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Implement point subtraction

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This commit is contained in:
Henry de Valence 2017-11-30 11:05:06 -08:00
parent 3094866442
commit 9213dc0bbb
2 changed files with 192 additions and 32 deletions
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144
src/backend/avx2/edwards.rs
View file

@ -14,7 +14,7 @@
#![allow(bad_style)] #![allow(bad_style)]
use std::convert::From; use std::convert::From;
use std::ops::{Add, Mul, Neg}; use std::ops::{Add, Sub, Mul, Neg};
use stdsimd::simd::{u32x8, i32x8}; use stdsimd::simd::{u32x8, i32x8};
@ -70,6 +70,7 @@ impl<'a> Neg for &'a ExtendedPoint {
fn neg(self) -> ExtendedPoint { fn neg(self) -> ExtendedPoint {
let mut neg = *self; let mut neg = *self;
// (X Y Z T) -> (-X Y Z -T)
neg.0.mask_negate(0b10100101); neg.0.mask_negate(0b10100101);
neg neg
} }
@ -216,36 +217,114 @@ impl<'a, 'b> Add<&'b ExtendedPoint> for &'a ExtendedPoint {
let mut t0 = FieldElement32x4::zero(); let mut t0 = FieldElement32x4::zero();
let mut t1 = FieldElement32x4::zero(); let mut t1 = FieldElement32x4::zero();
// set t0 = (X1 Y1 X2 Y2)
for i in 0..5 { for i in 0..5 {
t0.0[i] = _mm256_permute2x128_si256(P.0[i].into(), Q.0[i].into(), 32).into(); t0.0[i] = _mm256_permute2x128_si256(P.0[i].into(), Q.0[i].into(), 32).into();
} }
// set t0 = (Y1-X1 Y1+X1 Y2-X2 Y2+X2) = (S0 S1 S2 S3)
t0.diff_sum(); t0.diff_sum();
// set t1 = (S0 S1 Z1 T1)
// set t0 = (S2 S3 Z2 T2)
for i in 0..5 { for i in 0..5 {
t1.0[i] = _mm256_blend_epi32(t0.0[i].into(), P.0[i].into(), 0b11110000).into(); t1.0[i] = _mm256_blend_epi32(t0.0[i].into(), P.0[i].into(), 0b11110000).into();
t0.0[i] = _mm256_permute2x128_si256(t0.0[i].into(), Q.0[i].into(), 49).into(); t0.0[i] = _mm256_permute2x128_si256(t0.0[i].into(), Q.0[i].into(), 49).into();
} }
// set t2 = (S0*S2 S1*S3 Z1*Z2 T1*T2) = (S4 S5 S6 S7)
let mut t2 = &t0 * &t1; let mut t2 = &t0 * &t1;
t2.scale_by_curve_constants();
for i in 0..5 {
let swapped = _mm256_shuffle_epi32(t2.0[i].into(), 0b10_11_00_01);
t2.0[i] = _mm256_blend_epi32(t2.0[i].into(), swapped, 0b11110000).into();
}
// set t2 = (S8 S9 S10 S11)
t2.scale_by_curve_constants(true);
// set t2 = (S8 S9 S11 S10)
t2.swap_CD();
// set t2 = (S9-S8 S9+S8 S10-S11 S10+S11) = (S12 S13 S14 S15)
t2.diff_sum(); t2.diff_sum();
let c0 = u32x8::new(0,5,2,7,5,0,7,2); // (ABCD) -> (ADDA) let c0 = u32x8::new(0,5,2,7,5,0,7,2); // (ABCD) -> (ADDA)
let c1 = u32x8::new(4,1,6,3,4,1,6,3); // (ABCD) -> (CBCB) let c1 = u32x8::new(4,1,6,3,4,1,6,3); // (ABCD) -> (CBCB)
// set t0 = (S12 S15 S15 S12)
// set t1 = (S14 S13 S14 S13)
for i in 0..5 { for i in 0..5 {
t0.0[i] = _mm256_permutevar8x32_epi32(t2.0[i], c0); t0.0[i] = _mm256_permutevar8x32_epi32(t2.0[i], c0);
t1.0[i] = _mm256_permutevar8x32_epi32(t2.0[i], c1); t1.0[i] = _mm256_permutevar8x32_epi32(t2.0[i], c1);
} }
// return (S12*S14 S15*S13 S15*S14 S12*S13) = (X3 Y3 Z3 T3)
ExtendedPoint(&t0 * &t1)
}
}
}
impl<'a, 'b> Sub<&'b ExtendedPoint> for &'a ExtendedPoint {
type Output = ExtendedPoint;
/// Uses a slight tweak of the parallel unified formulas of HWCD'08
fn sub(self, other: &'b ExtendedPoint) -> ExtendedPoint {
unsafe {
use stdsimd::vendor::_mm256_permute2x128_si256;
use stdsimd::vendor::_mm256_permutevar8x32_epi32;
use stdsimd::vendor::_mm256_blend_epi32;
use stdsimd::vendor::_mm256_shuffle_epi32;
let P: &FieldElement32x4 = &self.0;
let Q: &FieldElement32x4 = &other.0;
let mut t0 = FieldElement32x4::zero();
let mut t1 = FieldElement32x4::zero();
// set t0 = (X1 Y1 X2 Y2)
for i in 0..5 {
t0.0[i] = _mm256_permute2x128_si256(P.0[i].into(), Q.0[i].into(), 32).into();
}
// Since we're subtracting instead of adding, we want to add the point (-X2 Y2 Z2 -T2).
// Set (X2' Y2' Z2' T2') = (-X2 Y2 Z2 -T2)
//
// so S2 = Y2 - X2' = Y2 - (-X2) = Y2 + X2
// and S3 = Y2 + X2' = Y2 + (-X2) = Y2 - X2
// set t0 = (Y1-X1 Y1+X1 Y2-X2 Y2+X2) = (S0 S1 S3 S2)
t0.diff_sum();
// set t0 = (S0 S1 S2 S3)
t0.swap_CD();
// set t1 = (S0 S1 Z1 T1)
// set t0 = (S2 S3 Z2 T2) = (S2 S3 Z2' -T2')
for i in 0..5 {
t1.0[i] = _mm256_blend_epi32(t0.0[i].into(), P.0[i].into(), 0b11110000).into();
t0.0[i] = _mm256_permute2x128_si256(t0.0[i].into(), Q.0[i].into(), 49).into();
}
// set t2 = (S0*S2 S1*S3 Z1*Z2 T1*T2 )
// = (S0*S2 S1*S3 Z1*Z2' -T1*T2') = (S4 S5 S6 -S7)
let mut t2 = &t0 * &t1;
// set t2 = (S8 S9 S10 S11)
t2.scale_by_curve_constants(false);
// set t2 = (S8 S9 S11 S10)
t2.swap_CD();
// set t2 = (S9-S8 S9+S8 S10-S11 S10+S11) = (S12 S13 S14 S15)
t2.diff_sum();
let c0 = u32x8::new(0,5,2,7,5,0,7,2); // (ABCD) -> (ADDA)
let c1 = u32x8::new(4,1,6,3,4,1,6,3); // (ABCD) -> (CBCB)
// set t0 = (S12 S15 S15 S12)
// set t1 = (S14 S13 S14 S13)
for i in 0..5 {
t0.0[i] = _mm256_permutevar8x32_epi32(t2.0[i], c0);
t1.0[i] = _mm256_permutevar8x32_epi32(t2.0[i], c1);
}
// return (S12*S14 S15*S13 S15*S14 S12*S13) = (X3 Y3 Z3 T3)
ExtendedPoint(&t0 * &t1) ExtendedPoint(&t0 * &t1)
} }
} }
@ -502,7 +581,7 @@ pub mod vartime {
Q = &Q + &odd_multiple[( naf[i]/2) as usize]; Q = &Q + &odd_multiple[( naf[i]/2) as usize];
} else if naf[i] < 0 { } else if naf[i] < 0 {
// XXX impl Sub // XXX impl Sub
Q = &Q + &(-&odd_multiple[(-naf[i]/2) as usize]); Q = &Q - &odd_multiple[(-naf[i]/2) as usize];
} }
} }
} }
@ -577,40 +656,65 @@ mod test {
} }
fn addition_test_helper(P: edwards::ExtendedPoint, Q: edwards::ExtendedPoint) { fn addition_test_helper(P: edwards::ExtendedPoint, Q: edwards::ExtendedPoint) {
let R1: edwards::ExtendedPoint = serial_add(P.into(), Q.into()).into(); // Test the serial implementation of the parallel addition formulas
let R2: edwards::ExtendedPoint = (&ExtendedPoint::from(P) + &ExtendedPoint::from(Q)).into(); let R_serial: edwards::ExtendedPoint = serial_add(P.into(), Q.into()).into();
// Test the vector implementation of the parallel addition formulas
let R_vector: edwards::ExtendedPoint = (&ExtendedPoint::from(P) + &ExtendedPoint::from(Q)).into();
// Test the vector implementation of the parallel subtraction formulas
let S_vector: edwards::ExtendedPoint = (&ExtendedPoint::from(P) - &ExtendedPoint::from(Q)).into();
println!("Testing point addition:"); println!("Testing point addition:");
println!("P = {:?}", P); println!("P = {:?}", P);
println!("Q = {:?}", Q); println!("Q = {:?}", Q);
println!("(serial) R1 = {:?}", R1); println!("R = P + Q = {:?}", &P + &Q);
println!("(vector) R2 = {:?}", R2); println!("R_serial = {:?}", R_serial);
println!("P + Q = {:?}", &P + &Q); println!("R_vector = {:?}", R_vector);
assert_eq!(R1.compress(), (&P + &Q).compress()); println!("S = P - Q = {:?}", &P - &Q);
assert_eq!(R2.compress(), (&P + &Q).compress()); 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"); println!("OK!\n");
} }
#[test]
fn sub_vs_add_minus() {
let P: ExtendedPoint = edwards::ExtendedPoint::identity().into();
let Q: ExtendedPoint = edwards::ExtendedPoint::identity().into();
let mQ = -&Q;
println!("sub");
let R1: edwards::ExtendedPoint = (&P - &Q).into();
println!("add neg");
let R2: edwards::ExtendedPoint = (&P + &mQ).into();
assert_eq!(R2.compress(), edwards::ExtendedPoint::identity().compress());
assert_eq!(R1.compress(), edwards::ExtendedPoint::identity().compress());
}
#[test] #[test]
fn vector_addition_vs_serial_addition_vs_edwards_extendedpoint() { fn vector_addition_vs_serial_addition_vs_edwards_extendedpoint() {
use constants; use constants;
use scalar::Scalar; use scalar::Scalar;
println!("Testing id + id"); println!("Testing id +- id");
let P = edwards::ExtendedPoint::identity(); let P = edwards::ExtendedPoint::identity();
let Q = edwards::ExtendedPoint::identity(); let Q = edwards::ExtendedPoint::identity();
addition_test_helper(P, Q); addition_test_helper(P, Q);
println!("Testing id + B"); println!("Testing id +- B");
let P = edwards::ExtendedPoint::identity(); let P = edwards::ExtendedPoint::identity();
let Q = constants::ED25519_BASEPOINT_POINT; let Q = constants::ED25519_BASEPOINT_POINT;
addition_test_helper(P, Q); addition_test_helper(P, Q);
println!("Testing B + B"); println!("Testing B +- B");
let P = constants::ED25519_BASEPOINT_POINT; let P = constants::ED25519_BASEPOINT_POINT;
let Q = constants::ED25519_BASEPOINT_POINT; let Q = constants::ED25519_BASEPOINT_POINT;
addition_test_helper(P, Q); addition_test_helper(P, Q);
println!("Testing B + kB"); println!("Testing B +- kB");
let P = constants::ED25519_BASEPOINT_POINT; let P = constants::ED25519_BASEPOINT_POINT;
let Q = &constants::ED25519_BASEPOINT_TABLE * &Scalar::from_u64(8475983829); let Q = &constants::ED25519_BASEPOINT_TABLE * &Scalar::from_u64(8475983829);
addition_test_helper(P, Q); addition_test_helper(P, Q);

80
src/backend/avx2/field.rs
View file

@ -114,6 +114,18 @@ impl FieldElement32x4 {
self.reduce32(); self.reduce32();
} }
// Given `self = (A,B,C,D)`, set `self = (A,B,D,C)`
pub fn swap_CD(&mut self) {
unsafe {
use stdsimd::vendor::_mm256_shuffle_epi32;
use stdsimd::vendor::_mm256_blend_epi32;
for i in 0..5 {
let swapped = _mm256_shuffle_epi32(self.0[i].into(), 0b10_11_00_01);
self.0[i] = _mm256_blend_epi32(self.0[i].into(), swapped, 0b11110000).into();
}
}
}
// Given `self = (A,B,C,D)`, set `self = (B - A, B + A, D - C, D + C)`. // Given `self = (A,B,C,D)`, set `self = (B - A, B + A, D - C, D + C)`.
pub fn diff_sum(&mut self) { pub fn diff_sum(&mut self) {
/// (v0 v1 v2 v3 v4 v5 v6 v7) -> (v1 v0 v3 v2 v5 v4 v7 v6) /// (v0 v1 v2 v3 v4 v5 v6 v7) -> (v1 v0 v3 v2 v5 v4 v7 v6)
@ -188,7 +200,17 @@ impl FieldElement32x4 {
FieldElement32x4(out) FieldElement32x4(out)
} }
pub fn scale_by_curve_constants(&mut self) { /// Let `self` \\(= (A, B, C, D) \\).
///
/// If `negate_121665 = true`, compute
///
/// $$( 121666A, 121666B, 2\cdot 121666C, -2\cdot 121665 D).$$
///
/// If `negate_121665 = false`, compute
///
/// $$( 121666A, 121666B, 2\cdot 121666C, 2\cdot 121665 D).$$
///
pub fn scale_by_curve_constants(&mut self, negate_121665: bool) {
let mut b = [u64x4::splat(0); 10]; let mut b = [u64x4::splat(0); 10];
let consts = u32x8::new(121666, 0, 121666, 0, 2*121666, 0, 2*121665, 0); let consts = u32x8::new(121666, 0, 121666, 0, 2*121666, 0, 2*121665, 0);
@ -203,32 +225,57 @@ impl FieldElement32x4 {
let (b0, b1) = unpack_pair(self.0[0]); let (b0, b1) = unpack_pair(self.0[0]);
let b0 = _mm256_mul_epu32(b0, consts); // need a new binding since now let b0 = _mm256_mul_epu32(b0, consts); // need a new binding since now
let b1 = _mm256_mul_epu32(b1, consts); // b0 has type u64x4 let b1 = _mm256_mul_epu32(b1, consts); // b0 has type u64x4
b[0] = _mm256_blend_epi32(b0.into(), (low__p20 - b0).into(), 0b11_00_00_00).into(); if negate_121665 {
b[1] = _mm256_blend_epi32(b1.into(), (odd__p20 - b1).into(), 0b11_00_00_00).into(); b[0] = _mm256_blend_epi32(b0.into(), (low__p20 - b0).into(), 0b11_00_00_00).into();
b[1] = _mm256_blend_epi32(b1.into(), (odd__p20 - b1).into(), 0b11_00_00_00).into();
} else {
b[0] = b0;
b[1] = b1;
}
let (b2, b3) = unpack_pair(self.0[1]); let (b2, b3) = unpack_pair(self.0[1]);
let b2 = _mm256_mul_epu32(b2, consts); let b2 = _mm256_mul_epu32(b2, consts);
let b3 = _mm256_mul_epu32(b3, consts); let b3 = _mm256_mul_epu32(b3, consts);
b[2] = _mm256_blend_epi32(b2.into(), (even_p20 - b2).into(), 0b11_00_00_00).into(); if negate_121665 {
b[3] = _mm256_blend_epi32(b3.into(), (odd__p20 - b3).into(), 0b11_00_00_00).into(); b[2] = _mm256_blend_epi32(b2.into(), (even_p20 - b2).into(), 0b11_00_00_00).into();
b[3] = _mm256_blend_epi32(b3.into(), (odd__p20 - b3).into(), 0b11_00_00_00).into();
} else {
b[2] = b2;
b[3] = b3;
}
let (b4, b5) = unpack_pair(self.0[2]); let (b4, b5) = unpack_pair(self.0[2]);
let b4 = _mm256_mul_epu32(b4, consts); let b4 = _mm256_mul_epu32(b4, consts);
let b5 = _mm256_mul_epu32(b5, consts); let b5 = _mm256_mul_epu32(b5, consts);
b[4] = _mm256_blend_epi32(b4.into(), (even_p20 - b4).into(), 0b11_00_00_00).into(); if negate_121665 {
b[5] = _mm256_blend_epi32(b5.into(), (odd__p20 - b5).into(), 0b11_00_00_00).into(); b[4] = _mm256_blend_epi32(b4.into(), (even_p20 - b4).into(), 0b11_00_00_00).into();
b[5] = _mm256_blend_epi32(b5.into(), (odd__p20 - b5).into(), 0b11_00_00_00).into();
} else {
b[4] = b4;
b[5] = b5;
}
let (b6, b7) = unpack_pair(self.0[3]); let (b6, b7) = unpack_pair(self.0[3]);
let b6 = _mm256_mul_epu32(b6, consts); let b6 = _mm256_mul_epu32(b6, consts);
let b7 = _mm256_mul_epu32(b7, consts); let b7 = _mm256_mul_epu32(b7, consts);
b[6] = _mm256_blend_epi32(b6.into(), (even_p20 - b6).into(), 0b11_00_00_00).into(); if negate_121665 {
b[7] = _mm256_blend_epi32(b7.into(), (odd__p20 - b7).into(), 0b11_00_00_00).into(); b[6] = _mm256_blend_epi32(b6.into(), (even_p20 - b6).into(), 0b11_00_00_00).into();
b[7] = _mm256_blend_epi32(b7.into(), (odd__p20 - b7).into(), 0b11_00_00_00).into();
} else {
b[6] = b6;
b[7] = b7;
}
let (b8, b9) = unpack_pair(self.0[4]); let (b8, b9) = unpack_pair(self.0[4]);
let b8 = _mm256_mul_epu32(b8, consts); let b8 = _mm256_mul_epu32(b8, consts);
let b9 = _mm256_mul_epu32(b9, consts); let b9 = _mm256_mul_epu32(b9, consts);
b[8] = _mm256_blend_epi32(b8.into(), (even_p20 - b8).into(), 0b11_00_00_00).into(); if negate_121665 {
b[9] = _mm256_blend_epi32(b9.into(), (odd__p20 - b9).into(), 0b11_00_00_00).into(); b[8] = _mm256_blend_epi32(b8.into(), (even_p20 - b8).into(), 0b11_00_00_00).into();
b[9] = _mm256_blend_epi32(b9.into(), (odd__p20 - b9).into(), 0b11_00_00_00).into();
} else {
b[8] = b8;
b[9] = b9;
}
} }
*self = FieldElement32x4::reduce64(b); *self = FieldElement32x4::reduce64(b);
@ -517,13 +564,22 @@ mod test {
#[test] #[test]
fn scale_by_curve_constants() { fn scale_by_curve_constants() {
let mut x = FieldElement32x4::splat(&FieldElement64::one()); let mut x = FieldElement32x4::splat(&FieldElement64::one());
x.scale_by_curve_constants(); x.scale_by_curve_constants(true);
let xs = x.split(); let xs = x.split();
assert_eq!(xs[0], FieldElement64([ 121666,0,0,0,0])); assert_eq!(xs[0], FieldElement64([ 121666,0,0,0,0]));
assert_eq!(xs[1], FieldElement64([ 121666,0,0,0,0])); assert_eq!(xs[1], FieldElement64([ 121666,0,0,0,0]));
assert_eq!(xs[2], FieldElement64([2*121666,0,0,0,0])); assert_eq!(xs[2], FieldElement64([2*121666,0,0,0,0]));
assert_eq!(xs[3], -&FieldElement64([2*121665,0,0,0,0])); assert_eq!(xs[3], -&FieldElement64([2*121665,0,0,0,0]));
let mut y = FieldElement32x4::splat(&FieldElement64::one());
y.scale_by_curve_constants(false);
let ys = y.split();
assert_eq!(ys[0], FieldElement64([ 121666,0,0,0,0]));
assert_eq!(ys[1], FieldElement64([ 121666,0,0,0,0]));
assert_eq!(ys[2], FieldElement64([2*121666,0,0,0,0]));
assert_eq!(ys[3], FieldElement64([2*121665,0,0,0,0]));
} }
#[test] #[test]