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 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.