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Use more efficient addition chain for scalar inversion.

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Use the addition chain from
https://briansmith.org/ecc-inversion-addition-chains-01#curve25519_scalar_inversion.

In my benchmarking, this consistently runs at least 20% faster.
This commit is contained in:
Brian Smith 2017-09-03 16:49:26 -10:00
parent 5494648718
commit 91a7c641c2
1 changed files with 53 additions and 6 deletions
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59
src/scalar.rs
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@ -2,11 +2,13 @@
//
// This file is part of curve25519-dalek.
// Copyright (c) 2016-2017 Isis Lovecruft, Henry de Valence
// Portions Copyright 2017 Brian Smith
// See LICENSE for licensing information.
//
// Authors:
// - Isis Agora Lovecruft <isis@patternsinthevoid.net>
// - Henry de Valence <hdevalence@hdevalence.ca>
// - Brian Smith <brian@briansmith.org>
//! Arithmetic for scalar multiplication.
//!
@ -565,14 +567,59 @@ impl UnpackedScalar {
/// Compute the multiplicative inverse of this scalar.
pub fn invert(&self) -> UnpackedScalar {
let mut y = UnpackedScalar::one();
// Run through bits of l-2 from highest to least
for bit in constants::l_minus_2.bits().iter().rev() {
y = y.square();
if *bit == 1 {
y = UnpackedScalar::multiply_add(&y, self, &UnpackedScalar::zero());
// This is a direct transliteration of the addition chain from
// https://briansmith.org/ecc-inversion-addition-chains-01#curve25519_scalar_inversion
// as it was published on 2017-09-03.
let _1 = *self;
let _10 = _1.square();
let _11 = UnpackedScalar::multiply_add(&_10, &_1, &UnpackedScalar::zero());
let _101 = UnpackedScalar::multiply_add(&_11, &_10, &UnpackedScalar::zero());
let _111 = UnpackedScalar::multiply_add(&_101, &_10, &UnpackedScalar::zero());
let _1001 = UnpackedScalar::multiply_add(&_111, &_10, &UnpackedScalar::zero());
let _1011 = UnpackedScalar::multiply_add(&_1001, &_10, &UnpackedScalar::zero());
let _1101 = UnpackedScalar::multiply_add(&_1011, &_10, &UnpackedScalar::zero());
let _1111 = UnpackedScalar::multiply_add(&_1101, &_10, &UnpackedScalar::zero());
// 0b10000
let mut y = UnpackedScalar::multiply_add(&_1111, &_1, &UnpackedScalar::zero());
#[inline]
fn square_multiply(y: &mut UnpackedScalar, squarings: usize, x: &UnpackedScalar) {
for _ in 0..squarings {
*y = y.square();
}
*y = UnpackedScalar::multiply_add(y, x, &UnpackedScalar::zero());
}
square_multiply(&mut y, 123 + 3, &_101);
square_multiply(&mut y, 2 + 2, &_11);
square_multiply(&mut y, 1 + 4, &_1111);
square_multiply(&mut y, 1 + 4, &_1111);
square_multiply(&mut y, 4, &_1001);
square_multiply(&mut y, 4, &_1101);
square_multiply(&mut y, 3, &_111);
square_multiply(&mut y, 1 + 3, &_101);
square_multiply(&mut y, 3 + 3, &_101);
square_multiply(&mut y, 3, &_111);
square_multiply(&mut y, 1 + 4, &_1111);
square_multiply(&mut y, 2 + 3, &_111);
square_multiply(&mut y, 2 + 2, &_11);
square_multiply(&mut y, 1 + 4, &_1011);
square_multiply(&mut y, 2 + 4, &_1011);
square_multiply(&mut y, 6 + 4, &_1001);
square_multiply(&mut y, 2 + 2, &_11);
square_multiply(&mut y, 3 + 2, &_11);
square_multiply(&mut y, 3 + 2, &_11);
square_multiply(&mut y, 1 + 4, &_1001);
square_multiply(&mut y, 1 + 3, &_111);
square_multiply(&mut y, 2 + 4, &_1111);
square_multiply(&mut y, 1 + 4, &_1011);
square_multiply(&mut y, 3, &_101);
square_multiply(&mut y, 2 + 4, &_1111);
square_multiply(&mut y, 3, &_101);
square_multiply(&mut y, 1 + 2, &_11);
y
}