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Polish sqrt in fr.rs: use pattern matching with Legendre enums.

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Michele Orrù 2017-08-10 18:18:46 +02:00
parent 57b4e73627
commit 2d3f498e75
1 changed files with 29 additions and 31 deletions
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60
src/bls12_381/fr.rs
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@ -555,45 +555,42 @@ impl SqrtField for Fr {
fn sqrt(&self) -> Option<Self> {
// Tonelli-Shank's algorithm for q mod 16 = 1
// https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
match self.legendre() {
Zero => Some(*self),
QNonResidue => None,
QResidue => {
let mut c = Fr(ROOT_OF_UNITY);
// r = self^((t + 1) // 2)
let mut r = self.pow([0x7fff2dff80000000, 0x4d0ec02a9ded201, 0x94cebea4199cec04, 0x39f6d3a9]);
// t = self^t
let mut t = self.pow([0xfffe5bfeffffffff, 0x9a1d80553bda402, 0x299d7d483339d808, 0x73eda753]);
let mut m = S;
if self.is_zero() {
return Some(*self);
}
if let QNonResidue = self.legendre() {
None
} else {
let mut c = Fr(ROOT_OF_UNITY);
// r = self^((t + 1) // 2)
let mut r = self.pow([0x7fff2dff80000000, 0x4d0ec02a9ded201, 0x94cebea4199cec04, 0x39f6d3a9]);
// t = self^t
let mut t = self.pow([0xfffe5bfeffffffff, 0x9a1d80553bda402, 0x299d7d483339d808, 0x73eda753]);
let mut m = S;
while t != Self::one() {
while t != Self::one() {
let mut i = 1;
{
let mut t2i = t;
t2i.square();
loop {
if t2i == Self::one() {
break;
}
{
let mut t2i = t;
t2i.square();
i += 1;
loop {
if t2i == Self::one() {
break;
}
t2i.square();
i += 1;
}
}
}
for _ in 0..(m - i - 1) {
for _ in 0..(m - i - 1) {
c.square();
}
r.mul_assign(&c);
c.square();
t.mul_assign(&c);
m = i;
}
r.mul_assign(&c);
c.square();
t.mul_assign(&c);
m = i;
}
Some(r)
Some(r)
}
}
}
}
@ -606,6 +603,7 @@ impl LegendreField for Fr {
else { QNonResidue }
}
}
#[cfg(test)]
use rand::{SeedableRng, XorShiftRng, Rand};