Constant curve25519_dalek::constants::EIGHT_TORSION
[−]
[src]
pub const EIGHT_TORSION: [ExtendedPoint; 8]=
[ExtendedPoint{X: FieldElement32([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), Y: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]), Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]), T: FieldElement32([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),}, ExtendedPoint{X: FieldElement32([21352778, 5345713, 4660180, 25206575, 24143089, 14568123, 30185756, 21306662, 33579924, 8345318]), Y: FieldElement32([6952903, 1265500, 60246523, 7057497, 4037696, 5447722, 35427965, 15325401, 19365852, 31985330]), Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]), T: FieldElement32([41846657, 21581751, 11716001, 27684820, 48915701, 16297738, 20670665, 24995334, 3541542, 28543251]),}, ExtendedPoint{X: FieldElement32([32595773, 7943725, 57730914, 30054016, 54719391, 272472, 25146209, 2005654, 66782178, 22147949]), Y: FieldElement32([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]), T: FieldElement32([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),}, ExtendedPoint{X: FieldElement32([21352778, 5345713, 4660180, 25206575, 24143089, 14568123, 30185756, 21306662, 33579924, 8345318]), Y: FieldElement32([60155942, 32288931, 6862340, 26496934, 63071167, 28106709, 31680898, 18229030, 47743011, 1569101]), Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]), T: FieldElement32([25262188, 11972680, 55392862, 5869611, 18193162, 17256693, 46438198, 8559097, 63567321, 5011180]),}, ExtendedPoint{X: FieldElement32([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), Y: FieldElement32([67108844, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431]), Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]), T: FieldElement32([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),}, ExtendedPoint{X: FieldElement32([45756067, 28208718, 62448683, 8347856, 42965774, 18986308, 36923107, 12247769, 33528939, 25209113]), Y: FieldElement32([60155942, 32288931, 6862340, 26496934, 63071167, 28106709, 31680898, 18229030, 47743011, 1569101]), Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]), T: FieldElement32([41846657, 21581751, 11716001, 27684820, 48915701, 16297738, 20670665, 24995334, 3541542, 28543251]),}, ExtendedPoint{X: FieldElement32([34513072, 25610706, 9377949, 3500415, 12389472, 33281959, 41962654, 31548777, 326685, 11406482]), Y: FieldElement32([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]), T: FieldElement32([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),}, ExtendedPoint{X: FieldElement32([45756067, 28208718, 62448683, 8347856, 42965774, 18986308, 36923107, 12247769, 33528939, 25209113]), Y: FieldElement32([6952903, 1265500, 60246523, 7057497, 4037696, 5447722, 35427965, 15325401, 19365852, 31985330]), Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]), T: FieldElement32([25262188, 11972680, 55392862, 5869611, 18193162, 17256693, 46438198, 8559097, 63567321, 5011180]),}]
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.