mirror of
https://github.com/logos-storage/plonky2.git
synced 2026-01-13 11:13:07 +00:00
cleanup
This commit is contained in:
Dmitry Vagner
parent
530fb65b7e
commit
769c615cf1
@ -185,7 +185,7 @@ fn normalize_fp2(a: Fp2) -> Fp2 {
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/// The degree 3 field extension Fp6 over Fp2 is given by adjoining t, where t^3 = 9 + i
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/// We begin by defining a helper function which multiplies an Fp2 element by 9 + i
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fn i9(a: Fp2) -> Fp2 {
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let nine = Fp { val: U256::from(9) };
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let nine = make_fp(9);
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Fp2 {
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re: nine * a.re - a.im,
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im: a.re + nine * a.im,
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@ -4,52 +4,58 @@ use crate::bn254_arithmetic::{
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frob_fp12, inv_fp12, make_fp, mul_fp_fp2, sparse_embed, Fp, Fp12, Fp2, UNIT_FP12,
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};
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pub type Curve = [Fp; 2];
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pub type TwistedCurve = [Fp2; 2];
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pub fn curve_generator() -> Curve {
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[make_fp(1), make_fp(2)]
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// The curve consists of pairs (x, y): (Fp, Fp) | y^2 = x^3 + 2
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#[derive(Debug, Copy, Clone, PartialEq)]
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pub struct Curve {
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x: Fp,
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y: Fp,
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}
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pub fn twisted_curve_generator() -> TwistedCurve {
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[
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Fp2 {
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re: Fp {
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val: U256([
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0x46debd5cd992f6ed,
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0x674322d4f75edadd,
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0x426a00665e5c4479,
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0x1800deef121f1e76,
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]),
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},
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im: Fp {
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val: U256([
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0x97e485b7aef312c2,
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0xf1aa493335a9e712,
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0x7260bfb731fb5d25,
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0x198e9393920d483a,
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]),
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},
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},
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Fp2 {
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re: Fp {
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val: U256([
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0x4ce6cc0166fa7daa,
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0xe3d1e7690c43d37b,
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0x4aab71808dcb408f,
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0x12c85ea5db8c6deb,
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]),
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},
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im: Fp {
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val: U256([
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0x55acdadcd122975b,
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0xbc4b313370b38ef3,
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0xec9e99ad690c3395,
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0x90689d0585ff075,
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]),
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},
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},
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]
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// The twisted consists of pairs (x, y): (Fp2, Fp2) |
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#[derive(Debug, Copy, Clone, PartialEq)]
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pub struct TwistedCurve {
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x: Fp2,
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y: Fp2,
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}
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// The tate pairing takes point each from the curve and its twist and outputs an Fp12
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pub fn tate(p: Curve, q: TwistedCurve) -> Fp12 {
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let miller_output = miller_loop(p, q);
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let post_mul_1 = frob_fp12(6, miller_output) / miller_output;
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let post_mul_2 = frob_fp12(2, post_mul_1) * post_mul_1;
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let power_output = power(post_mul_2);
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frob_fp12(3, post_mul_2) * power_output
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}
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pub fn miller_loop(p: Curve, q: TwistedCurve) -> Fp12 {
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const EXP: [usize; 253] = [
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1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1,
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1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
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1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0,
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1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0,
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1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0,
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1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0,
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1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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];
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let mut o = p;
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let mut acc = UNIT_FP12;
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let mut line;
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for i in EXP {
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acc = acc * acc;
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line = tangent(o, q);
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acc = line * acc;
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o = curve_double(o);
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if i != 0 {
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line = cord(p, o, q);
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acc = line * acc;
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o = curve_add(p, o);
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}
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}
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acc
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}
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pub fn power(f: Fp12) -> Fp12 {
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@ -242,107 +248,94 @@ pub fn power(f: Fp12) -> Fp12 {
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}
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pub fn tangent(p: Curve, q: TwistedCurve) -> Fp12 {
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let [px, py] = p;
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let [qx, qy] = q;
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let cx = -make_fp(3) * px * px;
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let cy = make_fp(2) * py;
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sparse_embed(py * py - make_fp(9), mul_fp_fp2(cx, qx), mul_fp_fp2(cy, qy))
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}
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pub fn cord(p1: Curve, p2: Curve, q: TwistedCurve) -> Fp12 {
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let [p1x, p1y] = p1;
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let [p2x, p2y] = p2;
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let [qx, qy] = q;
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let cx = p2y - p1y;
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let cy = p1x - p2x;
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let cx = -make_fp(3) * p.x * p.x;
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let cy = make_fp(2) * p.y;
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sparse_embed(
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p1y * p2x - p2y * p1x,
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mul_fp_fp2(cx, qx),
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mul_fp_fp2(cy, qy),
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p.y * p.y - make_fp(9),
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mul_fp_fp2(cx, q.x),
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mul_fp_fp2(cy, q.y),
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)
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}
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fn tangent_slope(p: Curve) -> Fp {
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let [px, py] = p;
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let num = px * px * make_fp(3);
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let denom = py * make_fp(2);
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num / denom
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}
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pub fn cord(p1: Curve, p2: Curve, q: TwistedCurve) -> Fp12 {
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let cx = p2.y - p1.y;
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let cy = p1.x - p2.x;
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fn cord_slope(p: Curve, q: Curve) -> Fp {
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let [px, py] = p;
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let [qx, qy] = q;
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let num = qy - py;
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let denom = qx - px;
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num / denom
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sparse_embed(
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p1.y * p2.x - p2.y * p1.x,
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mul_fp_fp2(cx, q.x),
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mul_fp_fp2(cy, q.y),
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)
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}
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fn third_point(m: Fp, p: Curve, q: Curve) -> Curve {
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let [px, py] = p;
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let [qx, _] = q;
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let ox = m * m - (px + qx);
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let oy = m * (px - ox) - py;
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[ox, oy]
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let x = m * m - (p.x + q.x);
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Curve {
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x,
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y: m * (p.x - x) - p.y,
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}
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}
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fn curve_add(p: Curve, q: Curve) -> Curve {
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if p == q {
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curve_double(p)
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} else {
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third_point(cord_slope(p, q), p, q)
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let slope = (q.y - p.y) / (q.x - p.x);
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third_point(slope, p, q)
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}
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}
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fn curve_double(p: Curve) -> Curve {
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third_point(tangent_slope(p), p, p)
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let slope = p.x * p.x * make_fp(3) / (p.y * make_fp(2));
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third_point(slope, p, p)
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}
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pub fn miller_loop(p: Curve, q: TwistedCurve) -> Fp12 {
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const EXP: [usize; 253] = [
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1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1,
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1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
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1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0,
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1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0,
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1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0,
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1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0,
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1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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];
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let mut o = p;
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let mut acc = UNIT_FP12;
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let mut line;
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for i in EXP {
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acc = acc * acc;
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line = tangent(o, q);
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acc = line * acc;
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o = curve_double(o);
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if i != 0 {
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line = cord(p, o, q);
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acc = line * acc;
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o = curve_add(p, o);
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}
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// This curve is cyclic with generator (1, 2)
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pub fn curve_generator() -> Curve {
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Curve {
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x: make_fp(1),
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y: make_fp(2),
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}
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acc
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}
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pub fn tate(p: Curve, q: TwistedCurve) -> Fp12 {
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let mut out = miller_loop(p, q);
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let inv = inv_fp12(out);
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out = frob_fp12(6, out);
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out = out * inv;
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let acc = frob_fp12(2, out);
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out = out * acc;
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let pow = power(out);
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out = frob_fp12(3, out);
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out * pow
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// This curve is cyclic with generator (x, y) as follows
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pub fn twisted_curve_generator() -> TwistedCurve {
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TwistedCurve {
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x: Fp2 {
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re: Fp {
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val: U256([
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0x46debd5cd992f6ed,
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0x674322d4f75edadd,
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0x426a00665e5c4479,
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0x1800deef121f1e76,
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]),
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},
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im: Fp {
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val: U256([
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0x97e485b7aef312c2,
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0xf1aa493335a9e712,
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0x7260bfb731fb5d25,
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0x198e9393920d483a,
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]),
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},
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},
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y: Fp2 {
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re: Fp {
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val: U256([
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0x4ce6cc0166fa7daa,
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0xe3d1e7690c43d37b,
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0x4aab71808dcb408f,
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0x12c85ea5db8c6deb,
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]),
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},
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im: Fp {
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val: U256([
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0x55acdadcd122975b,
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0xbc4b313370b38ef3,
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0xec9e99ad690c3395,
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0x090689d0585ff075,
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]),
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},
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},
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}
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}
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@ -9,7 +9,7 @@
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pub mod all_stark;
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pub mod arithmetic;
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pub mod bn254_arithmetic;
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pub mod bn254_curve_pairing;
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pub mod bn254_pairing;
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pub mod config;
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pub mod constraint_consumer;
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pub mod cpu;
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