nim-libp2p/libp2p/crypto/ed25519/constants.nim

## Nim-Libp2p
## Copyright (c) 2018 Status Research & Development GmbH
## Licensed under either of
##  * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE))
##  * MIT license ([LICENSE-MIT](LICENSE-MIT))
## at your option.
## This file may not be copied, modified, or distributed except according to
## those terms.

## This module implements ED25519.
## This is pure nim implementation of ED25519 ref10.

type
  Fe* = array[10, int32]

  GeP2* = object
    x*, y*, z*: Fe

  GeP3* = object
    x*, y*, z*, t*: Fe

  GeP1P1* = object
    x*, y*, z*, t*: Fe

  GePrecomp* = object
    yplusx*, yminusx*, xy2d*: Fe

  GeCached* = object
    yplusx*, yminusx*, z*, t2d*: Fe

const
  CurveOrder* = [
    0xED'u8, 0xD3'u8, 0xF5'u8, 0x5C'u8, 0x1A'u8, 0x63'u8, 0x12'u8, 0x58'u8,
    0xD6'u8, 0x9C'u8, 0xF7'u8, 0xA2'u8, 0xDE'u8, 0xF9'u8, 0xDE'u8, 0x14'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x10'u8
  ]

  ZeroFe* = [
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8
  ]

  BasePrecomp* = [
    [
      GePrecomp(
        yplusx: [
          25967493'i32, -14356035, 29566456, 3660896, -12694345,
          4014787, 27544626, -11754271, -6079156, 2047605
        ],
        yminusx: [
          -12545711'i32, 934262, -2722910, 3049990, -727428,
          9406986, 12720692, 5043384, 19500929, -15469378
        ],
        xy2d: [
          -8738181'i32, 4489570, 9688441, -14785194, 10184609,
          -12363380, 29287919, 11864899, -24514362, -4438546
        ]
      ),
      GePrecomp(
        yplusx: [
          -12815894'i32, -12976347, -21581243, 11784320, -25355658,
          -2750717, -11717903, -3814571, -358445, -10211303
        ],
        yminusx: [
          -21703237'i32, 6903825, 27185491, 6451973, -29577724,
          -9554005, -15616551, 11189268, -26829678, -5319081
        ],
        xy2d: [
          26966642'i32, 11152617, 32442495, 15396054, 14353839,
          -12752335, -3128826, -9541118, -15472047, -4166697
        ]
      ),
      GePrecomp(
        yplusx: [
          15636291'i32, -9688557, 24204773, -7912398, 616977,
          -16685262, 27787600, -14772189, 28944400, -1550024
        ],
        yminusx: [
          16568933'i32, 4717097, -11556148, -1102322, 15682896,
          -11807043, 16354577, -11775962, 7689662, 11199574
        ],
        xy2d: [
          30464156'i32, -5976125, -11779434, -15670865, 23220365,
          15915852, 7512774, 10017326, -17749093, -9920357
        ]
      ),
      GePrecomp(
        yplusx: [
          -17036878'i32, 13921892, 10945806, -6033431, 27105052,
          -16084379, -28926210, 15006023, 3284568, -6276540
        ],
        yminusx: [
          23599295'i32, -8306047, -11193664, -7687416, 13236774,
          10506355, 7464579, 9656445, 13059162, 10374397
        ],
        xy2d: [
          7798556'i32, 16710257, 3033922, 2874086, 28997861,
          2835604, 32406664, -3839045, -641708, -101325
        ]
      ),
      GePrecomp(
        yplusx: [
          10861363'i32, 11473154, 27284546, 1981175, -30064349,
          12577861, 32867885, 14515107, -15438304, 10819380
        ],
        yminusx: [
          4708026'i32, 6336745, 20377586, 9066809, -11272109,
          6594696, -25653668, 12483688, -12668491, 5581306
        ],
        xy2d: [
          19563160'i32, 16186464, -29386857, 4097519, 10237984,
          -4348115, 28542350, 13850243, -23678021, -15815942
        ]
      ),
      GePrecomp(
        yplusx: [
          -15371964'i32, -12862754, 32573250, 4720197, -26436522,
          5875511, -19188627, -15224819, -9818940, -12085777
        ],
        yminusx: [
          -8549212'i32, 109983, 15149363, 2178705, 22900618,
          4543417, 3044240, -15689887, 1762328, 14866737
        ],
        xy2d: [
          -18199695'i32, -15951423, -10473290, 1707278, -17185920,
          3916101, -28236412, 3959421, 27914454, 4383652
        ]
      ),
      GePrecomp(
        yplusx: [
          5153746'i32, 9909285, 1723747, -2777874, 30523605,
          5516873, 19480852, 5230134, -23952439, -15175766
        ],
        yminusx: [
          -30269007'i32, -3463509, 7665486, 10083793, 28475525,
          1649722, 20654025, 16520125, 30598449, 7715701
        ],
        xy2d: [
          28881845'i32, 14381568, 9657904, 3680757, -20181635,
          7843316, -31400660, 1370708, 29794553, -1409300
        ]
      ),
      GePrecomp(
        yplusx: [
          14499471'i32, -2729599, -33191113, -4254652, 28494862,
          14271267, 30290735, 10876454, -33154098, 2381726
        ],
        yminusx: [
          -7195431'i32, -2655363, -14730155, 462251, -27724326,
          3941372, -6236617, 3696005, -32300832, 15351955
        ],
        xy2d: [
          27431194'i32, 8222322, 16448760, -3907995, -18707002,
          11938355, -32961401, -2970515, 29551813, 10109425
        ]
      )
    ],
    [
      GePrecomp(
        yplusx: [
          -13657040'i32, -13155431, -31283750, 11777098, 21447386,
          6519384, -2378284, -1627556, 10092783, -4764171
        ],
        yminusx: [
          27939166'i32, 14210322, 4677035, 16277044, -22964462,
          -12398139, -32508754, 12005538, -17810127, 12803510
        ],
        xy2d: [
          17228999'i32, -15661624, -1233527, 300140, -1224870,
          -11714777, 30364213, -9038194, 18016357, 4397660
        ]
      ),
      GePrecomp(
        yplusx: [
          -10958843'i32, -7690207, 4776341, -14954238, 27850028,
          -15602212, -26619106, 14544525, -17477504, 982639
        ],
        yminusx: [
          29253598'i32, 15796703, -2863982, -9908884, 10057023,
          3163536, 7332899, -4120128, -21047696, 9934963
        ],
        xy2d: [
          5793303'i32, 16271923, -24131614, -10116404, 29188560,
          1206517, -14747930, 4559895, -30123922, -10897950
        ]
      ),
      GePrecomp(
        yplusx: [
          -27643952'i32, -11493006, 16282657, -11036493, 28414021,
          -15012264, 24191034, 4541697, -13338309,5500568
        ],
        yminusx: [
          12650548'i32, -1497113, 9052871, 11355358, -17680037,
          -8400164, -17430592, 12264343, 10874051, 13524335
        ],
        xy2d: [
          25556948'i32, -3045990, 714651, 2510400, 23394682,
          -10415330, 33119038, 5080568, -22528059, 5376628
        ]
      ),
      GePrecomp(
        yplusx: [
          -26088264'i32, -4011052, -17013699, -3537628, -6726793,
          1920897, -22321305, -9447443, 4535768, 1569007
        ],
        yminusx: [
          -2255422'i32, 14606630, -21692440, -8039818, 28430649,
          8775819, -30494562, 3044290, 31848280, 12543772
        ],
        xy2d: [
          -22028579'i32, 2943893, -31857513, 6777306, 13784462,
          -4292203, -27377195, -2062731, 7718482, 14474653
        ]
      ),
      GePrecomp(
        yplusx: [
          2385315'i32, 2454213, -22631320, 46603, -4437935,
          -15680415, 656965, -7236665, 24316168, -5253567
        ],
        yminusx: [
          13741529'i32, 10911568, -33233417, -8603737, -20177830,
          -1033297, 33040651, -13424532, -20729456, 8321686
        ],
        xy2d: [
          21060490'i32, -2212744, 15712757, -4336099, 1639040,
          10656336, 23845965, -11874838, -9984458, 608372
        ]
      ),
      GePrecomp(
        yplusx: [
          -13672732'i32, -15087586, -10889693, -7557059, -6036909,
          11305547, 1123968, -6780577, 27229399, 23887
        ],
        yminusx: [
          -23244140'i32, -294205, -11744728, 14712571, -29465699,
          -2029617, 12797024, -6440308, -1633405, 16678954
        ],
        xy2d: [
          -29500620'i32, 4770662, -16054387, 14001338, 7830047,
          9564805, -1508144, -4795045, -17169265, 4904953
        ]
      ),
      GePrecomp(
        yplusx: [
          24059557'i32, 14617003, 19037157, -15039908, 19766093,
          -14906429, 5169211, 16191880, 2128236, -4326833
        ],
        yminusx: [
          -16981152'i32, 4124966, -8540610, -10653797, 30336522,
          -14105247, -29806336, 916033, -6882542, -2986532
        ],
        xy2d: [
          -22630907'i32, 12419372, -7134229, -7473371, -16478904,
          16739175, 285431, 2763829, 15736322, 4143876
        ]
      ),
      GePrecomp(
        yplusx: [
          2379352'i32, 11839345, -4110402, -5988665, 11274298,
          794957, 212801, -14594663, 23527084, -16458268
        ],
        yminusx: [
          33431127'i32, -11130478, -17838966, -15626900, 8909499,
          8376530, -32625340, 4087881, -15188911, -14416214
        ],
        xy2d: [
          1767683'i32, 7197987, -13205226, -2022635, -13091350,
          448826, 5799055, 4357868, -4774191, -16323038
        ]
      )
    ],
    [
      GePrecomp(
        yplusx: [
          6721966'i32, 13833823, -23523388, -1551314, 26354293,
          -11863321, 23365147, -3949732, 7390890, 2759800
        ],
        yminusx: [
          4409041'i32, 2052381, 23373853, 10530217, 7676779,
          -12885954, 21302353, -4264057, 1244380, -12919645
        ],
        xy2d: [
          -4421239'i32, 7169619, 4982368, -2957590, 30256825,
          -2777540, 14086413, 9208236, 15886429, 16489664
        ]
      ),
      GePrecomp(
        yplusx: [
          1996075'i32, 10375649, 14346367, 13311202, -6874135,
          -16438411, -13693198, 398369, -30606455, -712933
        ],
        yminusx: [
          -25307465'i32, 9795880, -2777414, 14878809, -33531835,
          14780363, 13348553, 12076947, -30836462, 5113182
        ],
        xy2d: [
          -17770784'i32, 11797796, 31950843, 13929123, -25888302,
          12288344, -30341101, -7336386, 13847711, 5387222
        ]
      ),
      GePrecomp(
        yplusx: [
          -18582163'i32, -3416217, 17824843, -2340966, 22744343,
          -10442611, 8763061, 3617786, -19600662, 10370991
        ],
        yminusx: [
          20246567'i32, -14369378, 22358229, -543712, 18507283,
          -10413996, 14554437, -8746092, 32232924, 16763880
        ],
        xy2d: [
          9648505'i32, 10094563, 26416693, 14745928, -30374318,
          -6472621, 11094161, 15689506, 3140038, -16510092
        ]
      ),
      GePrecomp(
        yplusx: [
          -16160072'i32, 5472695, 31895588, 4744994, 8823515,
          10365685, -27224800, 9448613, -28774454, 366295
        ],
        yminusx: [
          19153450'i32, 11523972, -11096490, -6503142, -24647631,
          5420647, 28344573, 8041113, 719605, 11671788
        ],
        xy2d: [
          8678025'i32, 2694440, -6808014, 2517372, 4964326,
          11152271, -15432916, -15266516, 27000813, -10195553
        ]
      ),
      GePrecomp(
        yplusx: [
          -15157904'i32, 7134312, 8639287, -2814877, -7235688,
          10421742, 564065, 5336097, 6750977, -14521026
        ],
        yminusx: [
          11836410'i32, -3979488, 26297894, 16080799, 23455045,
          15735944, 1695823, -8819122, 8169720, 16220347
        ],
        xy2d: [
          -18115838'i32, 8653647, 17578566, -6092619, -8025777,
          -16012763, -11144307, -2627664, -5990708, -14166033
        ]
      ),
      GePrecomp(
        yplusx: [
          -23308498'i32, -10968312, 15213228, -10081214, -30853605,
          -11050004, 27884329, 2847284, 2655861, 1738395
        ],
        yminusx: [
          -27537433'i32, -14253021, -25336301, -8002780, -9370762,
          8129821, 21651608, -3239336, -19087449, -11005278
        ],
        xy2d: [
          1533110'i32, 3437855, 23735889, 459276, 29970501,
          11335377, 26030092, 5821408, 10478196, 8544890
        ]
      ),
      GePrecomp(
        yplusx: [
          32173121'i32, -16129311, 24896207, 3921497, 22579056,
          -3410854, 19270449, 12217473, 17789017, -3395995
        ],
        yminusx: [
          -30552961'i32, -2228401, -15578829, -10147201, 13243889,
          517024, 15479401, -3853233, 30460520, 1052596
        ],
        xy2d: [
          -11614875'i32, 13323618, 32618793, 8175907, -15230173,
          12596687, 27491595, -4612359, 3179268, -9478891
        ]
      ),
      GePrecomp(
        yplusx: [
          31947069'i32, -14366651, -4640583, -15339921, -15125977,
          -6039709, -14756777, -16411740, 19072640, -9511060
        ],
        yminusx: [
          11685058'i32, 11822410, 3158003, -13952594, 33402194,
          -4165066, 5977896, -5215017, 473099, 5040608
        ],
        xy2d: [
          -20290863'i32, 8198642, -27410132, 11602123, 1290375,
          -2799760, 28326862, 1721092, -19558642, -3131606
        ]
      )
    ],
    [
      GePrecomp(
        yplusx: [
          7881532'i32, 10687937, 7578723, 7738378, -18951012,
          -2553952, 21820786, 8076149, -27868496, 11538389
        ],
        yminusx: [
          -19935666'i32, 3899861, 18283497, -6801568, -15728660,
          -11249211, 8754525, 7446702, -5676054, 5797016
        ],
        xy2d: [
          -11295600'i32, -3793569, -15782110, -7964573, 12708869,
          -8456199, 2014099, -9050574, -2369172, -5877341
        ]
      ),
      GePrecomp(
        yplusx: [
          -22472376'i32, -11568741, -27682020, 1146375, 18956691,
          16640559, 1192730, -3714199, 15123619, 10811505
        ],
        yminusx: [
          14352098'i32, -3419715, -18942044, 10822655, 32750596,
          4699007, -70363, 15776356, -28886779, -11974553
        ],
        xy2d: [
          -28241164'i32, -8072475, -4978962, -5315317, 29416931,
          1847569, -20654173, -16484855, 4714547, -9600655
        ]
      ),
      GePrecomp(
        yplusx: [
          15200332'i32, 8368572, 19679101, 15970074, -31872674,
          1959451, 24611599, -4543832, -11745876, 12340220
        ],
        yminusx: [
          12876937'i32, -10480056, 33134381, 6590940, -6307776,
          14872440, 9613953, 8241152, 15370987, 9608631
        ],
        xy2d: [
          -4143277'i32, -12014408, 8446281, -391603, 4407738,
          13629032, -7724868, 15866074, -28210621, -8814099
        ]
      ),
      GePrecomp(
        yplusx: [
          26660628'i32, -15677655, 8393734, 358047, -7401291,
          992988, -23904233, 858697, 20571223, 8420556
        ],
        yminusx: [
          14620715'i32, 13067227, -15447274, 8264467, 14106269,
          15080814, 33531827, 12516406, -21574435, -12476749
        ],
        xy2d: [
          236881'i32, 10476226, 57258, -14677024, 6472998,
          2466984, 17258519, 7256740, 8791136, 15069930
        ]
      ),
      GePrecomp(
        yplusx: [
          1276410'i32, -9371918, 22949635, -16322807, -23493039,
          -5702186, 14711875, 4874229, -30663140, -2331391
        ],
        yminusx: [
          5855666'i32, 4990204, -13711848, 7294284, -7804282,
          1924647, -1423175, -7912378, -33069337, 9234253
        ],
        xy2d: [
          20590503'i32, -9018988, 31529744, -7352666, -2706834,
          10650548, 31559055, -11609587, 18979186, 13396066
        ]
      ),
      GePrecomp(
        yplusx: [
          24474287'i32, 4968103, 22267082, 4407354, 24063882,
          -8325180, -18816887, 13594782, 33514650, 7021958
        ],
        yminusx: [
          -11566906'i32, -6565505, -21365085, 15928892, -26158305,
          4315421, -25948728, -3916677, -21480480, 12868082
        ],
        xy2d: [
          -28635013'i32, 13504661, 19988037, -2132761, 21078225,
          6443208, -21446107, 2244500, -12455797, -8089383
        ]
      ),
      GePrecomp(
        yplusx: [
          -30595528'i32, 13793479, -5852820, 319136, -25723172,
          -6263899, 33086546, 8957937, -15233648, 5540521
        ],
        yminusx: [
          -11630176'i32, -11503902, -8119500, -7643073, 2620056,
          1022908, -23710744, -1568984, -16128528, -14962807
        ],
        xy2d: [
          23152971'i32, 775386, 27395463, 14006635, -9701118,
          4649512, 1689819, 892185, -11513277, -15205948
        ]
      ),
      GePrecomp(
        yplusx: [
          9770129'i32, 9586738, 26496094, 4324120, 1556511,
          -3550024, 27453819, 4763127, -19179614, 5867134
        ],
        yminusx: [
          -32765025'i32, 1927590, 31726409, -4753295, 23962434,
          -16019500, 27846559, 5931263, -29749703, -16108455
        ],
        xy2d: [
          27461885'i32, -2977536, 22380810, 1815854, -23033753,
          -3031938, 7283490, -15148073, -19526700, 7734629
        ]
      )
    ],
    [
      GePrecomp(
        yplusx: [
          -8010264'i32, -9590817, -11120403, 6196038, 29344158,
          -13430885, 7585295, -3176626, 18549497, 15302069
        ],
        yminusx: [
          -32658337'i32, -6171222, -7672793, -11051681, 6258878,
          13504381, 10458790, -6418461, -8872242, 8424746
        ],
        xy2d: [
          24687205'i32, 8613276, -30667046, -3233545, 1863892,
          -1830544, 19206234, 7134917, -11284482, -828919
        ]
      ),
      GePrecomp(
        yplusx: [
          11334899'i32, -9218022, 8025293, 12707519, 17523892,
          -10476071, 10243738, -14685461, -5066034, 16498837
        ],
        yminusx: [
          8911542'i32, 6887158, -9584260, -6958590, 11145641,
          -9543680, 17303925, -14124238, 6536641, 10543906
        ],
        xy2d: [
          -28946384'i32, 15479763, -17466835, 568876, -1497683,
          11223454, -2669190, -16625574, -27235709, 8876771
        ]
      ),
      GePrecomp(
        yplusx: [
          -25742899'i32, -12566864, -15649966, -846607, -33026686,
          -796288, -33481822, 15824474, -604426, -9039817
        ],
        yminusx: [
          10330056'i32, 70051, 7957388, -9002667, 9764902,
          15609756, 27698697, -4890037, 1657394, 3084098
        ],
        xy2d: [
          10477963'i32, -7470260, 12119566, -13250805, 29016247,
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    GePrecomp(
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      xy2d: [
        -3099351'i32, 10324967, -2241613, 7453183, -5446979,
        -2735503, -13812022, -16236442, -32461234, -12290683
      ]
    )
  ]

  DConst* = [
    -10913610'i32, 13857413, -15372611, 6949391, 114729, -8787816,
    -6275908, -3247719, -18696448, -12055116
  ]

  D2Const* = [
    -21827239'i32, -5839606, -30745221, 13898782, 229458, 15978800,
    -12551817, -6495438, 29715968, 9444199
  ]

  SqrTm1* = [
    -32595792'i32, -7943725, 9377950, 3500415, 12389472, -272473,
    -25146209, -2005654, 326686, 11406482
  ]