logos-storage/plonky2
1
0
Fork 0
mirror of https://github.com/logos-storage/plonky2.git synced 2026-01-10 01:33:07 +00:00
Code Issues Packages Projects Releases Wiki Activity

transmute + comments

Browse Source
This commit is contained in:
Dmitry Vagner 2023-01-18 20:53:59 +07:00
parent 6e21538673
commit 985e816039
1 changed files with 40 additions and 44 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

84
evm/src/bn254_arithmetic.rs
View File

@ -1,4 +1,4 @@
use std::ops::{Add, Div, Mul, Neg, Sub};
use std::{ops::{Add, Div, Mul, Neg, Sub}, mem::transmute};
use ethereum_types::U256;
use itertools::Itertools;
@ -164,7 +164,7 @@ fn conj_fp2(a: Fp2) -> Fp2 {
}
}
// This function function normalizes the input to the complex unit circle
// This function normalizes the input to the complex unit circle
fn normalize_fp2(a: Fp2) -> Fp2 {
let norm = a.re * a.re + a.im * a.im;
Fp2 {
@ -281,31 +281,6 @@ fn sh(c: Fp6) -> Fp6 {
}
}
/// The nth frobenius endomorphism is given by sending a field element r to r^(p^n)
/// Hence an Fp6 element a + bt + ct^2 is sent to
/// a^(p^n) + b^(p^n) * t^(p^n) + c^(p^n) * t^(2p^n)
/// the constant arrays FROB_T1 and FROB_T2 record the values of t^(p^n) and t^(2p^n), respectively
/// By the comment in conj_fp2, x^(p^n) = x when n is even and conj_fp2(x) when n is odd
fn frob_fp6(n: usize, c: Fp6) -> Fp6 {
let n = n % 6;
let frob_t1 = FROB_T1[n];
let frob_t2 = FROB_T2[n];
if n % 2 != 0 {
Fp6 {
t0: conj_fp2(c.t0),
t1: frob_t1 * conj_fp2(c.t1),
t2: frob_t2 * conj_fp2(c.t2),
}
} else {
Fp6 {
t0: c.t0,
t1: frob_t1 * c.t1,
t2: frob_t2 * c.t2,
}
}
}
/// The degree 2 field extension Fp12 over Fp6 is given by adjoining z, where z^2 = t.
/// It thus has basis 1, z over Fp6
#[derive(Debug, Copy, Clone, PartialEq)]
@ -373,10 +348,44 @@ fn sparse_embed(g000: Fp, g01: Fp2, g11: Fp2) -> Fp12 {
Fp12 { z0: g0, z1: g1 }
}
/// The nth frobenius endomorphism is given by sending a field element r to r^(p^n)
/// Hence an Fp12 element a + bz is sent to
/// The nth frobenius endomorphism of a finite field F of order p^q is given by sending x: F to x^(p^n)
/// since any element x: F satisfies x^(p^q) = x = x^(p^0), these endomorphisms cycle modulo q
///
/// Thus in the case of Fp, there are no nontrivial such endomorphisms since x^p = x.
///
/// In the case of Fp2, the first and only nontrivial frobenius map sends a + bi to its complex conjugate:
/// a^p + b^p(i^p) = a - bi
/// since p == 3 mod 4, and i^3 = -i
///
/// An Fp6 element a + bt + ct^2 is sent to
/// a^(p^n) + b^(p^n) * t^(p^n) + c^(p^n) * t^(2p^n)
/// where the values of t^(p^n) and t^(2p^n) are precomputed in the constant arrays FROB_T1 and FROB_T2
///
///
/// An Fp12 element a + bz is sent to
/// a^(p^n) + b^(p^n) * z^(p^n)
/// the constant array FROB_Z records the values of z^p^n
/// where the values of z^(p^n) are precomputed in the constant array FROB_Z
fn frob_fp6(n: usize, c: Fp6) -> Fp6 {
let n = n % 6;
let frob_t1 = FROB_T1[n];
let frob_t2 = FROB_T2[n];
if n % 2 != 0 {
Fp6 {
t0: conj_fp2(c.t0),
t1: frob_t1 * conj_fp2(c.t1),
t2: frob_t2 * conj_fp2(c.t2),
}
} else {
Fp6 {
t0: c.t0,
t1: frob_t1 * c.t1,
t2: frob_t2 * c.t2,
}
}
}
pub fn frob_fp12(n: usize, f: Fp12) -> Fp12 {
let n = n % 12;
Fp12 {
@ -386,20 +395,7 @@ pub fn frob_fp12(n: usize, f: Fp12) -> Fp12 {
}
pub fn fp12_to_array(f: Fp12) -> [U256; 12] {
[
f.z0.t0.re.val,
f.z0.t0.im.val,
f.z0.t1.re.val,
f.z0.t1.im.val,
f.z0.t2.re.val,
f.z0.t2.im.val,
f.z1.t0.re.val,
f.z1.t0.im.val,
f.z1.t1.re.val,
f.z1.t1.im.val,
f.z1.t2.re.val,
f.z1.t2.im.val,
]
unsafe { transmute(f) }
}
pub fn fp12_to_vec(f: Fp12) -> Vec<U256> {