316 lines
9.6 KiB
Rust
316 lines
9.6 KiB
Rust
// -*- mode: rust; -*-
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//
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// This file is part of curve25519-dalek.
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// Copyright (c) 2018-2019 Henry de Valence
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// See LICENSE for licensing information.
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//
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// Authors:
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// - Henry de Valence <hdevalence@hdevalence.ca>
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#![allow(non_snake_case)]
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use traits::Identity;
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use std::ops::{Add, Neg, Sub};
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use subtle::Choice;
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use subtle::ConditionallySelectable;
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use edwards;
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use window::{LookupTable, NafLookupTable5, NafLookupTable8};
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use super::constants;
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use super::field::{F51x4Reduced, F51x4Unreduced, Lanes, Shuffle};
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#[derive(Copy, Clone, Debug)]
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pub struct ExtendedPoint(pub(super) F51x4Unreduced);
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#[derive(Copy, Clone, Debug)]
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pub struct CachedPoint(pub(super) F51x4Reduced);
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impl From<edwards::EdwardsPoint> for ExtendedPoint {
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fn from(P: edwards::EdwardsPoint) -> ExtendedPoint {
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ExtendedPoint(F51x4Unreduced::new(&P.X, &P.Y, &P.Z, &P.T))
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}
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}
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impl From<ExtendedPoint> for edwards::EdwardsPoint {
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fn from(P: ExtendedPoint) -> edwards::EdwardsPoint {
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let reduced = F51x4Reduced::from(P.0);
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let tmp = F51x4Unreduced::from(reduced).split();
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edwards::EdwardsPoint {
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X: tmp[0],
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Y: tmp[1],
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Z: tmp[2],
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T: tmp[3],
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}
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}
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}
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impl From<ExtendedPoint> for CachedPoint {
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fn from(P: ExtendedPoint) -> CachedPoint {
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let mut x = P.0;
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x = x.blend(&x.diff_sum(), Lanes::AB);
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x = &F51x4Reduced::from(x) * (121666, 121666, 2 * 121666, 2 * 121665);
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x = x.blend(&x.negate_lazy(), Lanes::D);
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CachedPoint(F51x4Reduced::from(x))
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}
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}
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impl Default for ExtendedPoint {
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fn default() -> ExtendedPoint {
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ExtendedPoint::identity()
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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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constants::EXTENDEDPOINT_IDENTITY
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}
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}
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impl ExtendedPoint {
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pub fn double(&self) -> ExtendedPoint {
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// (Y1 X1 T1 Z1) -- uses vpshufd (1c latency @ 1/c)
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let mut tmp0 = self.0.shuffle(Shuffle::BADC);
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// (X1+Y1 X1+Y1 X1+Y1 X1+Y1) -- can use vpinserti128
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let mut tmp1 = (self.0 + tmp0).shuffle(Shuffle::ABAB);
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// (X1 Y1 Z1 X1+Y1)
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tmp0 = self.0.blend(&tmp1, Lanes::D);
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tmp1 = F51x4Reduced::from(tmp0).square();
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// Now tmp1 = (S1 S2 S3 S4)
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// We want to compute
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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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// + | |16p |16p |16p |
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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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let zero = F51x4Unreduced::zero();
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let S1_S1_S1_S1 = tmp1.shuffle(Shuffle::AAAA);
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let S2_S2_S2_S2 = tmp1.shuffle(Shuffle::BBBB);
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let S2_S2_S2_S4 = S2_S2_S2_S2.blend(&tmp1, Lanes::D).negate_lazy();
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tmp0 = S1_S1_S1_S1 + zero.blend(&(tmp1 + tmp1), Lanes::C);
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tmp0 = tmp0 + zero.blend(&S2_S2_S2_S2, Lanes::AD);
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tmp0 = tmp0 + zero.blend(&S2_S2_S2_S4, Lanes::BCD);
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let tmp2 = F51x4Reduced::from(tmp0);
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ExtendedPoint(&tmp2.shuffle(Shuffle::DBBD) * &tmp2.shuffle(Shuffle::CACA))
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}
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pub fn mul_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 CachedPoint> for &'a ExtendedPoint {
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type Output = ExtendedPoint;
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/// Add an `ExtendedPoint` and a `CachedPoint`.
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fn add(self, other: &'b CachedPoint) -> ExtendedPoint {
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let mut tmp = self.0;
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tmp = tmp.blend(&tmp.diff_sum(), Lanes::AB);
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// tmp = (Y1-X1 Y1+X1 Z1 T1) = (S0 S1 Z1 T1)
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tmp = &F51x4Reduced::from(tmp) * &other.0;
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// tmp = (S0*S2' S1*S3' Z1*Z2' T1*T2') = (S8 S9 S10 S11)
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tmp = tmp.shuffle(Shuffle::ABDC);
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// tmp = (S8 S9 S11 S10)
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let tmp = F51x4Reduced::from(tmp.diff_sum());
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// tmp = (S9-S8 S9+S8 S10-S11 S10+S11) = (S12 S13 S14 S15)
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let t0 = tmp.shuffle(Shuffle::ADDA);
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// t0 = (S12 S15 S15 S12)
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let t1 = tmp.shuffle(Shuffle::CBCB);
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// t1 = (S14 S13 S14 S13)
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// Return (S12*S14 S15*S13 S15*S14 S12*S13) = (X3 Y3 Z3 T3)
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ExtendedPoint(&t0 * &t1)
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}
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}
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impl Default for CachedPoint {
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fn default() -> CachedPoint {
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CachedPoint::identity()
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}
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}
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impl Identity for CachedPoint {
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fn identity() -> CachedPoint {
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constants::CACHEDPOINT_IDENTITY
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}
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}
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impl ConditionallySelectable for CachedPoint {
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fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
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CachedPoint(F51x4Reduced::conditional_select(&a.0, &b.0, choice))
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}
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fn conditional_assign(&mut self, other: &Self, choice: Choice) {
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self.0.conditional_assign(&other.0, choice);
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}
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}
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impl<'a> Neg for &'a CachedPoint {
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type Output = CachedPoint;
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fn neg(self) -> CachedPoint {
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let swapped = self.0.shuffle(Shuffle::BACD);
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CachedPoint(swapped.blend(&(-self.0), Lanes::D))
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}
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}
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impl<'a, 'b> Sub<&'b CachedPoint> for &'a ExtendedPoint {
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type Output = ExtendedPoint;
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/// Implement subtraction by negating the point and adding.
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fn sub(self, other: &'b CachedPoint) -> ExtendedPoint {
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self + &(-other)
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}
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}
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impl<'a> From<&'a edwards::EdwardsPoint> for LookupTable<CachedPoint> {
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fn from(point: &'a edwards::EdwardsPoint) -> Self {
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let P = ExtendedPoint::from(*point);
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let mut points = [CachedPoint::from(P); 8];
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for i in 0..7 {
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points[i + 1] = (&P + &points[i]).into();
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}
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LookupTable(points)
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}
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}
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impl<'a> From<&'a edwards::EdwardsPoint> for NafLookupTable5<CachedPoint> {
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fn from(point: &'a edwards::EdwardsPoint) -> Self {
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let A = ExtendedPoint::from(*point);
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let mut Ai = [CachedPoint::from(A); 8];
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let A2 = A.double();
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for i in 0..7 {
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Ai[i + 1] = (&A2 + &Ai[i]).into();
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}
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// Now Ai = [A, 3A, 5A, 7A, 9A, 11A, 13A, 15A]
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NafLookupTable5(Ai)
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}
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}
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impl<'a> From<&'a edwards::EdwardsPoint> for NafLookupTable8<CachedPoint> {
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fn from(point: &'a edwards::EdwardsPoint) -> Self {
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let A = ExtendedPoint::from(*point);
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let mut Ai = [CachedPoint::from(A); 64];
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let A2 = A.double();
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for i in 0..63 {
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Ai[i + 1] = (&A2 + &Ai[i]).into();
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}
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// Now Ai = [A, 3A, 5A, 7A, 9A, 11A, 13A, 15A, ..., 127A]
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NafLookupTable8(Ai)
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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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fn addition_test_helper(P: edwards::EdwardsPoint, Q: edwards::EdwardsPoint) {
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// Test the serial implementation of the parallel addition formulas
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//let R_serial: edwards::EdwardsPoint = serial_add(P.into(), Q.into()).into();
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// Test the vector implementation of the parallel readdition formulas
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let cached_Q = CachedPoint::from(ExtendedPoint::from(Q));
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let R_vector: edwards::EdwardsPoint = (&ExtendedPoint::from(P) + &cached_Q).into();
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let S_vector: edwards::EdwardsPoint = (&ExtendedPoint::from(P) - &cached_Q).into();
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println!("Testing point addition:");
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println!("P = {:?}", P);
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println!("Q = {:?}", Q);
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println!("cached Q = {:?}", cached_Q);
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println!("R = P + Q = {:?}", &P + &Q);
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//println!("R_serial = {:?}", R_serial);
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println!("R_vector = {:?}", R_vector);
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println!("S = P - Q = {:?}", &P - &Q);
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println!("S_vector = {:?}", S_vector);
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//assert_eq!(R_serial.compress(), (&P + &Q).compress());
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assert_eq!(R_vector.compress(), (&P + &Q).compress());
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assert_eq!(S_vector.compress(), (&P - &Q).compress());
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println!("OK!\n");
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}
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#[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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println!("Testing id +- id");
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let P = edwards::EdwardsPoint::identity();
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let Q = edwards::EdwardsPoint::identity();
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addition_test_helper(P, Q);
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println!("Testing id +- B");
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let P = edwards::EdwardsPoint::identity();
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let Q = constants::ED25519_BASEPOINT_POINT;
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addition_test_helper(P, Q);
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println!("Testing B +- B");
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let P = constants::ED25519_BASEPOINT_POINT;
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let Q = constants::ED25519_BASEPOINT_POINT;
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addition_test_helper(P, Q);
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println!("Testing B +- kB");
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let P = constants::ED25519_BASEPOINT_POINT;
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let Q = &constants::ED25519_BASEPOINT_TABLE * &Scalar::from(8475983829u64);
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addition_test_helper(P, Q);
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}
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fn doubling_test_helper(P: edwards::EdwardsPoint) {
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//let R1: edwards::EdwardsPoint = serial_double(P.into()).into();
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let R2: edwards::EdwardsPoint = 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!("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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#[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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println!("Testing [2]id");
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let P = edwards::EdwardsPoint::identity();
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doubling_test_helper(P);
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println!("Testing [2]B");
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let P = constants::ED25519_BASEPOINT_POINT;
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doubling_test_helper(P);
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println!("Testing [2]([k]B)");
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let P = &constants::ED25519_BASEPOINT_TABLE * &Scalar::from(8475983829u64);
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doubling_test_helper(P);
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}
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}
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