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Add constants for points of the eight-torsion subgroup.

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Henry de Valence 2017-02-19 19:11:41 -05:00
parent ee5ea0a013
commit 5720e249ab
1 changed files with 99 additions and 0 deletions
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src/constants.rs
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@ -17,8 +17,10 @@
#![allow(non_snake_case)]
#![allow(non_upper_case_globals)]
#![allow(missing_docs)]
#![allow(non_snake_case)]
use field::FieldElement;
use curve::ExtendedPoint;
use curve::PreComputedPoint;
use curve::CompressedEdwardsY;
use scalar::Scalar;
@ -105,6 +107,63 @@ pub const lminus1: Scalar = Scalar([ 0xec, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0
0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10 ]);
/// The 8-torsion subgroup Ɛ[8].
///
/// In the case of Curve25519, it is cyclic; the `i`th element of the
/// array is `i*P`, where `P` is a point of order 8 generating Ɛ[8].
///
/// Thus Ɛ[4] is the points indexed by 0,2,4,6 and Ɛ[2] is the points
/// indexed by 0,4.
pub const EIGHT_TORSION: [ExtendedPoint; 8] = [
ExtendedPoint{
X: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
Y: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
T: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
},
ExtendedPoint{
X: FieldElement([21352778, 5345713, 4660180, -8347857, 24143090, 14568123, 30185756, -12247770, -33528939, 8345319]),
Y: FieldElement([6952922, 1265500, -6862341, 7057498, 4037696, 5447722, -31680899, 15325402, 19365852, -1569102]),
Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
T: FieldElement([-25262188, -11972680, 11716002, -5869612, -18193162, 16297739, 20670665, -8559098, 3541543, -5011181])
},
ExtendedPoint{
X: FieldElement([32595792, 7943725, -9377950, -3500415, -12389472, 272473, 25146209, 2005654, -326686, -11406482]),
Y: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
T: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
},
ExtendedPoint{
X: FieldElement([21352778, 5345713, 4660180, -8347857, 24143090, 14568123, 30185756, -12247770, -33528939, 8345319]),
Y: FieldElement([-6952922, -1265500, 6862341, -7057498, -4037696, -5447722, 31680899, -15325402, -19365852, 1569102]),
Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
T: FieldElement([25262188, 11972680, -11716002, 5869612, 18193162, -16297739, -20670665, 8559098, -3541543, 5011181])
},
ExtendedPoint{
X: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
Y: FieldElement([-1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
T: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
},
ExtendedPoint{
X: FieldElement([-21352778, -5345713, -4660180, 8347857, -24143090, -14568123, -30185756, 12247770, 33528939, -8345319]),
Y: FieldElement([-6952922, -1265500, 6862341, -7057498, -4037696, -5447722, 31680899, -15325402, -19365852, 1569102]),
Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
T: FieldElement([-25262188, -11972680, 11716002, -5869612, -18193162, 16297739, 20670665, -8559098, 3541543, -5011181])
},
ExtendedPoint{
X: FieldElement([-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482]),
Y: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
T: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
},
ExtendedPoint{
X: FieldElement([-21352778, -5345713, -4660180, 8347857, -24143090, -14568123, -30185756, 12247770, 33528939, -8345319]),
Y: FieldElement([6952922, 1265500, -6862341, 7057498, 4037696, 5447722, -31680899, 15325402, 19365852, -1569102]),
Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
T: FieldElement([25262188, 11972680, -11716002, 5869612, 18193162, -16297739, -20670665, 8559098, -3541543, 5011181])
},
];
pub const bi: [PreComputedPoint; 8] = [
PreComputedPoint{
@ -1503,8 +1562,48 @@ pub const base: [[PreComputedPoint; 8]; 32] = [
mod test {
use field::FieldElement;
use curve::PreComputedPoint;
use curve::CompressedEdwardsY;
use curve::ExtendedPoint;
use curve::Identity;
use curve::ValidityCheck;
use constants;
#[test]
fn test_eight_torsion() {
let mut bytes = [0;32];
bytes[0] = 1;
let compressed_id = CompressedEdwardsY(bytes);
for i in 0..8 {
let Q = constants::EIGHT_TORSION[i].mult_by_pow_2(3);
assert!(Q.is_valid());
assert!(Q.compress() == compressed_id);
}
}
#[test]
fn test_four_torsion() {
let mut bytes = [0;32];
bytes[0] = 1;
let compressed_id = CompressedEdwardsY(bytes);
for i in (0..8).filter(|i| i % 2 == 0) {
let Q = constants::EIGHT_TORSION[i].mult_by_pow_2(2);
assert!(Q.is_valid());
assert!(Q.compress() == compressed_id);
}
}
#[test]
fn test_two_torsion() {
let mut bytes = [0;32];
bytes[0] = 1;
let compressed_id = CompressedEdwardsY(bytes);
for i in (0..8).filter(|i| i % 4 == 0) {
let Q = constants::EIGHT_TORSION[i].mult_by_pow_2(1);
assert!(Q.is_valid());
assert!(Q.compress() == compressed_id);
}
}
#[test]
fn test_half() {
let one = FieldElement([1,0,0,0,0,0,0,0,0,0]);