curve25519_dalek/backend/serial/u64/
constants.rs

1// -*- mode: rust; -*-
2//
3// This file is part of curve25519-dalek.
4// Copyright (c) 2016-2021 isis lovecruft
5// Copyright (c) 2016-2019 Henry de Valence
6// See LICENSE for licensing information.
7//
8// Authors:
9// - isis agora lovecruft <isis@patternsinthevoid.net>
10// - Henry de Valence <hdevalence@hdevalence.ca>
11
12//! This module contains backend-specific constant values, such as the 64-bit limbs of curve constants.
13
14use super::field::FieldElement51;
15use super::scalar::Scalar52;
16use crate::edwards::EdwardsPoint;
17
18#[cfg(feature = "precomputed-tables")]
19use crate::{
20    backend::serial::curve_models::AffineNielsPoint,
21    edwards::EdwardsBasepointTable,
22    window::{LookupTable, NafLookupTable8},
23};
24
25/// The value of minus one, equal to `-&FieldElement::ONE`
26pub(crate) const MINUS_ONE: FieldElement51 = FieldElement51::from_limbs([
27    2251799813685228,
28    2251799813685247,
29    2251799813685247,
30    2251799813685247,
31    2251799813685247,
32]);
33
34/// Edwards `d` value, equal to `-121665/121666 mod p`.
35pub(crate) const EDWARDS_D: FieldElement51 = FieldElement51::from_limbs([
36    929955233495203,
37    466365720129213,
38    1662059464998953,
39    2033849074728123,
40    1442794654840575,
41]);
42
43/// Edwards `2*d` value, equal to `2*(-121665/121666) mod p`.
44pub(crate) const EDWARDS_D2: FieldElement51 = FieldElement51::from_limbs([
45    1859910466990425,
46    932731440258426,
47    1072319116312658,
48    1815898335770999,
49    633789495995903,
50]);
51
52/// One minus edwards `d` value squared, equal to `(1 - (-121665/121666) mod p) pow 2`
53pub(crate) const ONE_MINUS_EDWARDS_D_SQUARED: FieldElement51 = FieldElement51::from_limbs([
54    1136626929484150,
55    1998550399581263,
56    496427632559748,
57    118527312129759,
58    45110755273534,
59]);
60
61/// Edwards `d` value minus one squared, equal to `(((-121665/121666) mod p) - 1) pow 2`
62pub(crate) const EDWARDS_D_MINUS_ONE_SQUARED: FieldElement51 = FieldElement51::from_limbs([
63    1507062230895904,
64    1572317787530805,
65    683053064812840,
66    317374165784489,
67    1572899562415810,
68]);
69
70/// `= sqrt(a*d - 1)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
71pub(crate) const SQRT_AD_MINUS_ONE: FieldElement51 = FieldElement51::from_limbs([
72    2241493124984347,
73    425987919032274,
74    2207028919301688,
75    1220490630685848,
76    974799131293748,
77]);
78
79/// `= 1/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
80pub(crate) const INVSQRT_A_MINUS_D: FieldElement51 = FieldElement51::from_limbs([
81    278908739862762,
82    821645201101625,
83    8113234426968,
84    1777959178193151,
85    2118520810568447,
86]);
87
88/// Precomputed value of one of the square roots of -1 (mod p)
89pub(crate) const SQRT_M1: FieldElement51 = FieldElement51::from_limbs([
90    1718705420411056,
91    234908883556509,
92    2233514472574048,
93    2117202627021982,
94    765476049583133,
95]);
96
97/// `APLUS2_OVER_FOUR` is (A+2)/4. (This is used internally within the Montgomery ladder.)
98pub(crate) const APLUS2_OVER_FOUR: FieldElement51 =
99    FieldElement51::from_limbs([121666, 0, 0, 0, 0]);
100
101/// `MONTGOMERY_A` is equal to 486662, which is a constant of the curve equation
102/// for Curve25519 in its Montgomery form. (This is used internally within the
103/// Elligator map.)
104pub(crate) const MONTGOMERY_A: FieldElement51 = FieldElement51::from_limbs([486662, 0, 0, 0, 0]);
105
106/// `MONTGOMERY_A_NEG` is equal to -486662. (This is used internally within the
107/// Elligator map.)
108pub(crate) const MONTGOMERY_A_NEG: FieldElement51 = FieldElement51::from_limbs([
109    2251799813198567,
110    2251799813685247,
111    2251799813685247,
112    2251799813685247,
113    2251799813685247,
114]);
115
116/// `L` is the order of base point, i.e. 2^252 + 27742317777372353535851937790883648493
117pub(crate) const L: Scalar52 = Scalar52([
118    0x0002631a5cf5d3ed,
119    0x000dea2f79cd6581,
120    0x000000000014def9,
121    0x0000000000000000,
122    0x0000100000000000,
123]);
124
125/// `L` * `LFACTOR` = -1 (mod 2^52)
126pub(crate) const LFACTOR: u64 = 0x51da312547e1b;
127
128/// `R` = R % L where R = 2^260
129pub(crate) const R: Scalar52 = Scalar52([
130    0x000f48bd6721e6ed,
131    0x0003bab5ac67e45a,
132    0x000fffffeb35e51b,
133    0x000fffffffffffff,
134    0x00000fffffffffff,
135]);
136
137/// `RR` = (R^2) % L where R = 2^260
138pub(crate) const RR: Scalar52 = Scalar52([
139    0x0009d265e952d13b,
140    0x000d63c715bea69f,
141    0x0005be65cb687604,
142    0x0003dceec73d217f,
143    0x000009411b7c309a,
144]);
145
146/// The Ed25519 basepoint, as an `EdwardsPoint`.
147///
148/// This is called `_POINT` to distinguish it from
149/// `ED25519_BASEPOINT_TABLE`, which should be used for scalar
150/// multiplication (it's much faster).
151pub const ED25519_BASEPOINT_POINT: EdwardsPoint = EdwardsPoint {
152    X: FieldElement51::from_limbs([
153        1738742601995546,
154        1146398526822698,
155        2070867633025821,
156        562264141797630,
157        587772402128613,
158    ]),
159    Y: FieldElement51::from_limbs([
160        1801439850948184,
161        1351079888211148,
162        450359962737049,
163        900719925474099,
164        1801439850948198,
165    ]),
166    Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
167    T: FieldElement51::from_limbs([
168        1841354044333475,
169        16398895984059,
170        755974180946558,
171        900171276175154,
172        1821297809914039,
173    ]),
174};
175
176/// The 8-torsion subgroup \\(\mathcal E \[8\]\\).
177///
178/// In the case of Curve25519, it is cyclic; the \\(i\\)-th element of
179/// the array is \\(\[i\]P\\), where \\(P\\) is a point of order \\(8\\)
180/// generating \\(\mathcal E\[8\]\\).
181///
182/// Thus \\(\mathcal E\[4\]\\) is the points indexed by `0,2,4,6`, and
183/// \\(\mathcal E\[2\]\\) is the points indexed by `0,4`.
184pub const EIGHT_TORSION: [EdwardsPoint; 8] = EIGHT_TORSION_INNER_DOC_HIDDEN;
185
186/// Inner item used to hide limb constants from cargo doc output.
187#[doc(hidden)]
188pub const EIGHT_TORSION_INNER_DOC_HIDDEN: [EdwardsPoint; 8] = [
189    EdwardsPoint {
190        X: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
191        Y: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
192        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
193        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
194    },
195    EdwardsPoint {
196        X: FieldElement51::from_limbs([
197            358744748052810,
198            1691584618240980,
199            977650209285361,
200            1429865912637724,
201            560044844278676,
202        ]),
203        Y: FieldElement51::from_limbs([
204            84926274344903,
205            473620666599931,
206            365590438845504,
207            1028470286882429,
208            2146499180330972,
209        ]),
210        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
211        T: FieldElement51::from_limbs([
212            1448326834587521,
213            1857896831960481,
214            1093722731865333,
215            1677408490711241,
216            1915505153018406,
217        ]),
218    },
219    EdwardsPoint {
220        X: FieldElement51::from_limbs([
221            533094393274173,
222            2016890930128738,
223            18285341111199,
224            134597186663265,
225            1486323764102114,
226        ]),
227        Y: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
228        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
229        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
230    },
231    EdwardsPoint {
232        X: FieldElement51::from_limbs([
233            358744748052810,
234            1691584618240980,
235            977650209285361,
236            1429865912637724,
237            560044844278676,
238        ]),
239        Y: FieldElement51::from_limbs([
240            2166873539340326,
241            1778179147085316,
242            1886209374839743,
243            1223329526802818,
244            105300633354275,
245        ]),
246        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
247        T: FieldElement51::from_limbs([
248            803472979097708,
249            393902981724766,
250            1158077081819914,
251            574391322974006,
252            336294660666841,
253        ]),
254    },
255    EdwardsPoint {
256        X: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
257        Y: FieldElement51::from_limbs([
258            2251799813685228,
259            2251799813685247,
260            2251799813685247,
261            2251799813685247,
262            2251799813685247,
263        ]),
264        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
265        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
266    },
267    EdwardsPoint {
268        X: FieldElement51::from_limbs([
269            1893055065632419,
270            560215195444267,
271            1274149604399886,
272            821933901047523,
273            1691754969406571,
274        ]),
275        Y: FieldElement51::from_limbs([
276            2166873539340326,
277            1778179147085316,
278            1886209374839743,
279            1223329526802818,
280            105300633354275,
281        ]),
282        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
283        T: FieldElement51::from_limbs([
284            1448326834587521,
285            1857896831960481,
286            1093722731865333,
287            1677408490711241,
288            1915505153018406,
289        ]),
290    },
291    EdwardsPoint {
292        X: FieldElement51::from_limbs([
293            1718705420411056,
294            234908883556509,
295            2233514472574048,
296            2117202627021982,
297            765476049583133,
298        ]),
299        Y: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
300        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
301        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
302    },
303    EdwardsPoint {
304        X: FieldElement51::from_limbs([
305            1893055065632419,
306            560215195444267,
307            1274149604399886,
308            821933901047523,
309            1691754969406571,
310        ]),
311        Y: FieldElement51::from_limbs([
312            84926274344903,
313            473620666599931,
314            365590438845504,
315            1028470286882429,
316            2146499180330972,
317        ]),
318        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
319        T: FieldElement51::from_limbs([
320            803472979097708,
321            393902981724766,
322            1158077081819914,
323            574391322974006,
324            336294660666841,
325        ]),
326    },
327];
328
329/// Table containing precomputed multiples of the Ed25519 basepoint \\(B = (x, 4/5)\\).
330#[cfg(feature = "precomputed-tables")]
331pub static ED25519_BASEPOINT_TABLE: &EdwardsBasepointTable =
332    &ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN;
333
334/// Inner constant, used to avoid filling the docs with precomputed points.
335#[doc(hidden)]
336#[cfg(feature = "precomputed-tables")]
337static ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN: EdwardsBasepointTable = EdwardsBasepointTable([
338    LookupTable([
339        AffineNielsPoint {
340            y_plus_x: FieldElement51::from_limbs([
341                3540182452943730,
342                2497478415033846,
343                2521227595762870,
344                1462984067271729,
345                2389212253076811,
346            ]),
347            y_minus_x: FieldElement51::from_limbs([
348                62697248952638,
349                204681361388450,
350                631292143396476,
351                338455783676468,
352                1213667448819585,
353            ]),
354            xy2d: FieldElement51::from_limbs([
355                301289933810280,
356                1259582250014073,
357                1422107436869536,
358                796239922652654,
359                1953934009299142,
360            ]),
361        },
362        AffineNielsPoint {
363            y_plus_x: FieldElement51::from_limbs([
364                3632771708514775,
365                790832306631235,
366                2067202295274102,
367                1995808275510000,
368                1566530869037010,
369            ]),
370            y_minus_x: FieldElement51::from_limbs([
371                463307831301544,
372                432984605774163,
373                1610641361907204,
374                750899048855000,
375                1894842303421586,
376            ]),
377            xy2d: FieldElement51::from_limbs([
378                748439484463711,
379                1033211726465151,
380                1396005112841647,
381                1611506220286469,
382                1972177495910992,
383            ]),
384        },
385        AffineNielsPoint {
386            y_plus_x: FieldElement51::from_limbs([
387                1601611775252272,
388                1720807796594148,
389                1132070835939856,
390                3512254832574799,
391                2147779492816910,
392            ]),
393            y_minus_x: FieldElement51::from_limbs([
394                316559037616741,
395                2177824224946892,
396                1459442586438991,
397                1461528397712656,
398                751590696113597,
399            ]),
400            xy2d: FieldElement51::from_limbs([
401                1850748884277385,
402                1200145853858453,
403                1068094770532492,
404                672251375690438,
405                1586055907191707,
406            ]),
407        },
408        AffineNielsPoint {
409            y_plus_x: FieldElement51::from_limbs([
410                934282339813791,
411                1846903124198670,
412                1172395437954843,
413                1007037127761661,
414                1830588347719256,
415            ]),
416            y_minus_x: FieldElement51::from_limbs([
417                1694390458783935,
418                1735906047636159,
419                705069562067493,
420                648033061693059,
421                696214010414170,
422            ]),
423            xy2d: FieldElement51::from_limbs([
424                1121406372216585,
425                192876649532226,
426                190294192191717,
427                1994165897297032,
428                2245000007398739,
429            ]),
430        },
431        AffineNielsPoint {
432            y_plus_x: FieldElement51::from_limbs([
433                769950342298400,
434                2384754244604994,
435                3095885746880802,
436                3225892188161580,
437                2977876099231263,
438            ]),
439            y_minus_x: FieldElement51::from_limbs([
440                425251763115706,
441                608463272472562,
442                442562545713235,
443                837766094556764,
444                374555092627893,
445            ]),
446            xy2d: FieldElement51::from_limbs([
447                1086255230780037,
448                274979815921559,
449                1960002765731872,
450                929474102396301,
451                1190409889297339,
452            ]),
453        },
454        AffineNielsPoint {
455            y_plus_x: FieldElement51::from_limbs([
456                1388594989461809,
457                316767091099457,
458                2646098655878230,
459                1230079486801004,
460                1440737038838979,
461            ]),
462            y_minus_x: FieldElement51::from_limbs([
463                7380825640100,
464                146210432690483,
465                304903576448906,
466                1198869323871120,
467                997689833219095,
468            ]),
469            xy2d: FieldElement51::from_limbs([
470                1181317918772081,
471                114573476638901,
472                262805072233344,
473                265712217171332,
474                294181933805782,
475            ]),
476        },
477        AffineNielsPoint {
478            y_plus_x: FieldElement51::from_limbs([
479                2916800678241215,
480                2065379846933858,
481                2622030924071124,
482                2602788184473875,
483                1233371373142984,
484            ]),
485            y_minus_x: FieldElement51::from_limbs([
486                2019367628972465,
487                676711900706637,
488                110710997811333,
489                1108646842542025,
490                517791959672113,
491            ]),
492            xy2d: FieldElement51::from_limbs([
493                965130719900578,
494                247011430587952,
495                526356006571389,
496                91986625355052,
497                2157223321444601,
498            ]),
499        },
500        AffineNielsPoint {
501            y_plus_x: FieldElement51::from_limbs([
502                4320419353804412,
503                4218074731744053,
504                957728544705548,
505                729906502578991,
506                2411634706750414,
507            ]),
508            y_minus_x: FieldElement51::from_limbs([
509                2073601412052185,
510                31021124762708,
511                264500969797082,
512                248034690651703,
513                1030252227928288,
514            ]),
515            xy2d: FieldElement51::from_limbs([
516                551790716293402,
517                1989538725166328,
518                801169423371717,
519                2052451893578887,
520                678432056995012,
521            ]),
522        },
523    ]),
524    LookupTable([
525        AffineNielsPoint {
526            y_plus_x: FieldElement51::from_limbs([
527                1368953770187805,
528                3042147450398169,
529                2689308289352409,
530                2142576377050579,
531                1932081720066286,
532            ]),
533            y_minus_x: FieldElement51::from_limbs([
534                953638594433374,
535                1092333936795051,
536                1419774766716690,
537                805677984380077,
538                859228993502513,
539            ]),
540            xy2d: FieldElement51::from_limbs([
541                1200766035879111,
542                20142053207432,
543                1465634435977050,
544                1645256912097844,
545                295121984874596,
546            ]),
547        },
548        AffineNielsPoint {
549            y_plus_x: FieldElement51::from_limbs([
550                1735718747031538,
551                1248237894295956,
552                1204753118328107,
553                976066523550493,
554                2317743583219840,
555            ]),
556            y_minus_x: FieldElement51::from_limbs([
557                1060098822528990,
558                1586825862073490,
559                212301317240126,
560                1975302711403555,
561                666724059764335,
562            ]),
563            xy2d: FieldElement51::from_limbs([
564                1091990273418756,
565                1572899409348578,
566                80968014455247,
567                306009358661350,
568                1520450739132526,
569            ]),
570        },
571        AffineNielsPoint {
572            y_plus_x: FieldElement51::from_limbs([
573                3732317023121341,
574                1511153322193951,
575                3496143672676420,
576                2556587964178488,
577                2620936670181690,
578            ]),
579            y_minus_x: FieldElement51::from_limbs([
580                2151330273626164,
581                762045184746182,
582                1688074332551515,
583                823046109005759,
584                907602769079491,
585            ]),
586            xy2d: FieldElement51::from_limbs([
587                2047386910586836,
588                168470092900250,
589                1552838872594810,
590                340951180073789,
591                360819374702533,
592            ]),
593        },
594        AffineNielsPoint {
595            y_plus_x: FieldElement51::from_limbs([
596                1982622644432037,
597                2014393600336956,
598                2380709022489462,
599                3869592437614438,
600                2357094095599062,
601            ]),
602            y_minus_x: FieldElement51::from_limbs([
603                980234343912898,
604                1712256739246056,
605                588935272190264,
606                204298813091998,
607                841798321043288,
608            ]),
609            xy2d: FieldElement51::from_limbs([
610                197561292938973,
611                454817274782871,
612                1963754960082318,
613                2113372252160468,
614                971377527342673,
615            ]),
616        },
617        AffineNielsPoint {
618            y_plus_x: FieldElement51::from_limbs([
619                2416499262514576,
620                2254927265442919,
621                3451304785234000,
622                1766155447043651,
623                1899238924683527,
624            ]),
625            y_minus_x: FieldElement51::from_limbs([
626                732262946680281,
627                1674412764227063,
628                2182456405662809,
629                1350894754474250,
630                558458873295247,
631            ]),
632            xy2d: FieldElement51::from_limbs([
633                2103305098582922,
634                1960809151316468,
635                715134605001343,
636                1454892949167181,
637                40827143824949,
638            ]),
639        },
640        AffineNielsPoint {
641            y_plus_x: FieldElement51::from_limbs([
642                1239289043050193,
643                1744654158124578,
644                758702410031698,
645                4048562808759936,
646                2253402870349013,
647            ]),
648            y_minus_x: FieldElement51::from_limbs([
649                2232056027107988,
650                987343914584615,
651                2115594492994461,
652                1819598072792159,
653                1119305654014850,
654            ]),
655            xy2d: FieldElement51::from_limbs([
656                320153677847348,
657                939613871605645,
658                641883205761567,
659                1930009789398224,
660                329165806634126,
661            ]),
662        },
663        AffineNielsPoint {
664            y_plus_x: FieldElement51::from_limbs([
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6036                3119119231364171,
6037                2872271776627789,
6038                2477832016990963,
6039                2593801257642876,
6040                1761675818237335,
6041            ]),
6042            y_minus_x: FieldElement51::from_limbs([
6043                1295072362439987,
6044                931227904689414,
6045                1355731432641687,
6046                922235735834035,
6047                892227229410209,
6048            ]),
6049            xy2d: FieldElement51::from_limbs([
6050                1680989767906154,
6051                535362787031440,
6052                2136691276706570,
6053                1942228485381244,
6054                1267350086882274,
6055            ]),
6056        },
6057        AffineNielsPoint {
6058            y_plus_x: FieldElement51::from_limbs([
6059                2617818047455756,
6060                2684460443440843,
6061                2378209521329782,
6062                1973842949591661,
6063                2897427157127624,
6064            ]),
6065            y_minus_x: FieldElement51::from_limbs([
6066                535509430575217,
6067                546885533737322,
6068                1524675609547799,
6069                2138095752851703,
6070                1260738089896827,
6071            ]),
6072            xy2d: FieldElement51::from_limbs([
6073                1159906385590467,
6074                2198530004321610,
6075                714559485023225,
6076                81880727882151,
6077                1484020820037082,
6078            ]),
6079        },
6080        AffineNielsPoint {
6081            y_plus_x: FieldElement51::from_limbs([
6082                1377485731340769,
6083                2046328105512000,
6084                1802058637158797,
6085                2313945950453421,
6086                1356993908853900,
6087            ]),
6088            y_minus_x: FieldElement51::from_limbs([
6089                2013612215646735,
6090                1830770575920375,
6091                536135310219832,
6092                609272325580394,
6093                270684344495013,
6094            ]),
6095            xy2d: FieldElement51::from_limbs([
6096                1237542585982777,
6097                2228682050256790,
6098                1385281931622824,
6099                593183794882890,
6100                493654978552689,
6101            ]),
6102        },
6103    ]),
6104    LookupTable([
6105        AffineNielsPoint {
6106            y_plus_x: FieldElement51::from_limbs([
6107                2299141301692989,
6108                1891414891220256,
6109                983894663308928,
6110                2427961581972066,
6111                3378060928864955,
6112            ]),
6113            y_minus_x: FieldElement51::from_limbs([
6114                1694030170963455,
6115                502038567066200,
6116                1691160065225467,
6117                949628319562187,
6118                275110186693066,
6119            ]),
6120            xy2d: FieldElement51::from_limbs([
6121                1124515748676336,
6122                1661673816593408,
6123                1499640319059718,
6124                1584929449166988,
6125                558148594103306,
6126            ]),
6127        },
6128        AffineNielsPoint {
6129            y_plus_x: FieldElement51::from_limbs([
6130                1784525599998356,
6131                1619698033617383,
6132                2097300287550715,
6133                2510065271789004,
6134                1905684794832757,
6135            ]),
6136            y_minus_x: FieldElement51::from_limbs([
6137                1288941072872766,
6138                931787902039402,
6139                190731008859042,
6140                2006859954667190,
6141                1005931482221702,
6142            ]),
6143            xy2d: FieldElement51::from_limbs([
6144                1465551264822703,
6145                152905080555927,
6146                680334307368453,
6147                173227184634745,
6148                666407097159852,
6149            ]),
6150        },
6151        AffineNielsPoint {
6152            y_plus_x: FieldElement51::from_limbs([
6153                2111017076203943,
6154                3630560299479595,
6155                1248583954016455,
6156                3604089008549670,
6157                1895180776543895,
6158            ]),
6159            y_minus_x: FieldElement51::from_limbs([
6160                171348223915638,
6161                662766099800389,
6162                462338943760497,
6163                466917763340314,
6164                656911292869115,
6165            ]),
6166            xy2d: FieldElement51::from_limbs([
6167                488623681976577,
6168                866497561541722,
6169                1708105560937768,
6170                1673781214218839,
6171                1506146329818807,
6172            ]),
6173        },
6174        AffineNielsPoint {
6175            y_plus_x: FieldElement51::from_limbs([
6176                2412225278142205,
6177                950394373239688,
6178                2682296937026182,
6179                711676555398831,
6180                320964687779005,
6181            ]),
6182            y_minus_x: FieldElement51::from_limbs([
6183                988979367990485,
6184                1359729327576302,
6185                1301834257246029,
6186                294141160829308,
6187                29348272277475,
6188            ]),
6189            xy2d: FieldElement51::from_limbs([
6190                1434382743317910,
6191                100082049942065,
6192                221102347892623,
6193                186982837860588,
6194                1305765053501834,
6195            ]),
6196        },
6197        AffineNielsPoint {
6198            y_plus_x: FieldElement51::from_limbs([
6199                2205916462268190,
6200                2751663643476068,
6201                961960554686615,
6202                2409862576442233,
6203                1841471168298304,
6204            ]),
6205            y_minus_x: FieldElement51::from_limbs([
6206                1191737341426592,
6207                1847042034978363,
6208                1382213545049056,
6209                1039952395710448,
6210                788812858896859,
6211            ]),
6212            xy2d: FieldElement51::from_limbs([
6213                1346965964571152,
6214                1291881610839830,
6215                2142916164336056,
6216                786821641205979,
6217                1571709146321039,
6218            ]),
6219        },
6220        AffineNielsPoint {
6221            y_plus_x: FieldElement51::from_limbs([
6222                787164375951248,
6223                2454669019058437,
6224                3608390234717387,
6225                1431233331032509,
6226                786341368775957,
6227            ]),
6228            y_minus_x: FieldElement51::from_limbs([
6229                492448143532951,
6230                304105152670757,
6231                1761767168301056,
6232                233782684697790,
6233                1981295323106089,
6234            ]),
6235            xy2d: FieldElement51::from_limbs([
6236                665807507761866,
6237                1343384868355425,
6238                895831046139653,
6239                439338948736892,
6240                1986828765695105,
6241            ]),
6242        },
6243        AffineNielsPoint {
6244            y_plus_x: FieldElement51::from_limbs([
6245                3007896024559801,
6246                1721699973539148,
6247                2510565115413133,
6248                1390588532210644,
6249                1212530909934781,
6250            ]),
6251            y_minus_x: FieldElement51::from_limbs([
6252                852891097972275,
6253                1816988871354562,
6254                1543772755726524,
6255                1174710635522444,
6256                202129090724628,
6257            ]),
6258            xy2d: FieldElement51::from_limbs([
6259                1205281565824323,
6260                22430498399418,
6261                992947814485516,
6262                1392458699738672,
6263                688441466734558,
6264            ]),
6265        },
6266        AffineNielsPoint {
6267            y_plus_x: FieldElement51::from_limbs([
6268                3302427242100220,
6269                1955849529137134,
6270                2171162376368357,
6271                2343545681983462,
6272                447733118757825,
6273            ]),
6274            y_minus_x: FieldElement51::from_limbs([
6275                1287181461435438,
6276                622722465530711,
6277                880952150571872,
6278                741035693459198,
6279                311565274989772,
6280            ]),
6281            xy2d: FieldElement51::from_limbs([
6282                1003649078149734,
6283                545233927396469,
6284                1849786171789880,
6285                1318943684880434,
6286                280345687170552,
6287            ]),
6288        },
6289    ]),
6290]);
6291
6292/// Odd multiples of the basepoint `[B, 3B, 5B, 7B, 9B, 11B, 13B, 15B, ..., 127B]`.
6293#[cfg(feature = "precomputed-tables")]
6294#[allow(dead_code)]
6295pub(crate) const AFFINE_ODD_MULTIPLES_OF_BASEPOINT: NafLookupTable8<AffineNielsPoint> =
6296    NafLookupTable8([
6297        AffineNielsPoint {
6298            y_plus_x: FieldElement51::from_limbs([
6299                3540182452943730,
6300                2497478415033846,
6301                2521227595762870,
6302                1462984067271729,
6303                2389212253076811,
6304            ]),
6305            y_minus_x: FieldElement51::from_limbs([
6306                62697248952638,
6307                204681361388450,
6308                631292143396476,
6309                338455783676468,
6310                1213667448819585,
6311            ]),
6312            xy2d: FieldElement51::from_limbs([
6313                301289933810280,
6314                1259582250014073,
6315                1422107436869536,
6316                796239922652654,
6317                1953934009299142,
6318            ]),
6319        },
6320        AffineNielsPoint {
6321            y_plus_x: FieldElement51::from_limbs([
6322                1601611775252272,
6323                1720807796594148,
6324                1132070835939856,
6325                3512254832574799,
6326                2147779492816910,
6327            ]),
6328            y_minus_x: FieldElement51::from_limbs([
6329                316559037616741,
6330                2177824224946892,
6331                1459442586438991,
6332                1461528397712656,
6333                751590696113597,
6334            ]),
6335            xy2d: FieldElement51::from_limbs([
6336                1850748884277385,
6337                1200145853858453,
6338                1068094770532492,
6339                672251375690438,
6340                1586055907191707,
6341            ]),
6342        },
6343        AffineNielsPoint {
6344            y_plus_x: FieldElement51::from_limbs([
6345                769950342298400,
6346                2384754244604994,
6347                3095885746880802,
6348                3225892188161580,
6349                2977876099231263,
6350            ]),
6351            y_minus_x: FieldElement51::from_limbs([
6352                425251763115706,
6353                608463272472562,
6354                442562545713235,
6355                837766094556764,
6356                374555092627893,
6357            ]),
6358            xy2d: FieldElement51::from_limbs([
6359                1086255230780037,
6360                274979815921559,
6361                1960002765731872,
6362                929474102396301,
6363                1190409889297339,
6364            ]),
6365        },
6366        AffineNielsPoint {
6367            y_plus_x: FieldElement51::from_limbs([
6368                2916800678241215,
6369                2065379846933858,
6370                2622030924071124,
6371                2602788184473875,
6372                1233371373142984,
6373            ]),
6374            y_minus_x: FieldElement51::from_limbs([
6375                2019367628972465,
6376                676711900706637,
6377                110710997811333,
6378                1108646842542025,
6379                517791959672113,
6380            ]),
6381            xy2d: FieldElement51::from_limbs([
6382                965130719900578,
6383                247011430587952,
6384                526356006571389,
6385                91986625355052,
6386                2157223321444601,
6387            ]),
6388        },
6389        AffineNielsPoint {
6390            y_plus_x: FieldElement51::from_limbs([
6391                1802695059464988,
6392                1664899123557221,
6393                2845359304426105,
6394                2160434469266658,
6395                3179370264440279,
6396            ]),
6397            y_minus_x: FieldElement51::from_limbs([
6398                1725674970513508,
6399                1933645953859181,
6400                1542344539275782,
6401                1767788773573747,
6402                1297447965928905,
6403            ]),
6404            xy2d: FieldElement51::from_limbs([
6405                1381809363726107,
6406                1430341051343062,
6407                2061843536018959,
6408                1551778050872521,
6409                2036394857967624,
6410            ]),
6411        },
6412        AffineNielsPoint {
6413            y_plus_x: FieldElement51::from_limbs([
6414                4222693909998302,
6415                2779866139518454,
6416                1619374932191226,
6417                2207306624415883,
6418                1169170329061080,
6419            ]),
6420            y_minus_x: FieldElement51::from_limbs([
6421                2070390218572616,
6422                1458919061857835,
6423                624171843017421,
6424                1055332792707765,
6425                433987520732508,
6426            ]),
6427            xy2d: FieldElement51::from_limbs([
6428                893653801273833,
6429                1168026499324677,
6430                1242553501121234,
6431                1306366254304474,
6432                1086752658510815,
6433            ]),
6434        },
6435        AffineNielsPoint {
6436            y_plus_x: FieldElement51::from_limbs([
6437                2465253816303469,
6438                3191571337672685,
6439                1159882208056013,
6440                2569188183312765,
6441                621213314200686,
6442            ]),
6443            y_minus_x: FieldElement51::from_limbs([
6444                1971678598905747,
6445                338026507889165,
6446                762398079972271,
6447                655096486107477,
6448                42299032696322,
6449            ]),
6450            xy2d: FieldElement51::from_limbs([
6451                177130678690680,
6452                1754759263300204,
6453                1864311296286618,
6454                1180675631479880,
6455                1292726903152791,
6456            ]),
6457        },
6458        AffineNielsPoint {
6459            y_plus_x: FieldElement51::from_limbs([
6460                1913163449625248,
6461                2712579013977241,
6462                2193883288642313,
6463                1008900146920800,
6464                1721983679009502,
6465            ]),
6466            y_minus_x: FieldElement51::from_limbs([
6467                1070401523076875,
6468                1272492007800961,
6469                1910153608563310,
6470                2075579521696771,
6471                1191169788841221,
6472            ]),
6473            xy2d: FieldElement51::from_limbs([
6474                692896803108118,
6475                500174642072499,
6476                2068223309439677,
6477                1162190621851337,
6478                1426986007309901,
6479            ]),
6480        },
6481        AffineNielsPoint {
6482            y_plus_x: FieldElement51::from_limbs([
6483                1819621230288238,
6484                2735700366193240,
6485                1755134670739586,
6486                3080648199451191,
6487                4172807995775876,
6488            ]),
6489            y_minus_x: FieldElement51::from_limbs([
6490                992069868904071,
6491                799011518185730,
6492                1777586403832768,
6493                1134820506145684,
6494                1999461475558530,
6495            ]),
6496            xy2d: FieldElement51::from_limbs([
6497                425204543703124,
6498                2040469794090382,
6499                1651690622153809,
6500                1500530168597569,
6501                1253908377065966,
6502            ]),
6503        },
6504        AffineNielsPoint {
6505            y_plus_x: FieldElement51::from_limbs([
6506                2105824306960939,
6507                1387520302709358,
6508                3633176580451016,
6509                2211816663841753,
6510                1629085891776489,
6511            ]),
6512            y_minus_x: FieldElement51::from_limbs([
6513                1485201376284999,
6514                1022406647424656,
6515                504181009209019,
6516                962621520820995,
6517                590876713147230,
6518            ]),
6519            xy2d: FieldElement51::from_limbs([
6520                265873406365287,
6521                1192742653492898,
6522                88553098803050,
6523                525037770869640,
6524                1266933811251234,
6525            ]),
6526        },
6527        AffineNielsPoint {
6528            y_plus_x: FieldElement51::from_limbs([
6529                3552316659826612,
6530                1254279525791875,
6531                1609927932077699,
6532                3578654071679972,
6533                3750681296069893,
6534            ]),
6535            y_minus_x: FieldElement51::from_limbs([
6536                37186803519861,
6537                1404297334376301,
6538                578519728836650,
6539                1740727951192592,
6540                2095534282477028,
6541            ]),
6542            xy2d: FieldElement51::from_limbs([
6543                833234263154399,
6544                2023862470013762,
6545                1854137933982069,
6546                853924318090959,
6547                1589812702805850,
6548            ]),
6549        },
6550        AffineNielsPoint {
6551            y_plus_x: FieldElement51::from_limbs([
6552                3679150557957763,
6553                1319179453661745,
6554                497496853611112,
6555                2665464286942351,
6556                1208137952365560,
6557            ]),
6558            y_minus_x: FieldElement51::from_limbs([
6559                1654513078530905,
6560                907489875842908,
6561                126098711296368,
6562                1726320004173677,
6563                28269495058173,
6564            ]),
6565            xy2d: FieldElement51::from_limbs([
6566                114436686957443,
6567                532739313025996,
6568                115428841215897,
6569                2191499400074366,
6570                370280402676434,
6571            ]),
6572        },
6573        AffineNielsPoint {
6574            y_plus_x: FieldElement51::from_limbs([
6575                1111146849833253,
6576                2016430049079759,
6577                1860522747477948,
6578                3537164738290194,
6579                4137142824844184,
6580            ]),
6581            y_minus_x: FieldElement51::from_limbs([
6582                429069864577128,
6583                975327637149449,
6584                237881983565075,
6585                1654761232378630,
6586                2122527599091807,
6587            ]),
6588            xy2d: FieldElement51::from_limbs([
6589                2093793463548278,
6590                754827233241879,
6591                1420389751719629,
6592                1829952782588138,
6593                2011865756773717,
6594            ]),
6595        },
6596        AffineNielsPoint {
6597            y_plus_x: FieldElement51::from_limbs([
6598                676293365438898,
6599                2850296017886344,
6600                1205350322490195,
6601                2763699392265669,
6602                2133931188538142,
6603            ]),
6604            y_minus_x: FieldElement51::from_limbs([
6605                48340340349120,
6606                1299261101494832,
6607                1137329686775218,
6608                1534848106674340,
6609                1351662218216799,
6610            ]),
6611            xy2d: FieldElement51::from_limbs([
6612                1904520614137939,
6613                1590301001714014,
6614                215781420985270,
6615                2043534301034629,
6616                1970888949300424,
6617            ]),
6618        },
6619        AffineNielsPoint {
6620            y_plus_x: FieldElement51::from_limbs([
6621                2365217962409710,
6622                2061307169694064,
6623                1887478590157603,
6624                2169639621284316,
6625                2373810867477200,
6626            ]),
6627            y_minus_x: FieldElement51::from_limbs([
6628                1020052624656948,
6629                1260412094216707,
6630                366721640607121,
6631                585331442306596,
6632                345876457758061,
6633            ]),
6634            xy2d: FieldElement51::from_limbs([
6635                975390299880933,
6636                1066555195234642,
6637                12651997758352,
6638                1184252205433068,
6639                1058378155074223,
6640            ]),
6641        },
6642        AffineNielsPoint {
6643            y_plus_x: FieldElement51::from_limbs([
6644                1431537716602643,
6645                2024827957433813,
6646                3746434518400495,
6647                1087794891033550,
6648                2156817571680455,
6649            ]),
6650            y_minus_x: FieldElement51::from_limbs([
6651                929288033346881,
6652                255179964546973,
6653                711057989588035,
6654                208899572612840,
6655                185348357387383,
6656            ]),
6657            xy2d: FieldElement51::from_limbs([
6658                823689746424808,
6659                47266130989546,
6660                209403309368097,
6661                1100966895202707,
6662                710792075292719,
6663            ]),
6664        },
6665        AffineNielsPoint {
6666            y_plus_x: FieldElement51::from_limbs([
6667                2311213117823762,
6668                3296668540922318,
6669                2004276520649823,
6670                1861500579441125,
6671                3148029033359833,
6672            ]),
6673            y_minus_x: FieldElement51::from_limbs([
6674                1563693677475261,
6675                1843782073741194,
6676                1950700654453170,
6677                911540858113949,
6678                2085151496302359,
6679            ]),
6680            xy2d: FieldElement51::from_limbs([
6681                1427880892005482,
6682                106216431121745,
6683                42608394782284,
6684                1217295886989793,
6685                1514235272796882,
6686            ]),
6687        },
6688        AffineNielsPoint {
6689            y_plus_x: FieldElement51::from_limbs([
6690                3544335535746750,
6691                2367994491347456,
6692                2567261456502612,
6693                1854058085060971,
6694                2263545563461076,
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curve25519_dalek/backend/serial/u64/constants.rs

curve25519_dalek/backend/serial/u64/
constants.rs
