Constant curve25519_dalek::constants::EIGHT_TORSION
[−]
[src]
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]),}]
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.