logos-storage/plonky2
1
0
Fork 0
mirror of https://github.com/logos-storage/plonky2.git synced 2026-02-06 23:13:13 +00:00
Code Issues Packages Projects Releases Wiki Activity

extra comments

Browse Source
This commit is contained in:
Dmitry Vagner 2023-01-21 15:55:45 +07:00
parent 8b670d54d1
commit 94d99cca9e
1 changed files with 25 additions and 27 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

52
evm/src/bn254_pairing.rs
View File

@ -1,7 +1,9 @@
use std::ops::Add;
use ethereum_types::U256;
use crate::bn254_arithmetic::{
frob_fp12, inv_fp12, make_fp, mul_fp_fp2, Fp, Fp12, Fp2, UNIT_FP12, sparse_embed
frob_fp12, inv_fp12, make_fp, mul_fp_fp2, sparse_embed, Fp, Fp12, Fp2, UNIT_FP12,
};
// The curve consists of pairs (x, y): (Fp, Fp) | y^2 = x^3 + 2
@ -11,7 +13,26 @@ pub struct Curve {
y: Fp,
}
// The twisted consists of pairs (x, y): (Fp2, Fp2) |
/// Standard addition formula for elliptic curves, source:
/// https://en.wikipedia.org/wiki/Elliptic_curve#Algebraic_interpretation
impl Add for Curve {
type Output = Self;
fn add(self, other: Self) -> Self {
let m = if self == other {
make_fp(3) * self.x * self.x / (make_fp(2) * self.y)
} else {
(other.y - self.y) / (other.x - self.x)
};
let x = m * m - (self.x + other.x);
Curve {
x,
y: m * (self.x - x) - self.y,
}
}
}
// The twisted curve consists of pairs (x, y): (Fp2, Fp2) | y^2 = x^3 + 3/(9 + i)
#[derive(Debug, Copy, Clone, PartialEq)]
pub struct TwistedCurve {
x: Fp2,
@ -48,11 +69,11 @@ pub fn miller_loop(p: Curve, q: TwistedCurve) -> Fp12 {
acc = acc * acc;
line = tangent(o, q);
acc = line * acc;
o = curve_double(o);
o = o + o;
if i != 0 {
line = cord(p, o, q);
acc = line * acc;
o = curve_add(p, o);
o = o + p;
}
}
acc
@ -260,7 +281,6 @@ pub fn tangent(p: Curve, q: TwistedCurve) -> Fp12 {
pub fn cord(p1: Curve, p2: Curve, q: TwistedCurve) -> Fp12 {
let cx = p2.y - p1.y;
let cy = p1.x - p2.x;
sparse_embed(
p1.y * p2.x - p2.y * p1.x,
mul_fp_fp2(cx, q.x),
@ -268,28 +288,6 @@ pub fn cord(p1: Curve, p2: Curve, q: TwistedCurve) -> Fp12 {
)
}
fn third_point(m: Fp, p: Curve, q: Curve) -> Curve {
let x = m * m - (p.x + q.x);
Curve {
x,
y: m * (p.x - x) - p.y,
}
}
fn curve_add(p: Curve, q: Curve) -> Curve {
if p == q {
curve_double(p)
} else {
let slope = (q.y - p.y) / (q.x - p.x);
third_point(slope, p, q)
}
}
fn curve_double(p: Curve) -> Curve {
let slope = p.x * p.x * make_fp(3) / (p.y * make_fp(2));
third_point(slope, p, p)
}
// This curve is cyclic with generator (1, 2)
pub fn curve_generator() -> Curve {
Curve {