curve25519-dalek 4.0.0-rc.0

// -*- mode: rust; -*-
//
// This file is part of curve25519-dalek.
// Copyright (c) 2018-2019 Henry de Valence
// See LICENSE for licensing information.
//
// Authors:
// - Henry de Valence <hdevalence@hdevalence.ca>

#![allow(non_snake_case)]

use crate::traits::Identity;

use core::ops::{Add, Neg, Sub};

use subtle::Choice;
use subtle::ConditionallySelectable;

use crate::edwards;
use crate::window::{LookupTable, NafLookupTable5, NafLookupTable8};

use super::constants;
use super::field::{F51x4Reduced, F51x4Unreduced, Lanes, Shuffle};

#[derive(Copy, Clone, Debug)]
pub struct ExtendedPoint(pub(super) F51x4Unreduced);

#[derive(Copy, Clone, Debug)]
pub struct CachedPoint(pub(super) F51x4Reduced);

impl From<edwards::EdwardsPoint> for ExtendedPoint {
    fn from(P: edwards::EdwardsPoint) -> ExtendedPoint {
        ExtendedPoint(F51x4Unreduced::new(&P.X, &P.Y, &P.Z, &P.T))
    }
}

impl From<ExtendedPoint> for edwards::EdwardsPoint {
    fn from(P: ExtendedPoint) -> edwards::EdwardsPoint {
        let reduced = F51x4Reduced::from(P.0);
        let tmp = F51x4Unreduced::from(reduced).split();
        edwards::EdwardsPoint {
            X: tmp[0],
            Y: tmp[1],
            Z: tmp[2],
            T: tmp[3],
        }
    }
}

impl From<ExtendedPoint> for CachedPoint {
    fn from(P: ExtendedPoint) -> CachedPoint {
        let mut x = P.0;

        x = x.blend(&x.diff_sum(), Lanes::AB);
        x = &F51x4Reduced::from(x) * (121666, 121666, 2 * 121666, 2 * 121665);
        x = x.blend(&x.negate_lazy(), Lanes::D);

        CachedPoint(F51x4Reduced::from(x))
    }
}

impl Default for ExtendedPoint {
    fn default() -> ExtendedPoint {
        ExtendedPoint::identity()
    }
}

impl Identity for ExtendedPoint {
    fn identity() -> ExtendedPoint {
        constants::EXTENDEDPOINT_IDENTITY
    }
}

impl ExtendedPoint {
    pub fn double(&self) -> ExtendedPoint {
        // (Y1 X1 T1 Z1) -- uses vpshufd (1c latency @ 1/c)
        let mut tmp0 = self.0.shuffle(Shuffle::BADC);

        // (X1+Y1 X1+Y1 X1+Y1 X1+Y1) -- can use vpinserti128
        let mut tmp1 = (self.0 + tmp0).shuffle(Shuffle::ABAB);

        // (X1 Y1 Z1 X1+Y1)
        tmp0 = self.0.blend(&tmp1, Lanes::D);

        tmp1 = F51x4Reduced::from(tmp0).square();
        // Now tmp1 = (S1 S2 S3 S4)

        // We want to compute
        //
        //    + | S1 | S1 | S1 | S1 |
        //    + | S2 |    |    | S2 |
        //    + |    |    | S3 |    |
        //    + |    |    | S3 |    |
        //    + |    |16p |16p |16p |
        //    - |    | S2 | S2 |    |
        //    - |    |    |    | S4 |
        //    =======================
        //        S5   S6   S8   S9

        let zero = F51x4Unreduced::ZERO;

        let S1_S1_S1_S1 = tmp1.shuffle(Shuffle::AAAA);
        let S2_S2_S2_S2 = tmp1.shuffle(Shuffle::BBBB);

        let S2_S2_S2_S4 = S2_S2_S2_S2.blend(&tmp1, Lanes::D).negate_lazy();

        tmp0 = S1_S1_S1_S1 + zero.blend(&(tmp1 + tmp1), Lanes::C);
        tmp0 = tmp0 + zero.blend(&S2_S2_S2_S2, Lanes::AD);
        tmp0 = tmp0 + zero.blend(&S2_S2_S2_S4, Lanes::BCD);

        let tmp2 = F51x4Reduced::from(tmp0);

        ExtendedPoint(&tmp2.shuffle(Shuffle::DBBD) * &tmp2.shuffle(Shuffle::CACA))
    }

    pub fn mul_by_pow_2(&self, k: u32) -> ExtendedPoint {
        let mut tmp: ExtendedPoint = *self;
        for _ in 0..k {
            tmp = tmp.double();
        }
        tmp
    }
}

impl<'a, 'b> Add<&'b CachedPoint> for &'a ExtendedPoint {
    type Output = ExtendedPoint;

    /// Add an `ExtendedPoint` and a `CachedPoint`.
    fn add(self, other: &'b CachedPoint) -> ExtendedPoint {
        let mut tmp = self.0;

        tmp = tmp.blend(&tmp.diff_sum(), Lanes::AB);
        // tmp = (Y1-X1 Y1+X1 Z1 T1) = (S0 S1 Z1 T1)

        tmp = &F51x4Reduced::from(tmp) * &other.0;
        // tmp = (S0*S2' S1*S3' Z1*Z2' T1*T2') = (S8 S9 S10 S11)

        tmp = tmp.shuffle(Shuffle::ABDC);
        // tmp = (S8 S9 S11 S10)

        let tmp = F51x4Reduced::from(tmp.diff_sum());
        // tmp = (S9-S8 S9+S8 S10-S11 S10+S11) = (S12 S13 S14 S15)

        let t0 = tmp.shuffle(Shuffle::ADDA);
        // t0 = (S12 S15 S15 S12)
        let t1 = tmp.shuffle(Shuffle::CBCB);
        // t1 = (S14 S13 S14 S13)

        // Return (S12*S14 S15*S13 S15*S14 S12*S13) = (X3 Y3 Z3 T3)
        ExtendedPoint(&t0 * &t1)
    }
}

impl Default for CachedPoint {
    fn default() -> CachedPoint {
        CachedPoint::identity()
    }
}

impl Identity for CachedPoint {
    fn identity() -> CachedPoint {
        constants::CACHEDPOINT_IDENTITY
    }
}

impl ConditionallySelectable for CachedPoint {
    fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
        CachedPoint(F51x4Reduced::conditional_select(&a.0, &b.0, choice))
    }

    fn conditional_assign(&mut self, other: &Self, choice: Choice) {
        self.0.conditional_assign(&other.0, choice);
    }
}

impl<'a> Neg for &'a CachedPoint {
    type Output = CachedPoint;

    fn neg(self) -> CachedPoint {
        let swapped = self.0.shuffle(Shuffle::BACD);
        CachedPoint(swapped.blend(&(-self.0), Lanes::D))
    }
}

impl<'a, 'b> Sub<&'b CachedPoint> for &'a ExtendedPoint {
    type Output = ExtendedPoint;

    /// Implement subtraction by negating the point and adding.
    fn sub(self, other: &'b CachedPoint) -> ExtendedPoint {
        self + &(-other)
    }
}

impl<'a> From<&'a edwards::EdwardsPoint> for LookupTable<CachedPoint> {
    fn from(point: &'a edwards::EdwardsPoint) -> Self {
        let P = ExtendedPoint::from(*point);
        let mut points = [CachedPoint::from(P); 8];
        for i in 0..7 {
            points[i + 1] = (&P + &points[i]).into();
        }
        LookupTable(points)
    }
}

impl<'a> From<&'a edwards::EdwardsPoint> for NafLookupTable5<CachedPoint> {
    fn from(point: &'a edwards::EdwardsPoint) -> Self {
        let A = ExtendedPoint::from(*point);
        let mut Ai = [CachedPoint::from(A); 8];
        let A2 = A.double();
        for i in 0..7 {
            Ai[i + 1] = (&A2 + &Ai[i]).into();
        }
        // Now Ai = [A, 3A, 5A, 7A, 9A, 11A, 13A, 15A]
        NafLookupTable5(Ai)
    }
}

impl<'a> From<&'a edwards::EdwardsPoint> for NafLookupTable8<CachedPoint> {
    fn from(point: &'a edwards::EdwardsPoint) -> Self {
        let A = ExtendedPoint::from(*point);
        let mut Ai = [CachedPoint::from(A); 64];
        let A2 = A.double();
        for i in 0..63 {
            Ai[i + 1] = (&A2 + &Ai[i]).into();
        }
        // Now Ai = [A, 3A, 5A, 7A, 9A, 11A, 13A, 15A, ..., 127A]
        NafLookupTable8(Ai)
    }
}

#[cfg(test)]
mod test {
    use super::*;

    fn addition_test_helper(P: edwards::EdwardsPoint, Q: edwards::EdwardsPoint) {
        // Test the serial implementation of the parallel addition formulas
        //let R_serial: edwards::EdwardsPoint = serial_add(P.into(), Q.into()).into();

        // Test the vector implementation of the parallel readdition formulas
        let cached_Q = CachedPoint::from(ExtendedPoint::from(Q));
        let R_vector: edwards::EdwardsPoint = (&ExtendedPoint::from(P) + &cached_Q).into();
        let S_vector: edwards::EdwardsPoint = (&ExtendedPoint::from(P) - &cached_Q).into();

        println!("Testing point addition:");
        println!("P = {:?}", P);
        println!("Q = {:?}", Q);
        println!("cached Q = {:?}", cached_Q);
        println!("R = P + Q = {:?}", &P + &Q);
        //println!("R_serial = {:?}", R_serial);
        println!("R_vector = {:?}", R_vector);
        println!("S = P - Q = {:?}", &P - &Q);
        println!("S_vector = {:?}", S_vector);
        //assert_eq!(R_serial.compress(), (&P + &Q).compress());
        assert_eq!(R_vector.compress(), (&P + &Q).compress());
        assert_eq!(S_vector.compress(), (&P - &Q).compress());
        println!("OK!\n");
    }

    #[test]
    fn vector_addition_vs_serial_addition_vs_edwards_extendedpoint() {
        use crate::constants;
        use crate::scalar::Scalar;

        println!("Testing id +- id");
        let P = edwards::EdwardsPoint::identity();
        let Q = edwards::EdwardsPoint::identity();
        addition_test_helper(P, Q);

        println!("Testing id +- B");
        let P = edwards::EdwardsPoint::identity();
        let Q = constants::ED25519_BASEPOINT_POINT;
        addition_test_helper(P, Q);

        println!("Testing B +- B");
        let P = constants::ED25519_BASEPOINT_POINT;
        let Q = constants::ED25519_BASEPOINT_POINT;
        addition_test_helper(P, Q);

        println!("Testing B +- kB");
        let P = constants::ED25519_BASEPOINT_POINT;
        let Q = constants::ED25519_BASEPOINT_TABLE * &Scalar::from(8475983829u64);
        addition_test_helper(P, Q);
    }

    fn doubling_test_helper(P: edwards::EdwardsPoint) {
        //let R1: edwards::EdwardsPoint = serial_double(P.into()).into();
        let R2: edwards::EdwardsPoint = ExtendedPoint::from(P).double().into();
        println!("Testing point doubling:");
        println!("P = {:?}", P);
        //println!("(serial) R1 = {:?}", R1);
        println!("(vector) R2 = {:?}", R2);
        println!("P + P = {:?}", &P + &P);
        //assert_eq!(R1.compress(), (&P + &P).compress());
        assert_eq!(R2.compress(), (&P + &P).compress());
        println!("OK!\n");
    }

    #[test]
    fn vector_doubling_vs_serial_doubling_vs_edwards_extendedpoint() {
        use crate::constants;
        use crate::scalar::Scalar;

        println!("Testing [2]id");
        let P = edwards::EdwardsPoint::identity();
        doubling_test_helper(P);

        println!("Testing [2]B");
        let P = constants::ED25519_BASEPOINT_POINT;
        doubling_test_helper(P);

        println!("Testing [2]([k]B)");
        let P = constants::ED25519_BASEPOINT_TABLE * &Scalar::from(8475983829u64);
        doubling_test_helper(P);
    }
}