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optimise fq non residue mul #24

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optimise fq non residue mul #24

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6 changes: 6 additions & 0 deletions src/fields/fp.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -257,6 +257,12 @@ impl Fq {
Some(a1a)
}
}

pub fn mul_by_nonresidue(&self) -> Self {
// (q - 1) is a quadratic nonresidue in Fq
// Additive inverse for mul by (q - 1) or (-1 mod q)
-*self
}
}

#[inline]
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12 changes: 6 additions & 6 deletions src/fields/fq2.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ use crate::fields::{const_fq, FieldElement, Fq};
use crate::arith::{U256, U512};

#[inline]
fn fq_non_residue() -> Fq {
fn _fq_non_residue() -> Fq {
// (q - 1) is a quadratic nonresidue in Fq
// 21888242871839275222246405745257275088696311157297823662689037894645226208582
const_fq([
Expand Down Expand Up @@ -62,7 +62,7 @@ impl Fq2 {
} else {
Fq2 {
c0: self.c0,
c1: self.c1 * fq_non_residue(),
c1: self.c1.mul_by_nonresidue(),
}
}
}
Expand Down Expand Up @@ -110,8 +110,8 @@ impl FieldElement for Fq2 {
let ab = self.c0 * self.c1;

Fq2 {
c0: (self.c1 * fq_non_residue() + self.c0) * (self.c0 + self.c1) - ab
- ab * fq_non_residue(),
c0: (self.c1.mul_by_nonresidue() + self.c0) * (self.c0 + self.c1) - ab
- ab.mul_by_nonresidue(),
c1: ab + ab,
}
}
Expand All @@ -120,7 +120,7 @@ impl FieldElement for Fq2 {
// "High-Speed Software Implementation of the Optimal Ate Pairing
// over Barreto–Naehrig Curves"; Algorithm 8

match (self.c0.squared() - (self.c1.squared() * fq_non_residue())).inverse() {
match (self.c0.squared() - (self.c1.squared().mul_by_nonresidue())).inverse() {
Some(t) => Some(Fq2 {
c0: self.c0 * t,
c1: -(self.c1 * t),
Expand All @@ -142,7 +142,7 @@ impl Mul for Fq2 {
let bb = self.c1 * other.c1;

Fq2 {
c0: bb * fq_non_residue() + aa,
c0: bb.mul_by_nonresidue() + aa,
c1: (self.c0 + self.c1) * (other.c0 + other.c1) - aa - bb,
}
}
Expand Down