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, -8347857,
                                   24143090, 14568123, 30185756, -12247770,
                                   -33528939, 8345319]),
               Y:
                   FieldElement32([6952922, 1265500, -6862341, 7057498,
                                   4037696, 5447722, -31680899, 15325402,
                                   19365852, -1569102]),
               Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
               T:
                   FieldElement32([-25262188, -11972680, 11716002, -5869612,
                                   -18193162, 16297739, 20670665, -8559098,
                                   3541543, -5011181]),},
 ExtendedPoint{X:
                   FieldElement32([32595792, 7943725, -9377950, -3500415,
                                   -12389472, 272473, 25146209, 2005654,
                                   -326686, -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([21352778, 5345713, 4660180, -8347857,
                                   24143090, 14568123, 30185756, -12247770,
                                   -33528939, 8345319]),
               Y:
                   FieldElement32([-6952922, -1265500, 6862341, -7057498,
                                   -4037696, -5447722, 31680899, -15325402,
                                   -19365852, 1569102]),
               Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
               T:
                   FieldElement32([25262188, 11972680, -11716002, 5869612,
                                   18193162, -16297739, -20670665, 8559098,
                                   -3541543, 5011181]),},
 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, 8347857,
                                   -24143090, -14568123, -30185756, 12247770,
                                   33528939, -8345319]),
               Y:
                   FieldElement32([-6952922, -1265500, 6862341, -7057498,
                                   -4037696, -5447722, 31680899, -15325402,
                                   -19365852, 1569102]),
               Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
               T:
                   FieldElement32([-25262188, -11972680, 11716002, -5869612,
                                   -18193162, 16297739, 20670665, -8559098,
                                   3541543, -5011181]),},
 ExtendedPoint{X:
                   FieldElement32([-32595792, -7943725, 9377950, 3500415,
                                   12389472, -272473, -25146209, -2005654,
                                   326686, 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([-21352778, -5345713, -4660180, 8347857,
                                   -24143090, -14568123, -30185756, 12247770,
                                   33528939, -8345319]),
               Y:
                   FieldElement32([6952922, 1265500, -6862341, 7057498,
                                   4037696, 5447722, -31680899, 15325402,
                                   19365852, -1569102]),
               Z: FieldElement32([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
               T:
                   FieldElement32([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 ith 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.