = Fp12 {
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// z0: Fp6::<T>::UNIT,
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// z1: Fp6::<T>::ZERO,
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// };
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// }
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impl Mul for Fp12 {
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type Output = Self;
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// // impl<T: Distribution<T>> Distribution<Fp12<T>> for Standard {
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// // fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Fp12<T> {
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// // let (z0, z1) = rng.gen::<(Fp6, Fp6)>();
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// // Fp12 { z0, z1 }
|
||||
// // }
|
||||
// // }
|
||||
|
||||
fn mul(self, other: Self) -> Self {
|
||||
let h0 = self.z0 * other.z0;
|
||||
let h1 = self.z1 * other.z1;
|
||||
let h01 = (self.z0 + self.z1) * (other.z0 + other.z1);
|
||||
Fp12 {
|
||||
z0: h0 + h1.sh(),
|
||||
z1: h01 - (h0 + h1),
|
||||
}
|
||||
}
|
||||
}
|
||||
// impl<T: Mul> Mul for Fp12<T> {
|
||||
// type Output = Self;
|
||||
|
||||
impl Fp12 {
|
||||
// This function scalar multiplies an Fp12 by an Fp6
|
||||
fn scale(self, x: Fp6) -> Fp12 {
|
||||
Fp12 {
|
||||
z0: x * self.z0,
|
||||
z1: x * self.z1,
|
||||
}
|
||||
}
|
||||
// fn mul(self, other: Self) -> Self {
|
||||
// let h0 = self.z0 * other.z0;
|
||||
// let h1 = self.z1 * other.z1;
|
||||
// let h01 = (self.z0 + self.z1) * (other.z0 + other.z1);
|
||||
// Fp12 {
|
||||
// z0: h0 + h1.sh(),
|
||||
// z1: h01 - (h0 + h1),
|
||||
// }
|
||||
// }
|
||||
// }
|
||||
|
||||
fn conj(self) -> Fp12 {
|
||||
Fp12 {
|
||||
z0: self.z0,
|
||||
z1: -self.z1,
|
||||
}
|
||||
}
|
||||
/// The nth frobenius endomorphism of a p^q field is given by mapping
|
||||
/// x to x^(p^n)
|
||||
/// which sends a + bz: Fp12 to
|
||||
/// a^(p^n) + b^(p^n) * z^(p^n)
|
||||
/// where the values of z^(p^n) are precomputed in the constant array FROB_Z
|
||||
pub fn frob(self, n: usize) -> Fp12 {
|
||||
let n = n % 12;
|
||||
Fp12 {
|
||||
z0: self.z0.frob(n),
|
||||
z1: self.z1.frob(n).scale(FROB_Z[n]),
|
||||
}
|
||||
}
|
||||
// impl<T> Fp12<T> {
|
||||
// // This function scalar multiplies an Fp12 by an Fp6
|
||||
// fn scale(self, x: Fp6<T>) -> Fp12<T> {
|
||||
// Fp12 {
|
||||
// z0: x * self.z0,
|
||||
// z1: x * self.z1,
|
||||
// }
|
||||
// }
|
||||
|
||||
/// By Galois Theory, given x: Fp12, the product
|
||||
/// phi = Prod_{i=0}^11 x_i
|
||||
/// lands in Fp, and hence the inverse of x is given by
|
||||
/// (Prod_{i=1}^11 x_i) / phi
|
||||
/// The 6th Frob map is nontrivial but leaves Fp6 fixed and hence must be the conjugate:
|
||||
/// x_6 = (a + bz)_6 = a - bz = x.conj()
|
||||
/// Letting prod_17 = x_1 * x_7, the remaining factors in the numerator can be expresed as:
|
||||
/// [(prod_17) * (prod_17)_2] * (prod_17)_4 * [(prod_17) * (prod_17)_2]_1
|
||||
/// By Galois theory, both the following are in Fp2 and are complex conjugates
|
||||
/// prod_odds, prod_evens
|
||||
/// Thus phi = ||prod_odds||^2, and hence the inverse is given by
|
||||
/// prod_odds * prod_evens_except_six * x.conj() / ||prod_odds||^2
|
||||
pub fn inv(self) -> Fp12 {
|
||||
let prod_17 = (self.frob(1) * self.frob(7)).z0;
|
||||
let prod_1379 = prod_17 * prod_17.frob(2);
|
||||
let prod_odds = (prod_1379 * prod_17.frob(4)).t0;
|
||||
let phi = prod_odds.norm_sq();
|
||||
let prod_odds_over_phi = prod_odds.scale(phi.inv());
|
||||
let prod_evens_except_six = prod_1379.frob(1);
|
||||
let prod_except_six = prod_evens_except_six.scale(prod_odds_over_phi);
|
||||
self.conj().scale(prod_except_six)
|
||||
}
|
||||
// fn conj(self) -> Fp12<T> {
|
||||
// Fp12 {
|
||||
// z0: self.z0,
|
||||
// z1: -self.z1,
|
||||
// }
|
||||
// }
|
||||
// }
|
||||
|
||||
pub fn on_stack(self) -> Vec<U512> {
|
||||
let f: [U512; 12] = unsafe { transmute(self) };
|
||||
f.into_iter().collect()
|
||||
}
|
||||
}
|
||||
// impl<T: Frob> Fp12<T> {
|
||||
// /// The nth frobenius endomorphism of a p^q field is given by mapping
|
||||
// /// x to x^(p^n)
|
||||
// /// which sends a + bz: Fp12 to
|
||||
// /// a^(p^n) + b^(p^n) * z^(p^n)
|
||||
// /// where the values of z^(p^n) are precomputed in the constant array FROB_Z
|
||||
// pub fn frob(self, n: usize) -> Fp12<T> {
|
||||
// let n = n % 12;
|
||||
// Fp12 {
|
||||
// z0: self.z0.frob(n),
|
||||
// z1: self.z1.frob(n).scale(Self::FROB_Z[n]),
|
||||
// }
|
||||
// }
|
||||
|
||||
#[allow(clippy::suspicious_arithmetic_impl)]
|
||||
impl Div for Fp12 {
|
||||
type Output = Self;
|
||||
// /// By Galois Theory, given x: Fp12, the product
|
||||
// /// phi = Prod_{i=0}^11 x_i
|
||||
// /// lands in Fp, and hence the inverse of x is given by
|
||||
// /// (Prod_{i=1}^11 x_i) / phi
|
||||
// /// The 6th Frob map is nontrivial but leaves Fp6 fixed and hence must be the conjugate:
|
||||
// /// x_6 = (a + bz)_6 = a - bz = x.conj()
|
||||
// /// Letting prod_17 = x_1 * x_7, the remaining factors in the numerator can be expresed as:
|
||||
// /// [(prod_17) * (prod_17)_2] * (prod_17)_4 * [(prod_17) * (prod_17)_2]_1
|
||||
// /// By Galois theory, both the following are in Fp2 and are complex conjugates
|
||||
// /// prod_odds, prod_evens
|
||||
// /// Thus phi = ||prod_odds||^2, and hence the inverse is given by
|
||||
// /// prod_odds * prod_evens_except_six * x.conj() / ||prod_odds||^2
|
||||
// pub fn inv(self) -> Fp12<T> {
|
||||
// let prod_17 = (self.frob(1) * self.frob(7)).z0;
|
||||
// let prod_1379 = prod_17 * prod_17.frob(2);
|
||||
// let prod_odds = (prod_1379 * prod_17.frob(4)).t0;
|
||||
// let phi = prod_odds.norm_sq();
|
||||
// let prod_odds_over_phi = prod_odds.scale(phi.inv());
|
||||
// let prod_evens_except_six = prod_1379.frob(1);
|
||||
// let prod_except_six = prod_evens_except_six.scale(prod_odds_over_phi);
|
||||
// self.conj().scale(prod_except_six)
|
||||
// }
|
||||
// }
|
||||
|
||||
fn div(self, rhs: Self) -> Self::Output {
|
||||
self * rhs.inv()
|
||||
}
|
||||
}
|
||||
// #[allow(clippy::suspicious_arithmetic_impl)]
|
||||
// impl<T: std::ops::Div<Output = T>> Div for Fp12<T> {
|
||||
// type Output = Self;
|
||||
|
||||
const FROB_T1: [Fp2; 6] = [ZERO_FP2; 6];
|
||||
// fn div(self, rhs: Self) -> Self::Output {
|
||||
// self * rhs.inv()
|
||||
// }
|
||||
// }
|
||||
|
||||
const FROB_T2: [Fp2; 6] = [ZERO_FP2; 6];
|
||||
|
||||
const FROB_Z: [Fp2; 12] = [ZERO_FP2; 12];
|
||||
// trait Stack {
|
||||
// fn on_stack(self) -> Vec<U256>;
|
||||
// }
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user