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/// sqrt(-486664)
35#[cfg(feature = "digest")]
36pub(crate) const ED25519_SQRTAM2: FieldElement51 = FieldElement51::from_limbs([
37    1693982333959686,
38    608509411481997,
39    2235573344831311,
40    947681270984193,
41    266558006233600,
42]);
43
44/// Edwards `d` value, equal to `-121665/121666 mod p`.
45pub(crate) const EDWARDS_D: FieldElement51 = FieldElement51::from_limbs([
46    929955233495203,
47    466365720129213,
48    1662059464998953,
49    2033849074728123,
50    1442794654840575,
51]);
52
53/// Edwards `2*d` value, equal to `2*(-121665/121666) mod p`.
54pub(crate) const EDWARDS_D2: FieldElement51 = FieldElement51::from_limbs([
55    1859910466990425,
56    932731440258426,
57    1072319116312658,
58    1815898335770999,
59    633789495995903,
60]);
61
62/// One minus edwards `d` value squared, equal to `(1 - (-121665/121666) mod p) pow 2`
63pub(crate) const ONE_MINUS_EDWARDS_D_SQUARED: FieldElement51 = FieldElement51::from_limbs([
64    1136626929484150,
65    1998550399581263,
66    496427632559748,
67    118527312129759,
68    45110755273534,
69]);
70
71/// Edwards `d` value minus one squared, equal to `(((-121665/121666) mod p) - 1) pow 2`
72pub(crate) const EDWARDS_D_MINUS_ONE_SQUARED: FieldElement51 = FieldElement51::from_limbs([
73    1507062230895904,
74    1572317787530805,
75    683053064812840,
76    317374165784489,
77    1572899562415810,
78]);
79
80/// `= sqrt(a*d - 1)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
81pub(crate) const SQRT_AD_MINUS_ONE: FieldElement51 = FieldElement51::from_limbs([
82    2241493124984347,
83    425987919032274,
84    2207028919301688,
85    1220490630685848,
86    974799131293748,
87]);
88
89/// `= 1/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
90pub(crate) const INVSQRT_A_MINUS_D: FieldElement51 = FieldElement51::from_limbs([
91    278908739862762,
92    821645201101625,
93    8113234426968,
94    1777959178193151,
95    2118520810568447,
96]);
97
98/// Precomputed value of one of the square roots of -1 (mod p)
99pub(crate) const SQRT_M1: FieldElement51 = FieldElement51::from_limbs([
100    1718705420411056,
101    234908883556509,
102    2233514472574048,
103    2117202627021982,
104    765476049583133,
105]);
106
107/// `APLUS2_OVER_FOUR` is (A+2)/4. (This is used internally within the Montgomery ladder.)
108pub(crate) const APLUS2_OVER_FOUR: FieldElement51 =
109    FieldElement51::from_limbs([121666, 0, 0, 0, 0]);
110
111/// `MONTGOMERY_A` is equal to 486662, which is a constant of the curve equation
112/// for Curve25519 in its Montgomery form. (This is used internally within the
113/// Elligator map.)
114pub(crate) const MONTGOMERY_A: FieldElement51 = FieldElement51::from_limbs([486662, 0, 0, 0, 0]);
115
116/// `MONTGOMERY_A_NEG` is equal to -486662. (This is used internally within the
117/// Elligator map.)
118pub(crate) const MONTGOMERY_A_NEG: FieldElement51 = FieldElement51::from_limbs([
119    2251799813198567,
120    2251799813685247,
121    2251799813685247,
122    2251799813685247,
123    2251799813685247,
124]);
125
126/// `L` is the order of base point, i.e. 2^252 + 27742317777372353535851937790883648493
127pub(crate) const L: Scalar52 = Scalar52([
128    0x0002631a5cf5d3ed,
129    0x000dea2f79cd6581,
130    0x000000000014def9,
131    0x0000000000000000,
132    0x0000100000000000,
133]);
134
135/// `L` * `LFACTOR` = -1 (mod 2^52)
136pub(crate) const LFACTOR: u64 = 0x51da312547e1b;
137
138/// `R` = R % L where R = 2^260
139pub(crate) const R: Scalar52 = Scalar52([
140    0x000f48bd6721e6ed,
141    0x0003bab5ac67e45a,
142    0x000fffffeb35e51b,
143    0x000fffffffffffff,
144    0x00000fffffffffff,
145]);
146
147/// `RR` = (R^2) % L where R = 2^260
148pub(crate) const RR: Scalar52 = Scalar52([
149    0x0009d265e952d13b,
150    0x000d63c715bea69f,
151    0x0005be65cb687604,
152    0x0003dceec73d217f,
153    0x000009411b7c309a,
154]);
155
156/// The Ed25519 basepoint, as an `EdwardsPoint`.
157///
158/// This is called `_POINT` to distinguish it from
159/// `ED25519_BASEPOINT_TABLE`, which should be used for scalar
160/// multiplication (it's much faster).
161pub const ED25519_BASEPOINT_POINT: EdwardsPoint = EdwardsPoint {
162    X: FieldElement51::from_limbs([
163        1738742601995546,
164        1146398526822698,
165        2070867633025821,
166        562264141797630,
167        587772402128613,
168    ]),
169    Y: FieldElement51::from_limbs([
170        1801439850948184,
171        1351079888211148,
172        450359962737049,
173        900719925474099,
174        1801439850948198,
175    ]),
176    Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
177    T: FieldElement51::from_limbs([
178        1841354044333475,
179        16398895984059,
180        755974180946558,
181        900171276175154,
182        1821297809914039,
183    ]),
184};
185
186/// The 8-torsion subgroup \\(\mathcal E \[8\]\\).
187///
188/// In the case of Curve25519, it is cyclic; the \\(i\\)-th element of
189/// the array is \\(\[i\]P\\), where \\(P\\) is a point of order \\(8\\)
190/// generating \\(\mathcal E\[8\]\\).
191///
192/// Thus \\(\mathcal E\[4\]\\) is the points indexed by `0,2,4,6`, and
193/// \\(\mathcal E\[2\]\\) is the points indexed by `0,4`.
194pub const EIGHT_TORSION: [EdwardsPoint; 8] = EIGHT_TORSION_INNER_DOC_HIDDEN;
195
196/// Inner item used to hide limb constants from cargo doc output.
197#[doc(hidden)]
198pub const EIGHT_TORSION_INNER_DOC_HIDDEN: [EdwardsPoint; 8] = [
199    EdwardsPoint {
200        X: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
201        Y: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
202        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
203        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
204    },
205    EdwardsPoint {
206        X: FieldElement51::from_limbs([
207            358744748052810,
208            1691584618240980,
209            977650209285361,
210            1429865912637724,
211            560044844278676,
212        ]),
213        Y: FieldElement51::from_limbs([
214            84926274344903,
215            473620666599931,
216            365590438845504,
217            1028470286882429,
218            2146499180330972,
219        ]),
220        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
221        T: FieldElement51::from_limbs([
222            1448326834587521,
223            1857896831960481,
224            1093722731865333,
225            1677408490711241,
226            1915505153018406,
227        ]),
228    },
229    EdwardsPoint {
230        X: FieldElement51::from_limbs([
231            533094393274173,
232            2016890930128738,
233            18285341111199,
234            134597186663265,
235            1486323764102114,
236        ]),
237        Y: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
238        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
239        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
240    },
241    EdwardsPoint {
242        X: FieldElement51::from_limbs([
243            358744748052810,
244            1691584618240980,
245            977650209285361,
246            1429865912637724,
247            560044844278676,
248        ]),
249        Y: FieldElement51::from_limbs([
250            2166873539340326,
251            1778179147085316,
252            1886209374839743,
253            1223329526802818,
254            105300633354275,
255        ]),
256        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
257        T: FieldElement51::from_limbs([
258            803472979097708,
259            393902981724766,
260            1158077081819914,
261            574391322974006,
262            336294660666841,
263        ]),
264    },
265    EdwardsPoint {
266        X: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
267        Y: FieldElement51::from_limbs([
268            2251799813685228,
269            2251799813685247,
270            2251799813685247,
271            2251799813685247,
272            2251799813685247,
273        ]),
274        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
275        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
276    },
277    EdwardsPoint {
278        X: FieldElement51::from_limbs([
279            1893055065632419,
280            560215195444267,
281            1274149604399886,
282            821933901047523,
283            1691754969406571,
284        ]),
285        Y: FieldElement51::from_limbs([
286            2166873539340326,
287            1778179147085316,
288            1886209374839743,
289            1223329526802818,
290            105300633354275,
291        ]),
292        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
293        T: FieldElement51::from_limbs([
294            1448326834587521,
295            1857896831960481,
296            1093722731865333,
297            1677408490711241,
298            1915505153018406,
299        ]),
300    },
301    EdwardsPoint {
302        X: FieldElement51::from_limbs([
303            1718705420411056,
304            234908883556509,
305            2233514472574048,
306            2117202627021982,
307            765476049583133,
308        ]),
309        Y: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
310        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
311        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
312    },
313    EdwardsPoint {
314        X: FieldElement51::from_limbs([
315            1893055065632419,
316            560215195444267,
317            1274149604399886,
318            821933901047523,
319            1691754969406571,
320        ]),
321        Y: FieldElement51::from_limbs([
322            84926274344903,
323            473620666599931,
324            365590438845504,
325            1028470286882429,
326            2146499180330972,
327        ]),
328        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
329        T: FieldElement51::from_limbs([
330            803472979097708,
331            393902981724766,
332            1158077081819914,
333            574391322974006,
334            336294660666841,
335        ]),
336    },
337];
338
339/// Table containing precomputed multiples of the Ed25519 basepoint \\(B = (x, 4/5)\\).
340#[cfg(feature = "precomputed-tables")]
341pub static ED25519_BASEPOINT_TABLE: &EdwardsBasepointTable =
342    &ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN;
343
344/// Inner constant, used to avoid filling the docs with precomputed points.
345#[doc(hidden)]
346#[cfg(feature = "precomputed-tables")]
347static ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN: EdwardsBasepointTable = EdwardsBasepointTable([
348    LookupTable([
349        AffineNielsPoint {
350            y_plus_x: FieldElement51::from_limbs([
351                3540182452943730,
352                2497478415033846,
353                2521227595762870,
354                1462984067271729,
355                2389212253076811,
356            ]),
357            y_minus_x: FieldElement51::from_limbs([
358                62697248952638,
359                204681361388450,
360                631292143396476,
361                338455783676468,
362                1213667448819585,
363            ]),
364            xy2d: FieldElement51::from_limbs([
365                301289933810280,
366                1259582250014073,
367                1422107436869536,
368                796239922652654,
369                1953934009299142,
370            ]),
371        },
372        AffineNielsPoint {
373            y_plus_x: FieldElement51::from_limbs([
374                3632771708514775,
375                790832306631235,
376                2067202295274102,
377                1995808275510000,
378                1566530869037010,
379            ]),
380            y_minus_x: FieldElement51::from_limbs([
381                463307831301544,
382                432984605774163,
383                1610641361907204,
384                750899048855000,
385                1894842303421586,
386            ]),
387            xy2d: FieldElement51::from_limbs([
388                748439484463711,
389                1033211726465151,
390                1396005112841647,
391                1611506220286469,
392                1972177495910992,
393            ]),
394        },
395        AffineNielsPoint {
396            y_plus_x: FieldElement51::from_limbs([
397                1601611775252272,
398                1720807796594148,
399                1132070835939856,
400                3512254832574799,
401                2147779492816910,
402            ]),
403            y_minus_x: FieldElement51::from_limbs([
404                316559037616741,
405                2177824224946892,
406                1459442586438991,
407                1461528397712656,
408                751590696113597,
409            ]),
410            xy2d: FieldElement51::from_limbs([
411                1850748884277385,
412                1200145853858453,
413                1068094770532492,
414                672251375690438,
415                1586055907191707,
416            ]),
417        },
418        AffineNielsPoint {
419            y_plus_x: FieldElement51::from_limbs([
420                934282339813791,
421                1846903124198670,
422                1172395437954843,
423                1007037127761661,
424                1830588347719256,
425            ]),
426            y_minus_x: FieldElement51::from_limbs([
427                1694390458783935,
428                1735906047636159,
429                705069562067493,
430                648033061693059,
431                696214010414170,
432            ]),
433            xy2d: FieldElement51::from_limbs([
434                1121406372216585,
435                192876649532226,
436                190294192191717,
437                1994165897297032,
438                2245000007398739,
439            ]),
440        },
441        AffineNielsPoint {
442            y_plus_x: FieldElement51::from_limbs([
443                769950342298400,
444                2384754244604994,
445                3095885746880802,
446                3225892188161580,
447                2977876099231263,
448            ]),
449            y_minus_x: FieldElement51::from_limbs([
450                425251763115706,
451                608463272472562,
452                442562545713235,
453                837766094556764,
454                374555092627893,
455            ]),
456            xy2d: FieldElement51::from_limbs([
457                1086255230780037,
458                274979815921559,
459                1960002765731872,
460                929474102396301,
461                1190409889297339,
462            ]),
463        },
464        AffineNielsPoint {
465            y_plus_x: FieldElement51::from_limbs([
466                1388594989461809,
467                316767091099457,
468                2646098655878230,
469                1230079486801004,
470                1440737038838979,
471            ]),
472            y_minus_x: FieldElement51::from_limbs([
473                7380825640100,
474                146210432690483,
475                304903576448906,
476                1198869323871120,
477                997689833219095,
478            ]),
479            xy2d: FieldElement51::from_limbs([
480                1181317918772081,
481                114573476638901,
482                262805072233344,
483                265712217171332,
484                294181933805782,
485            ]),
486        },
487        AffineNielsPoint {
488            y_plus_x: FieldElement51::from_limbs([
489                2916800678241215,
490                2065379846933858,
491                2622030924071124,
492                2602788184473875,
493                1233371373142984,
494            ]),
495            y_minus_x: FieldElement51::from_limbs([
496                2019367628972465,
497                676711900706637,
498                110710997811333,
499                1108646842542025,
500                517791959672113,
501            ]),
502            xy2d: FieldElement51::from_limbs([
503                965130719900578,
504                247011430587952,
505                526356006571389,
506                91986625355052,
507                2157223321444601,
508            ]),
509        },
510        AffineNielsPoint {
511            y_plus_x: FieldElement51::from_limbs([
512                4320419353804412,
513                4218074731744053,
514                957728544705548,
515                729906502578991,
516                2411634706750414,
517            ]),
518            y_minus_x: FieldElement51::from_limbs([
519                2073601412052185,
520                31021124762708,
521                264500969797082,
522                248034690651703,
523                1030252227928288,
524            ]),
525            xy2d: FieldElement51::from_limbs([
526                551790716293402,
527                1989538725166328,
528                801169423371717,
529                2052451893578887,
530                678432056995012,
531            ]),
532        },
533    ]),
534    LookupTable([
535        AffineNielsPoint {
536            y_plus_x: FieldElement51::from_limbs([
537                1368953770187805,
538                3042147450398169,
539                2689308289352409,
540                2142576377050579,
541                1932081720066286,
542            ]),
543            y_minus_x: FieldElement51::from_limbs([
544                953638594433374,
545                1092333936795051,
546                1419774766716690,
547                805677984380077,
548                859228993502513,
549            ]),
550            xy2d: FieldElement51::from_limbs([
551                1200766035879111,
552                20142053207432,
553                1465634435977050,
554                1645256912097844,
555                295121984874596,
556            ]),
557        },
558        AffineNielsPoint {
559            y_plus_x: FieldElement51::from_limbs([
560                1735718747031538,
561                1248237894295956,
562                1204753118328107,
563                976066523550493,
564                2317743583219840,
565            ]),
566            y_minus_x: FieldElement51::from_limbs([
567                1060098822528990,
568                1586825862073490,
569                212301317240126,
570                1975302711403555,
571                666724059764335,
572            ]),
573            xy2d: FieldElement51::from_limbs([
574                1091990273418756,
575                1572899409348578,
576                80968014455247,
577                306009358661350,
578                1520450739132526,
579            ]),
580        },
581        AffineNielsPoint {
582            y_plus_x: FieldElement51::from_limbs([
583                3732317023121341,
584                1511153322193951,
585                3496143672676420,
586                2556587964178488,
587                2620936670181690,
588            ]),
589            y_minus_x: FieldElement51::from_limbs([
590                2151330273626164,
591                762045184746182,
592                1688074332551515,
593                823046109005759,
594                907602769079491,
595            ]),
596            xy2d: FieldElement51::from_limbs([
597                2047386910586836,
598                168470092900250,
599                1552838872594810,
600                340951180073789,
601                360819374702533,
602            ]),
603        },
604        AffineNielsPoint {
605            y_plus_x: FieldElement51::from_limbs([
606                1982622644432037,
607                2014393600336956,
608                2380709022489462,
609                3869592437614438,
610                2357094095599062,
611            ]),
612            y_minus_x: FieldElement51::from_limbs([
613                980234343912898,
614                1712256739246056,
615                588935272190264,
616                204298813091998,
617                841798321043288,
618            ]),
619            xy2d: FieldElement51::from_limbs([
620                197561292938973,
621                454817274782871,
622                1963754960082318,
623                2113372252160468,
624                971377527342673,
625            ]),
626        },
627        AffineNielsPoint {
628            y_plus_x: FieldElement51::from_limbs([
629                2416499262514576,
630                2254927265442919,
631                3451304785234000,
632                1766155447043651,
633                1899238924683527,
634            ]),
635            y_minus_x: FieldElement51::from_limbs([
636                732262946680281,
637                1674412764227063,
638                2182456405662809,
639                1350894754474250,
640                558458873295247,
641            ]),
642            xy2d: FieldElement51::from_limbs([
643                2103305098582922,
644                1960809151316468,
645                715134605001343,
646                1454892949167181,
647                40827143824949,
648            ]),
649        },
650        AffineNielsPoint {
651            y_plus_x: FieldElement51::from_limbs([
652                1239289043050193,
653                1744654158124578,
654                758702410031698,
655                4048562808759936,
656                2253402870349013,
657            ]),
658            y_minus_x: FieldElement51::from_limbs([
659                2232056027107988,
660                987343914584615,
661                2115594492994461,
662                1819598072792159,
663                1119305654014850,
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6030                2022432361201842,
6031                1088816090685051,
6032                1977843398539868,
6033                1854834215890724,
6034                564238862029357,
6035            ]),
6036            xy2d: FieldElement51::from_limbs([
6037                938868489100585,
6038                1100285072929025,
6039                1017806255688848,
6040                1957262154788833,
6041                152787950560442,
6042            ]),
6043        },
6044        AffineNielsPoint {
6045            y_plus_x: FieldElement51::from_limbs([
6046                3119119231364171,
6047                2872271776627789,
6048                2477832016990963,
6049                2593801257642876,
6050                1761675818237335,
6051            ]),
6052            y_minus_x: FieldElement51::from_limbs([
6053                1295072362439987,
6054                931227904689414,
6055                1355731432641687,
6056                922235735834035,
6057                892227229410209,
6058            ]),
6059            xy2d: FieldElement51::from_limbs([
6060                1680989767906154,
6061                535362787031440,
6062                2136691276706570,
6063                1942228485381244,
6064                1267350086882274,
6065            ]),
6066        },
6067        AffineNielsPoint {
6068            y_plus_x: FieldElement51::from_limbs([
6069                2617818047455756,
6070                2684460443440843,
6071                2378209521329782,
6072                1973842949591661,
6073                2897427157127624,
6074            ]),
6075            y_minus_x: FieldElement51::from_limbs([
6076                535509430575217,
6077                546885533737322,
6078                1524675609547799,
6079                2138095752851703,
6080                1260738089896827,
6081            ]),
6082            xy2d: FieldElement51::from_limbs([
6083                1159906385590467,
6084                2198530004321610,
6085                714559485023225,
6086                81880727882151,
6087                1484020820037082,
6088            ]),
6089        },
6090        AffineNielsPoint {
6091            y_plus_x: FieldElement51::from_limbs([
6092                1377485731340769,
6093                2046328105512000,
6094                1802058637158797,
6095                2313945950453421,
6096                1356993908853900,
6097            ]),
6098            y_minus_x: FieldElement51::from_limbs([
6099                2013612215646735,
6100                1830770575920375,
6101                536135310219832,
6102                609272325580394,
6103                270684344495013,
6104            ]),
6105            xy2d: FieldElement51::from_limbs([
6106                1237542585982777,
6107                2228682050256790,
6108                1385281931622824,
6109                593183794882890,
6110                493654978552689,
6111            ]),
6112        },
6113    ]),
6114    LookupTable([
6115        AffineNielsPoint {
6116            y_plus_x: FieldElement51::from_limbs([
6117                2299141301692989,
6118                1891414891220256,
6119                983894663308928,
6120                2427961581972066,
6121                3378060928864955,
6122            ]),
6123            y_minus_x: FieldElement51::from_limbs([
6124                1694030170963455,
6125                502038567066200,
6126                1691160065225467,
6127                949628319562187,
6128                275110186693066,
6129            ]),
6130            xy2d: FieldElement51::from_limbs([
6131                1124515748676336,
6132                1661673816593408,
6133                1499640319059718,
6134                1584929449166988,
6135                558148594103306,
6136            ]),
6137        },
6138        AffineNielsPoint {
6139            y_plus_x: FieldElement51::from_limbs([
6140                1784525599998356,
6141                1619698033617383,
6142                2097300287550715,
6143                2510065271789004,
6144                1905684794832757,
6145            ]),
6146            y_minus_x: FieldElement51::from_limbs([
6147                1288941072872766,
6148                931787902039402,
6149                190731008859042,
6150                2006859954667190,
6151                1005931482221702,
6152            ]),
6153            xy2d: FieldElement51::from_limbs([
6154                1465551264822703,
6155                152905080555927,
6156                680334307368453,
6157                173227184634745,
6158                666407097159852,
6159            ]),
6160        },
6161        AffineNielsPoint {
6162            y_plus_x: FieldElement51::from_limbs([
6163                2111017076203943,
6164                3630560299479595,
6165                1248583954016455,
6166                3604089008549670,
6167                1895180776543895,
6168            ]),
6169            y_minus_x: FieldElement51::from_limbs([
6170                171348223915638,
6171                662766099800389,
6172                462338943760497,
6173                466917763340314,
6174                656911292869115,
6175            ]),
6176            xy2d: FieldElement51::from_limbs([
6177                488623681976577,
6178                866497561541722,
6179                1708105560937768,
6180                1673781214218839,
6181                1506146329818807,
6182            ]),
6183        },
6184        AffineNielsPoint {
6185            y_plus_x: FieldElement51::from_limbs([
6186                2412225278142205,
6187                950394373239688,
6188                2682296937026182,
6189                711676555398831,
6190                320964687779005,
6191            ]),
6192            y_minus_x: FieldElement51::from_limbs([
6193                988979367990485,
6194                1359729327576302,
6195                1301834257246029,
6196                294141160829308,
6197                29348272277475,
6198            ]),
6199            xy2d: FieldElement51::from_limbs([
6200                1434382743317910,
6201                100082049942065,
6202                221102347892623,
6203                186982837860588,
6204                1305765053501834,
6205            ]),
6206        },
6207        AffineNielsPoint {
6208            y_plus_x: FieldElement51::from_limbs([
6209                2205916462268190,
6210                2751663643476068,
6211                961960554686615,
6212                2409862576442233,
6213                1841471168298304,
6214            ]),
6215            y_minus_x: FieldElement51::from_limbs([
6216                1191737341426592,
6217                1847042034978363,
6218                1382213545049056,
6219                1039952395710448,
6220                788812858896859,
6221            ]),
6222            xy2d: FieldElement51::from_limbs([
6223                1346965964571152,
6224                1291881610839830,
6225                2142916164336056,
6226                786821641205979,
6227                1571709146321039,
6228            ]),
6229        },
6230        AffineNielsPoint {
6231            y_plus_x: FieldElement51::from_limbs([
6232                787164375951248,
6233                2454669019058437,
6234                3608390234717387,
6235                1431233331032509,
6236                786341368775957,
6237            ]),
6238            y_minus_x: FieldElement51::from_limbs([
6239                492448143532951,
6240                304105152670757,
6241                1761767168301056,
6242                233782684697790,
6243                1981295323106089,
6244            ]),
6245            xy2d: FieldElement51::from_limbs([
6246                665807507761866,
6247                1343384868355425,
6248                895831046139653,
6249                439338948736892,
6250                1986828765695105,
6251            ]),
6252        },
6253        AffineNielsPoint {
6254            y_plus_x: FieldElement51::from_limbs([
6255                3007896024559801,
6256                1721699973539148,
6257                2510565115413133,
6258                1390588532210644,
6259                1212530909934781,
6260            ]),
6261            y_minus_x: FieldElement51::from_limbs([
6262                852891097972275,
6263                1816988871354562,
6264                1543772755726524,
6265                1174710635522444,
6266                202129090724628,
6267            ]),
6268            xy2d: FieldElement51::from_limbs([
6269                1205281565824323,
6270                22430498399418,
6271                992947814485516,
6272                1392458699738672,
6273                688441466734558,
6274            ]),
6275        },
6276        AffineNielsPoint {
6277            y_plus_x: FieldElement51::from_limbs([
6278                3302427242100220,
6279                1955849529137134,
6280                2171162376368357,
6281                2343545681983462,
6282                447733118757825,
6283            ]),
6284            y_minus_x: FieldElement51::from_limbs([
6285                1287181461435438,
6286                622722465530711,
6287                880952150571872,
6288                741035693459198,
6289                311565274989772,
6290            ]),
6291            xy2d: FieldElement51::from_limbs([
6292                1003649078149734,
6293                545233927396469,
6294                1849786171789880,
6295                1318943684880434,
6296                280345687170552,
6297            ]),
6298        },
6299    ]),
6300]);
6301
6302/// Odd multiples of the basepoint `[B, 3B, 5B, 7B, 9B, 11B, 13B, 15B, ..., 127B]`.
6303#[cfg(feature = "precomputed-tables")]
6304#[allow(dead_code)]
6305pub(crate) const AFFINE_ODD_MULTIPLES_OF_BASEPOINT: NafLookupTable8<AffineNielsPoint> =
6306    NafLookupTable8([
6307        AffineNielsPoint {
6308            y_plus_x: FieldElement51::from_limbs([
6309                3540182452943730,
6310                2497478415033846,
6311                2521227595762870,
6312                1462984067271729,
6313                2389212253076811,
6314            ]),
6315            y_minus_x: FieldElement51::from_limbs([
6316                62697248952638,
6317                204681361388450,
6318                631292143396476,
6319                338455783676468,
6320                1213667448819585,
6321            ]),
6322            xy2d: FieldElement51::from_limbs([
6323                301289933810280,
6324                1259582250014073,
6325                1422107436869536,
6326                796239922652654,
6327                1953934009299142,
6328            ]),
6329        },
6330        AffineNielsPoint {
6331            y_plus_x: FieldElement51::from_limbs([
6332                1601611775252272,
6333                1720807796594148,
6334                1132070835939856,
6335                3512254832574799,
6336                2147779492816910,
6337            ]),
6338            y_minus_x: FieldElement51::from_limbs([
6339                316559037616741,
6340                2177824224946892,
6341                1459442586438991,
6342                1461528397712656,
6343                751590696113597,
6344            ]),
6345            xy2d: FieldElement51::from_limbs([
6346                1850748884277385,
6347                1200145853858453,
6348                1068094770532492,
6349                672251375690438,
6350                1586055907191707,
6351            ]),
6352        },
6353        AffineNielsPoint {
6354            y_plus_x: FieldElement51::from_limbs([
6355                769950342298400,
6356                2384754244604994,
6357                3095885746880802,
6358                3225892188161580,
6359                2977876099231263,
6360            ]),
6361            y_minus_x: FieldElement51::from_limbs([
6362                425251763115706,
6363                608463272472562,
6364                442562545713235,
6365                837766094556764,
6366                374555092627893,
6367            ]),
6368            xy2d: FieldElement51::from_limbs([
6369                1086255230780037,
6370                274979815921559,
6371                1960002765731872,
6372                929474102396301,
6373                1190409889297339,
6374            ]),
6375        },
6376        AffineNielsPoint {
6377            y_plus_x: FieldElement51::from_limbs([
6378                2916800678241215,
6379                2065379846933858,
6380                2622030924071124,
6381                2602788184473875,
6382                1233371373142984,
6383            ]),
6384            y_minus_x: FieldElement51::from_limbs([
6385                2019367628972465,
6386                676711900706637,
6387                110710997811333,
6388                1108646842542025,
6389                517791959672113,
6390            ]),
6391            xy2d: FieldElement51::from_limbs([
6392                965130719900578,
6393                247011430587952,
6394                526356006571389,
6395                91986625355052,
6396                2157223321444601,
6397            ]),
6398        },
6399        AffineNielsPoint {
6400            y_plus_x: FieldElement51::from_limbs([
6401                1802695059464988,
6402                1664899123557221,
6403                2845359304426105,
6404                2160434469266658,
6405                3179370264440279,
6406            ]),
6407            y_minus_x: FieldElement51::from_limbs([
6408                1725674970513508,
6409                1933645953859181,
6410                1542344539275782,
6411                1767788773573747,
6412                1297447965928905,
6413            ]),
6414            xy2d: FieldElement51::from_limbs([
6415                1381809363726107,
6416                1430341051343062,
6417                2061843536018959,
6418                1551778050872521,
6419                2036394857967624,
6420            ]),
6421        },
6422        AffineNielsPoint {
6423            y_plus_x: FieldElement51::from_limbs([
6424                4222693909998302,
6425                2779866139518454,
6426                1619374932191226,
6427                2207306624415883,
6428                1169170329061080,
6429            ]),
6430            y_minus_x: FieldElement51::from_limbs([
6431                2070390218572616,
6432                1458919061857835,
6433                624171843017421,
6434                1055332792707765,
6435                433987520732508,
6436            ]),
6437            xy2d: FieldElement51::from_limbs([
6438                893653801273833,
6439                1168026499324677,
6440                1242553501121234,
6441                1306366254304474,
6442                1086752658510815,
6443            ]),
6444        },
6445        AffineNielsPoint {
6446            y_plus_x: FieldElement51::from_limbs([
6447                2465253816303469,
6448                3191571337672685,
6449                1159882208056013,
6450                2569188183312765,
6451                621213314200686,
6452            ]),
6453            y_minus_x: FieldElement51::from_limbs([
6454                1971678598905747,
6455                338026507889165,
6456                762398079972271,
6457                655096486107477,
6458                42299032696322,
6459            ]),
6460            xy2d: FieldElement51::from_limbs([
6461                177130678690680,
6462                1754759263300204,
6463                1864311296286618,
6464                1180675631479880,
6465                1292726903152791,
6466            ]),
6467        },
6468        AffineNielsPoint {
6469            y_plus_x: FieldElement51::from_limbs([
6470                1913163449625248,
6471                2712579013977241,
6472                2193883288642313,
6473                1008900146920800,
6474                1721983679009502,
6475            ]),
6476            y_minus_x: FieldElement51::from_limbs([
6477                1070401523076875,
6478                1272492007800961,
6479                1910153608563310,
6480                2075579521696771,
6481                1191169788841221,
6482            ]),
6483            xy2d: FieldElement51::from_limbs([
6484                692896803108118,
6485                500174642072499,
6486                2068223309439677,
6487                1162190621851337,
6488                1426986007309901,
6489            ]),
6490        },
6491        AffineNielsPoint {
6492            y_plus_x: FieldElement51::from_limbs([
6493                1819621230288238,
6494                2735700366193240,
6495                1755134670739586,
6496                3080648199451191,
6497                4172807995775876,
6498            ]),
6499            y_minus_x: FieldElement51::from_limbs([
6500                992069868904071,
6501                799011518185730,
6502                1777586403832768,
6503                1134820506145684,
6504                1999461475558530,
6505            ]),
6506            xy2d: FieldElement51::from_limbs([
6507                425204543703124,
6508                2040469794090382,
6509                1651690622153809,
6510                1500530168597569,
6511                1253908377065966,
6512            ]),
6513        },
6514        AffineNielsPoint {
6515            y_plus_x: FieldElement51::from_limbs([
6516                2105824306960939,
6517                1387520302709358,
6518                3633176580451016,
6519                2211816663841753,
6520                1629085891776489,
6521            ]),
6522            y_minus_x: FieldElement51::from_limbs([
6523                1485201376284999,
6524                1022406647424656,
6525                504181009209019,
6526                962621520820995,
6527                590876713147230,
6528            ]),
6529            xy2d: FieldElement51::from_limbs([
6530                265873406365287,
6531                1192742653492898,
6532                88553098803050,
6533                525037770869640,
6534                1266933811251234,
6535            ]),
6536        },
6537        AffineNielsPoint {
6538            y_plus_x: FieldElement51::from_limbs([
6539                3552316659826612,
6540                1254279525791875,
6541                1609927932077699,
6542                3578654071679972,
6543                3750681296069893,
6544            ]),
6545            y_minus_x: FieldElement51::from_limbs([
6546                37186803519861,
6547                1404297334376301,
6548                578519728836650,
6549                1740727951192592,
6550                2095534282477028,
6551            ]),
6552            xy2d: FieldElement51::from_limbs([
6553                833234263154399,
6554                2023862470013762,
6555                1854137933982069,
6556                853924318090959,
6557                1589812702805850,
6558            ]),
6559        },
6560        AffineNielsPoint {
6561            y_plus_x: FieldElement51::from_limbs([
6562                3679150557957763,
6563                1319179453661745,
6564                497496853611112,
6565                2665464286942351,
6566                1208137952365560,
6567            ]),
6568            y_minus_x: FieldElement51::from_limbs([
6569                1654513078530905,
6570                907489875842908,
6571                126098711296368,
6572                1726320004173677,
6573                28269495058173,
6574            ]),
6575            xy2d: FieldElement51::from_limbs([
6576                114436686957443,
6577                532739313025996,
6578                115428841215897,
6579                2191499400074366,
6580                370280402676434,
6581            ]),
6582        },
6583        AffineNielsPoint {
6584            y_plus_x: FieldElement51::from_limbs([
6585                1111146849833253,
6586                2016430049079759,
6587                1860522747477948,
6588                3537164738290194,
6589                4137142824844184,
6590            ]),
6591            y_minus_x: FieldElement51::from_limbs([
6592                429069864577128,
6593                975327637149449,
6594                237881983565075,
6595                1654761232378630,
6596                2122527599091807,
6597            ]),
6598            xy2d: FieldElement51::from_limbs([
6599                2093793463548278,
6600                754827233241879,
6601                1420389751719629,
6602                1829952782588138,
6603                2011865756773717,
6604            ]),
6605        },
6606        AffineNielsPoint {
6607            y_plus_x: FieldElement51::from_limbs([
6608                676293365438898,
6609                2850296017886344,
6610                1205350322490195,
6611                2763699392265669,
6612                2133931188538142,
6613            ]),
6614            y_minus_x: FieldElement51::from_limbs([
6615                48340340349120,
6616                1299261101494832,
6617                1137329686775218,
6618                1534848106674340,
6619                1351662218216799,
6620            ]),
6621            xy2d: FieldElement51::from_limbs([
6622                1904520614137939,
6623                1590301001714014,
6624                215781420985270,
6625                2043534301034629,
6626                1970888949300424,
6627            ]),
6628        },
6629        AffineNielsPoint {
6630            y_plus_x: FieldElement51::from_limbs([
6631                2365217962409710,
6632                2061307169694064,
6633                1887478590157603,
6634                2169639621284316,
6635                2373810867477200,
6636            ]),
6637            y_minus_x: FieldElement51::from_limbs([
6638                1020052624656948,
6639                1260412094216707,
6640                366721640607121,
6641                585331442306596,
6642                345876457758061,
6643            ]),
6644            xy2d: FieldElement51::from_limbs([
6645                975390299880933,
6646                1066555195234642,
6647                12651997758352,
6648                1184252205433068,
6649                1058378155074223,
6650            ]),
6651        },
6652        AffineNielsPoint {
6653            y_plus_x: FieldElement51::from_limbs([
6654                1431537716602643,
6655                2024827957433813,
6656                3746434518400495,
6657                1087794891033550,
6658                2156817571680455,
6659            ]),
6660            y_minus_x: FieldElement51::from_limbs([
6661                929288033346881,
6662                255179964546973,
6663                711057989588035,
6664                208899572612840,
6665                185348357387383,
6666            ]),
6667            xy2d: FieldElement51::from_limbs([
6668                823689746424808,
6669                47266130989546,
6670                209403309368097,
6671                1100966895202707,
6672                710792075292719,
6673            ]),
6674        },
6675        AffineNielsPoint {
6676            y_plus_x: FieldElement51::from_limbs([
6677                2311213117823762,
6678                3296668540922318,
6679                2004276520649823,
6680                1861500579441125,
6681                3148029033359833,
6682            ]),
6683            y_minus_x: FieldElement51::from_limbs([
6684                1563693677475261,
6685                1843782073741194,
6686                1950700654453170,
6687                911540858113949,
6688                2085151496302359,
6689            ]),
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curve25519_dalek/backend/serial/u64/constants.rs

curve25519_dalek/backend/serial/u64/
constants.rs
