mirror of
https://github.com/saymrwulf/curve25519-dalek-source.git
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Add doubling skeleton and scalar mult
This commit is contained in:
Henry de Valence
Henry de Valence
parent
9e383ffccb
commit
2f32f6355c
2 changed files with 306 additions and 8 deletions
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@ -14,15 +14,22 @@
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#![allow(bad_style)]
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use std::convert::From;
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use std::ops::Add;
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use std::ops::{Add, Mul, Neg};
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use stdsimd::simd::u32x8;
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use stdsimd::simd::{u32x8, i32x8};
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use subtle::ConditionallyAssignable;
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use edwards;
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use scalar::Scalar;
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use traits::Identity;
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use avx2::field::FieldElement32x4;
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use avx2::field::P_TIMES_2;
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/// A point on Curve25519, represented in an AVX2-friendly format.
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#[derive(Copy, Clone, Debug)]
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pub(crate) struct ExtendedPoint(FieldElement32x4);
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// XXX need to cfg gate here to handle FieldElement64
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@ -40,6 +47,165 @@ impl From<ExtendedPoint> for edwards::ExtendedPoint {
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}
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}
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impl ConditionallyAssignable for ExtendedPoint {
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fn conditional_assign(&mut self, other: &ExtendedPoint, choice: u8) {
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self.0.conditional_assign(&other.0, choice);
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}
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}
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impl Identity for ExtendedPoint {
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fn identity() -> ExtendedPoint {
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ExtendedPoint(FieldElement32x4([
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u32x8::new(0,1,0,0,1,0,0,0),
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u32x8::splat(0),
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u32x8::splat(0),
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u32x8::splat(0),
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u32x8::splat(0),
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]))
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}
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}
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impl<'a> Neg for &'a ExtendedPoint {
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type Output = ExtendedPoint;
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fn neg(self) -> ExtendedPoint {
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let mut neg = *self;
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neg.0.mask_negate(0b10100101);
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neg
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}
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}
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impl ExtendedPoint {
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fn double(&self) -> ExtendedPoint {
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unsafe {
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use stdsimd::vendor::_mm256_permute2x128_si256;
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use stdsimd::vendor::_mm256_permutevar8x32_epi32;
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use stdsimd::vendor::_mm256_blend_epi32;
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use stdsimd::vendor::_mm256_shuffle_epi32;
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macro_rules! print_vec {
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($x:ident) => {
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let splits = $x.split();
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println!("{}[0] = {:?}", stringify!($x), splits[0].to_bytes());
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println!("{}[1] = {:?}", stringify!($x), splits[1].to_bytes());
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println!("{}[2] = {:?}", stringify!($x), splits[2].to_bytes());
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println!("{}[3] = {:?}", stringify!($x), splits[3].to_bytes());
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}
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}
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let P = &self.0;
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let mut t0 = FieldElement32x4::zero();
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let mut t1 = FieldElement32x4::zero();
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// Set t0 = (X1 Y1 X1 Y1)
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t0.0[0] = _mm256_permute2x128_si256(P.0[0].into(), P.0[0].into(), 0b0000_0000).into();
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t0.0[1] = _mm256_permute2x128_si256(P.0[1].into(), P.0[1].into(), 0b0000_0000).into();
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t0.0[2] = _mm256_permute2x128_si256(P.0[2].into(), P.0[2].into(), 0b0000_0000).into();
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t0.0[3] = _mm256_permute2x128_si256(P.0[3].into(), P.0[3].into(), 0b0000_0000).into();
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t0.0[4] = _mm256_permute2x128_si256(P.0[4].into(), P.0[4].into(), 0b0000_0000).into();
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// Set t1 = (Y1 X1 Y1 X1)
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t1.0[0] = _mm256_shuffle_epi32(t0.0[0].into(), 0b10_11_00_01).into();
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t1.0[1] = _mm256_shuffle_epi32(t0.0[1].into(), 0b10_11_00_01).into();
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t1.0[2] = _mm256_shuffle_epi32(t0.0[2].into(), 0b10_11_00_01).into();
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t1.0[3] = _mm256_shuffle_epi32(t0.0[3].into(), 0b10_11_00_01).into();
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t1.0[4] = _mm256_shuffle_epi32(t0.0[4].into(), 0b10_11_00_01).into();
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// Set t0 = (X1+Y1 X1+Y1 X1+Y1 X1+Y1)
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t0.0[0] = t0.0[0] + t1.0[0];
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t0.0[1] = t0.0[1] + t1.0[1];
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t0.0[2] = t0.0[2] + t1.0[2];
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t0.0[3] = t0.0[3] + t1.0[3];
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t0.0[4] = t0.0[4] + t1.0[4];
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// Set t0 = (X1 Y1 Z1 X1+Y1)
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t0.0[0] = _mm256_blend_epi32(t0.0[0].into(), P.0[0].into(), 0b01011111).into();
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t0.0[1] = _mm256_blend_epi32(t0.0[1].into(), P.0[1].into(), 0b01011111).into();
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t0.0[2] = _mm256_blend_epi32(t0.0[2].into(), P.0[2].into(), 0b01011111).into();
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t0.0[3] = _mm256_blend_epi32(t0.0[3].into(), P.0[3].into(), 0b01011111).into();
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t0.0[4] = _mm256_blend_epi32(t0.0[4].into(), P.0[4].into(), 0b01011111).into();
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t1 = &t0 * &t0; // replace with .square()
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// Now t1 = (S1 S2 S3 S4)
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let c0 = u32x8::new(0,0,2,2,0,0,2,2); // (ABCD) -> (AAAA)
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let c1 = u32x8::new(1,1,3,3,1,1,3,3); // (ABCD) -> (BBBB)
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// Horror block goes here: we want to compute the following table:
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// We know that the bit-excess b is bounded by eps, since S1 S2 S3 S4
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// are the outputs of a squaring, so they're freshly reduced.
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//
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// + | S1 | S1 | S1 | S1 |
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// + | S2 | | | S2 |
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// + | | | S3 | |
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// + | | | S3 | |
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// + | | 2p | 2p | 2p |
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// - | | S2 | S2 | |
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// - | | | | S4 |
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// =======================
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// S5 S6 S8 S9
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//
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// Bounds for even / odd limbs:
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//
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// + | 2^26 | 2^26 | 2^26 | 2^26 | + | 2^25 | 2^25 | 2^25 | 2^25 |
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// + | 2^26 | | | 2^26 | + | 2^25 | | | 2^25 |
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// + | | | 2^26 | | + | | | 2^25 | |
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// + | | | 2^26 | | + | | | 2^25 | |
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// + | | 2^27 | 2^27 | 2^27 | + | | 2^26 | 2^26 | 2^26 |
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// - | | 0 | 0 | | - | | 0 | 0 | |
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// - | | | | 0 | - | | | | 0 |
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// =================================== ===================================
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// < 2^27 2^27.59 2^28.33 2^28 2^26 2^26.59 2^27.33 2^27
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//
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// So, the bit-excess for (S5 S6 S8 S9) is (1, 1.59, 2.33, 2).
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//
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// However the multiplication routine only allows (1.75, 1.75, 1.75, 1.75).
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//
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// This is because we need to have 19*y[i] < 2^32. Otherwise I think we could get b < 2.5.
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//
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// Can we tighten these bounds to avoid a reduction? Alternately, can we do better than
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// the 64-bit reduction that reduce32() calls internally?
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//
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// Also, can we do better than the mess below?
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for i in 0..5 {
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let zero = i32x8::splat(0);
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let S1 = _mm256_permutevar8x32_epi32(t1.0[i], c0);
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let S2 = _mm256_permutevar8x32_epi32(t1.0[i], c1);
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let S3_2 = _mm256_blend_epi32(zero, (t1.0[i] + t1.0[i]).into(), 0b01010000).into();
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t0.0[i] = (P_TIMES_2.0[i] + S3_2) + S1;
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t0.0[i] = t0.0[i] + _mm256_blend_epi32(zero, S2.into(), 0b10100101).into();
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let S4 = _mm256_blend_epi32(zero, t1.0[i].into(), 0b10100000);
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let sub = _mm256_blend_epi32(S2.into(), S4, 0b10100101).into();
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t0.0[i] = t0.0[i] - sub;
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}
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// This is really sad, see above
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t0.reduce32();
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let c0 = u32x8::new(4,0,6,2,4,0,6,2); // (ABCD) -> (CACA)
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let c1 = u32x8::new(5,1,7,3,1,5,3,7); // (ABCD) -> (DBBD)
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for i in 0..5 {
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let tmp = t0.0[i];
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t0.0[i] = _mm256_permutevar8x32_epi32(tmp, c0);
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t1.0[i] = _mm256_permutevar8x32_epi32(tmp, c1);
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}
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ExtendedPoint(&t0 * &t1)
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}
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}
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pub fn mult_by_pow_2(&self, k: u32) -> ExtendedPoint {
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let mut tmp: ExtendedPoint = *self;
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for _ in 0..k {
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tmp = tmp.double();
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}
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tmp
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}
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}
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impl<'a, 'b> Add<&'b ExtendedPoint> for &'a ExtendedPoint {
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type Output = ExtendedPoint;
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@ -134,13 +300,56 @@ impl<'a, 'b> Add<&'b ExtendedPoint> for &'a ExtendedPoint {
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}
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}
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}
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impl<'a, 'b> Mul<&'b Scalar> for &'a ExtendedPoint {
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type Output = ExtendedPoint;
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/// Scalar multiplication: compute `scalar * self`.
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///
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/// Uses a window of size 4.
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fn mul(self, scalar: &'b Scalar) -> ExtendedPoint {
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use traits::select_precomputed_point;
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// Construct a lookup table of [P,2P,3P,4P,5P,6P,7P,8P]
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let mut lookup_table: [ExtendedPoint; 8] = [*self; 8];
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for i in 0..7 {
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lookup_table[i+1] = self + &lookup_table[i];
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}
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// Setting s = scalar, compute
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//
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// s = s_0 + s_1*16^1 + ... + s_63*16^63,
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//
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// with `-8 ≤ s_i < 8` for `0 ≤ i < 63` and `-8 ≤ s_63 ≤ 8`.
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let scalar_digits = scalar.to_radix_16();
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// Compute s*P as
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//
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// s*P = P*(s_0 + s_1*16^1 + s_2*16^2 + ... + s_63*16^63)
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// s*P = P*s_0 + P*s_1*16^1 + P*s_2*16^2 + ... + P*s_63*16^63
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// s*P = P*s_0 + 16*(P*s_1 + 16*(P*s_2 + 16*( ... + P*s_63)...))
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//
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// We sum right-to-left.
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let mut Q = ExtendedPoint::identity();
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for i in (0..64).rev() {
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// Q = 16*Q
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Q = Q.mult_by_pow_2(4);
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// R = s_i * Q
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let R = select_precomputed_point(scalar_digits[i], &lookup_table);
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// Q = Q + R
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Q = &Q + &R;
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}
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Q
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}
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}
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#[cfg(test)]
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mod test {
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use super::*;
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use constants;
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fn serial_add(P: edwards::ExtendedPoint, Q: edwards::ExtendedPoint) -> edwards::ExtendedPoint {
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use field_32bit::FieldElement32;
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use backend::u32::field::FieldElement32;
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let (X1, Y1, Z1, T1) = (P.X, P.Y, P.Z, P.T);
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let (X2, Y2, Z2, T2) = (Q.X, Q.Y, Q.Z, Q.T);
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@ -217,7 +426,6 @@ mod test {
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fn vector_addition_vs_serial_addition_vs_edwards_extendedpoint() {
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use constants;
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use scalar::Scalar;
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use edwards::Identity;
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println!("Testing id + id");
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let P = edwards::ExtendedPoint::identity();
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@ -243,18 +451,37 @@ mod test {
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fn serial_double(P: edwards::ExtendedPoint) -> edwards::ExtendedPoint {
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let (X1, Y1, Z1, T1) = (P.X, P.Y, P.Z, P.T);
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macro_rules! print_var {
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($x:ident) => {
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println!("{} = {:?}", stringify!($x), $x.to_bytes());
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}
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}
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let S0 = &X1 + &Y1; // R1
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print_var!(S0);
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println!("");
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let S1 = X1.square();
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let S2 = Y1.square();
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let S3 = Z1.square();
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let S4 = S0.square();
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print_var!(S1);
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print_var!(S2);
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print_var!(S3);
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print_var!(S4);
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println!("");
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let S5 = &S1 + &S2;
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let S6 = &S1 - &S2;
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let S7 = &S3 + &S3;
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let S8 = &S7 + &S6;
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let S9 = &S5 - &S4;
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print_var!(S5);
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print_var!(S6);
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print_var!(S7);
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print_var!(S8);
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print_var!(S9);
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println!("");
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let X3 = &S8 * &S9;
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let Y3 = &S5 * &S6;
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@ -266,12 +493,14 @@ mod test {
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fn doubling_test_helper(P: edwards::ExtendedPoint) {
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let R1: edwards::ExtendedPoint = serial_double(P.into()).into();
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let R2: edwards::ExtendedPoint = ExtendedPoint::from(P).double().into();
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println!("Testing point doubling:");
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println!("P = {:?}", P);
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println!("(serial) R1 = {:?}", R1);
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//println!("(vector) R2 = {:?}", R2);
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println!("(vector) R2 = {:?}", R2);
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println!("P + P = {:?}", &P + &P);
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assert_eq!(R1.compress(), (&P + &P).compress());
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assert_eq!(R2.compress(), (&P + &P).compress());
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println!("OK!\n");
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}
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@ -279,7 +508,6 @@ mod test {
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fn vector_doubling_vs_serial_doubling_vs_edwards_extendedpoint() {
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use constants;
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use scalar::Scalar;
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use edwards::Identity;
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println!("Testing [2]id");
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let P = edwards::ExtendedPoint::identity();
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@ -293,6 +521,33 @@ mod test {
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let P = &constants::ED25519_BASEPOINT_TABLE * &Scalar::from_u64(8475983829);
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doubling_test_helper(P);
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}
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#[test]
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fn identity_trait_vs_edwards_identity() {
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let id1: edwards::ExtendedPoint = ExtendedPoint::identity().into();
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let id2: edwards::ExtendedPoint = edwards::ExtendedPoint::identity();
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assert_eq!(id1.compress(), id2.compress());
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}
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#[test]
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fn neg_vs_edwards_neg() {
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let B: ExtendedPoint = constants::ED25519_BASEPOINT_POINT.into();
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let Bneg = -&B;
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assert_eq!(edwards::ExtendedPoint::from(Bneg).compress(),
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(-&constants::ED25519_BASEPOINT_POINT).compress());
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}
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#[test]
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fn scalar_mult_vs_edwards_scalar_mult() {
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let B: ExtendedPoint = constants::ED25519_BASEPOINT_POINT.into();
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// some random bytes
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let s = Scalar([233, 1, 233, 147, 113, 78, 244, 120, 40, 45, 103, 51, 224, 199, 189, 218, 96, 140, 211, 112, 39, 194, 73, 216, 173, 33, 102, 93, 76, 200, 84, 12]);
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let R1 = edwards::ExtendedPoint::from(&B * &s);
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let R2 = &constants::ED25519_BASEPOINT_TABLE * &s;
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assert_eq!(R1.compress(), R2.compress());
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}
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}
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#[cfg(all(test, feature = "bench"))]
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@ -311,5 +566,22 @@ mod bench {
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b.iter(|| &P + &Q );
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}
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#[bench]
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fn point_doubling(b: &mut Bencher) {
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let B = &constants::ED25519_BASEPOINT_TABLE;
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let P = ExtendedPoint::from(B * &Scalar::from_u64(83973422));
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b.iter(|| P.double() );
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}
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#[bench]
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fn scalar_mult(b: &mut Bencher) {
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let B = &constants::ED25519_BASEPOINT_TABLE;
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let P = ExtendedPoint::from(B * &Scalar::from_u64(83973422));
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let s = Scalar([233, 1, 233, 147, 113, 78, 244, 120, 40, 45, 103, 51, 224, 199, 189, 218, 96, 140, 211, 112, 39, 194, 73, 216, 173, 33, 102, 93, 76, 200, 84, 12]);
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b.iter(|| &P * &s );
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}
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}
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@ -19,7 +19,7 @@ use stdsimd::simd::{u32x8, i32x8, u64x4};
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use backend::u32::field::FieldElement32;
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static P_TIMES_2: FieldElement32x4 = FieldElement32x4([
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pub(crate) static P_TIMES_2: FieldElement32x4 = FieldElement32x4([
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u32x8::new(134217690, 134217690, 67108862, 67108862, 134217690, 134217690, 67108862, 67108862),
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u32x8::new(134217726, 134217726, 67108862, 67108862, 134217726, 134217726, 67108862, 67108862),
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u32x8::new(134217726, 134217726, 67108862, 67108862, 134217726, 134217726, 67108862, 67108862),
|
||||
|
|
@ -28,9 +28,22 @@ static P_TIMES_2: FieldElement32x4 = FieldElement32x4([
|
|||
]);
|
||||
|
||||
/// A vector of four `FieldElements`, implemented using AVX2.
|
||||
#[derive(Clone, Copy)]
|
||||
#[derive(Clone, Copy, Debug)]
|
||||
pub(crate) struct FieldElement32x4(pub(crate) [u32x8; 5]);
|
||||
|
||||
use subtle::ConditionallyAssignable;
|
||||
|
||||
impl ConditionallyAssignable for FieldElement32x4 {
|
||||
fn conditional_assign(&mut self, other: &FieldElement32x4, choice: u8) {
|
||||
let mask = (-(choice as i32)) as u32;
|
||||
let mask_vec = u32x8::splat(mask);
|
||||
for i in 0..5 {
|
||||
self.0[i] = self.0[i] ^ (mask_vec & (self.0[i] ^ other.0[i]));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
impl FieldElement32x4 {
|
||||
pub(crate) fn split(&self) -> [FieldElement32; 4] {
|
||||
let mut out = [FieldElement32::zero(); 4];
|
||||
|
|
@ -71,6 +84,19 @@ impl FieldElement32x4 {
|
|||
FieldElement32x4(buf)
|
||||
}
|
||||
|
||||
// Negate variables in lanes where mask is set
|
||||
// XXX fix up api
|
||||
pub fn mask_negate(&mut self, mask: u8) {
|
||||
unsafe {
|
||||
use stdsimd::vendor::_mm256_blend_epi32;
|
||||
for i in 0..5 {
|
||||
let negated = P_TIMES_2.0[i] - self.0[i];
|
||||
self.0[i] = _mm256_blend_epi32(self.0[i].into(), negated.into(), mask as i32).into();
|
||||
}
|
||||
}
|
||||
self.reduce32();
|
||||
}
|
||||
|
||||
// Given `self = (A,B,C,D)`, set `self = (B - A, B + A, D - C, D + C)`.
|
||||
pub fn diff_sum(&mut self) {
|
||||
/// (v0 v1 v2 v3 v4 v5 v6 v7) -> (v1 v0 v3 v2 v5 v4 v7 v6)
|
||||
|
|
|
|||
Loading…
Reference in a new issue