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 <[email protected]>
10// - Henry de Valence <[email protected]>
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#[cfg(feature = "digest")]
112/// `MONTGOMERY_A` is equal to 486662, which is a constant of the curve equation
113/// for Curve25519 in its Montgomery form. (This is used internally within the
114/// Elligator map.)
115pub(crate) const MONTGOMERY_A: FieldElement51 = FieldElement51::from_limbs([486662, 0, 0, 0, 0]);
116
117#[cfg(feature = "digest")]
118/// `MONTGOMERY_A_NEG` is equal to -486662. (This is used internally within the
119/// Elligator map.)
120pub(crate) const MONTGOMERY_A_NEG: FieldElement51 = FieldElement51::from_limbs([
121    2251799813198567,
122    2251799813685247,
123    2251799813685247,
124    2251799813685247,
125    2251799813685247,
126]);
127
128/// `L` is the order of base point, i.e. 2^252 + 27742317777372353535851937790883648493
129pub(crate) const L: Scalar52 = Scalar52([
130    0x0002631a5cf5d3ed,
131    0x000dea2f79cd6581,
132    0x000000000014def9,
133    0x0000000000000000,
134    0x0000100000000000,
135]);
136
137/// `L` * `LFACTOR` = -1 (mod 2^52)
138pub(crate) const LFACTOR: u64 = 0x51da312547e1b;
139
140/// `R` = R % L where R = 2^260
141pub(crate) const R: Scalar52 = Scalar52([
142    0x000f48bd6721e6ed,
143    0x0003bab5ac67e45a,
144    0x000fffffeb35e51b,
145    0x000fffffffffffff,
146    0x00000fffffffffff,
147]);
148
149/// `RR` = (R^2) % L where R = 2^260
150pub(crate) const RR: Scalar52 = Scalar52([
151    0x0009d265e952d13b,
152    0x000d63c715bea69f,
153    0x0005be65cb687604,
154    0x0003dceec73d217f,
155    0x000009411b7c309a,
156]);
157
158/// The Ed25519 basepoint, as an `EdwardsPoint`.
159///
160/// This is called `_POINT` to distinguish it from
161/// `ED25519_BASEPOINT_TABLE`, which should be used for scalar
162/// multiplication (it's much faster).
163pub const ED25519_BASEPOINT_POINT: EdwardsPoint = EdwardsPoint {
164    X: FieldElement51::from_limbs([
165        1738742601995546,
166        1146398526822698,
167        2070867633025821,
168        562264141797630,
169        587772402128613,
170    ]),
171    Y: FieldElement51::from_limbs([
172        1801439850948184,
173        1351079888211148,
174        450359962737049,
175        900719925474099,
176        1801439850948198,
177    ]),
178    Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
179    T: FieldElement51::from_limbs([
180        1841354044333475,
181        16398895984059,
182        755974180946558,
183        900171276175154,
184        1821297809914039,
185    ]),
186};
187
188/// The 8-torsion subgroup \\(\mathcal E \[8\]\\).
189///
190/// In the case of Curve25519, it is cyclic; the \\(i\\)-th element of
191/// the array is \\(\[i\]P\\), where \\(P\\) is a point of order \\(8\\)
192/// generating \\(\mathcal E\[8\]\\).
193///
194/// Thus \\(\mathcal E\[4\]\\) is the points indexed by `0,2,4,6`, and
195/// \\(\mathcal E\[2\]\\) is the points indexed by `0,4`.
196pub const EIGHT_TORSION: [EdwardsPoint; 8] = EIGHT_TORSION_INNER_DOC_HIDDEN;
197
198/// Inner item used to hide limb constants from cargo doc output.
199#[doc(hidden)]
200pub const EIGHT_TORSION_INNER_DOC_HIDDEN: [EdwardsPoint; 8] = [
201    EdwardsPoint {
202        X: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
203        Y: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
204        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
205        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
206    },
207    EdwardsPoint {
208        X: FieldElement51::from_limbs([
209            358744748052810,
210            1691584618240980,
211            977650209285361,
212            1429865912637724,
213            560044844278676,
214        ]),
215        Y: FieldElement51::from_limbs([
216            84926274344903,
217            473620666599931,
218            365590438845504,
219            1028470286882429,
220            2146499180330972,
221        ]),
222        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
223        T: FieldElement51::from_limbs([
224            1448326834587521,
225            1857896831960481,
226            1093722731865333,
227            1677408490711241,
228            1915505153018406,
229        ]),
230    },
231    EdwardsPoint {
232        X: FieldElement51::from_limbs([
233            533094393274173,
234            2016890930128738,
235            18285341111199,
236            134597186663265,
237            1486323764102114,
238        ]),
239        Y: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
240        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
241        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
242    },
243    EdwardsPoint {
244        X: FieldElement51::from_limbs([
245            358744748052810,
246            1691584618240980,
247            977650209285361,
248            1429865912637724,
249            560044844278676,
250        ]),
251        Y: FieldElement51::from_limbs([
252            2166873539340326,
253            1778179147085316,
254            1886209374839743,
255            1223329526802818,
256            105300633354275,
257        ]),
258        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
259        T: FieldElement51::from_limbs([
260            803472979097708,
261            393902981724766,
262            1158077081819914,
263            574391322974006,
264            336294660666841,
265        ]),
266    },
267    EdwardsPoint {
268        X: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
269        Y: FieldElement51::from_limbs([
270            2251799813685228,
271            2251799813685247,
272            2251799813685247,
273            2251799813685247,
274            2251799813685247,
275        ]),
276        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
277        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
278    },
279    EdwardsPoint {
280        X: FieldElement51::from_limbs([
281            1893055065632419,
282            560215195444267,
283            1274149604399886,
284            821933901047523,
285            1691754969406571,
286        ]),
287        Y: FieldElement51::from_limbs([
288            2166873539340326,
289            1778179147085316,
290            1886209374839743,
291            1223329526802818,
292            105300633354275,
293        ]),
294        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
295        T: FieldElement51::from_limbs([
296            1448326834587521,
297            1857896831960481,
298            1093722731865333,
299            1677408490711241,
300            1915505153018406,
301        ]),
302    },
303    EdwardsPoint {
304        X: FieldElement51::from_limbs([
305            1718705420411056,
306            234908883556509,
307            2233514472574048,
308            2117202627021982,
309            765476049583133,
310        ]),
311        Y: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
312        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
313        T: FieldElement51::from_limbs([0, 0, 0, 0, 0]),
314    },
315    EdwardsPoint {
316        X: FieldElement51::from_limbs([
317            1893055065632419,
318            560215195444267,
319            1274149604399886,
320            821933901047523,
321            1691754969406571,
322        ]),
323        Y: FieldElement51::from_limbs([
324            84926274344903,
325            473620666599931,
326            365590438845504,
327            1028470286882429,
328            2146499180330972,
329        ]),
330        Z: FieldElement51::from_limbs([1, 0, 0, 0, 0]),
331        T: FieldElement51::from_limbs([
332            803472979097708,
333            393902981724766,
334            1158077081819914,
335            574391322974006,
336            336294660666841,
337        ]),
338    },
339];
340
341/// Table containing precomputed multiples of the Ed25519 basepoint \\(B = (x, 4/5)\\).
342#[cfg(feature = "precomputed-tables")]
343pub static ED25519_BASEPOINT_TABLE: &EdwardsBasepointTable =
344    &ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN;
345
346/// Inner constant, used to avoid filling the docs with precomputed points.
347#[doc(hidden)]
348#[cfg(feature = "precomputed-tables")]
349static ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN: EdwardsBasepointTable = EdwardsBasepointTable([
350    LookupTable([
351        AffineNielsPoint {
352            y_plus_x: FieldElement51::from_limbs([
353                3540182452943730,
354                2497478415033846,
355                2521227595762870,
356                1462984067271729,
357                2389212253076811,
358            ]),
359            y_minus_x: FieldElement51::from_limbs([
360                62697248952638,
361                204681361388450,
362                631292143396476,
363                338455783676468,
364                1213667448819585,
365            ]),
366            xy2d: FieldElement51::from_limbs([
367                301289933810280,
368                1259582250014073,
369                1422107436869536,
370                796239922652654,
371                1953934009299142,
372            ]),
373        },
374        AffineNielsPoint {
375            y_plus_x: FieldElement51::from_limbs([
376                3632771708514775,
377                790832306631235,
378                2067202295274102,
379                1995808275510000,
380                1566530869037010,
381            ]),
382            y_minus_x: FieldElement51::from_limbs([
383                463307831301544,
384                432984605774163,
385                1610641361907204,
386                750899048855000,
387                1894842303421586,
388            ]),
389            xy2d: FieldElement51::from_limbs([
390                748439484463711,
391                1033211726465151,
392                1396005112841647,
393                1611506220286469,
394                1972177495910992,
395            ]),
396        },
397        AffineNielsPoint {
398            y_plus_x: FieldElement51::from_limbs([
399                1601611775252272,
400                1720807796594148,
401                1132070835939856,
402                3512254832574799,
403                2147779492816910,
404            ]),
405            y_minus_x: FieldElement51::from_limbs([
406                316559037616741,
407                2177824224946892,
408                1459442586438991,
409                1461528397712656,
410                751590696113597,
411            ]),
412            xy2d: FieldElement51::from_limbs([
413                1850748884277385,
414                1200145853858453,
415                1068094770532492,
416                672251375690438,
417                1586055907191707,
418            ]),
419        },
420        AffineNielsPoint {
421            y_plus_x: FieldElement51::from_limbs([
422                934282339813791,
423                1846903124198670,
424                1172395437954843,
425                1007037127761661,
426                1830588347719256,
427            ]),
428            y_minus_x: FieldElement51::from_limbs([
429                1694390458783935,
430                1735906047636159,
431                705069562067493,
432                648033061693059,
433                696214010414170,
434            ]),
435            xy2d: FieldElement51::from_limbs([
436                1121406372216585,
437                192876649532226,
438                190294192191717,
439                1994165897297032,
440                2245000007398739,
441            ]),
442        },
443        AffineNielsPoint {
444            y_plus_x: FieldElement51::from_limbs([
445                769950342298400,
446                2384754244604994,
447                3095885746880802,
448                3225892188161580,
449                2977876099231263,
450            ]),
451            y_minus_x: FieldElement51::from_limbs([
452                425251763115706,
453                608463272472562,
454                442562545713235,
455                837766094556764,
456                374555092627893,
457            ]),
458            xy2d: FieldElement51::from_limbs([
459                1086255230780037,
460                274979815921559,
461                1960002765731872,
462                929474102396301,
463                1190409889297339,
464            ]),
465        },
466        AffineNielsPoint {
467            y_plus_x: FieldElement51::from_limbs([
468                1388594989461809,
469                316767091099457,
470                2646098655878230,
471                1230079486801004,
472                1440737038838979,
473            ]),
474            y_minus_x: FieldElement51::from_limbs([
475                7380825640100,
476                146210432690483,
477                304903576448906,
478                1198869323871120,
479                997689833219095,
480            ]),
481            xy2d: FieldElement51::from_limbs([
482                1181317918772081,
483                114573476638901,
484                262805072233344,
485                265712217171332,
486                294181933805782,
487            ]),
488        },
489        AffineNielsPoint {
490            y_plus_x: FieldElement51::from_limbs([
491                2916800678241215,
492                2065379846933858,
493                2622030924071124,
494                2602788184473875,
495                1233371373142984,
496            ]),
497            y_minus_x: FieldElement51::from_limbs([
498                2019367628972465,
499                676711900706637,
500                110710997811333,
501                1108646842542025,
502                517791959672113,
503            ]),
504            xy2d: FieldElement51::from_limbs([
505                965130719900578,
506                247011430587952,
507                526356006571389,
508                91986625355052,
509                2157223321444601,
510            ]),
511        },
512        AffineNielsPoint {
513            y_plus_x: FieldElement51::from_limbs([
514                4320419353804412,
515                4218074731744053,
516                957728544705548,
517                729906502578991,
518                2411634706750414,
519            ]),
520            y_minus_x: FieldElement51::from_limbs([
521                2073601412052185,
522                31021124762708,
523                264500969797082,
524                248034690651703,
525                1030252227928288,
526            ]),
527            xy2d: FieldElement51::from_limbs([
528                551790716293402,
529                1989538725166328,
530                801169423371717,
531                2052451893578887,
532                678432056995012,
533            ]),
534        },
535    ]),
536    LookupTable([
537        AffineNielsPoint {
538            y_plus_x: FieldElement51::from_limbs([
539                1368953770187805,
540                3042147450398169,
541                2689308289352409,
542                2142576377050579,
543                1932081720066286,
544            ]),
545            y_minus_x: FieldElement51::from_limbs([
546                953638594433374,
547                1092333936795051,
548                1419774766716690,
549                805677984380077,
550                859228993502513,
551            ]),
552            xy2d: FieldElement51::from_limbs([
553                1200766035879111,
554                20142053207432,
555                1465634435977050,
556                1645256912097844,
557                295121984874596,
558            ]),
559        },
560        AffineNielsPoint {
561            y_plus_x: FieldElement51::from_limbs([
562                1735718747031538,
563                1248237894295956,
564                1204753118328107,
565                976066523550493,
566                2317743583219840,
567            ]),
568            y_minus_x: FieldElement51::from_limbs([
569                1060098822528990,
570                1586825862073490,
571                212301317240126,
572                1975302711403555,
573                666724059764335,
574            ]),
575            xy2d: FieldElement51::from_limbs([
576                1091990273418756,
577                1572899409348578,
578                80968014455247,
579                306009358661350,
580                1520450739132526,
581            ]),
582        },
583        AffineNielsPoint {
584            y_plus_x: FieldElement51::from_limbs([
585                3732317023121341,
586                1511153322193951,
587                3496143672676420,
588                2556587964178488,
589                2620936670181690,
590            ]),
591            y_minus_x: FieldElement51::from_limbs([
592                2151330273626164,
593                762045184746182,
594                1688074332551515,
595                823046109005759,
596                907602769079491,
597            ]),
598            xy2d: FieldElement51::from_limbs([
599                2047386910586836,
600                168470092900250,
601                1552838872594810,
602                340951180073789,
603                360819374702533,
604            ]),
605        },
606        AffineNielsPoint {
607            y_plus_x: FieldElement51::from_limbs([
608                1982622644432037,
609                2014393600336956,
610                2380709022489462,
611                3869592437614438,
612                2357094095599062,
613            ]),
614            y_minus_x: FieldElement51::from_limbs([
615                980234343912898,
616                1712256739246056,
617                588935272190264,
618                204298813091998,
619                841798321043288,
620            ]),
621            xy2d: FieldElement51::from_limbs([
622                197561292938973,
623                454817274782871,
624                1963754960082318,
625                2113372252160468,
626                971377527342673,
627            ]),
628        },
629        AffineNielsPoint {
630            y_plus_x: FieldElement51::from_limbs([
631                2416499262514576,
632                2254927265442919,
633                3451304785234000,
634                1766155447043651,
635                1899238924683527,
636            ]),
637            y_minus_x: FieldElement51::from_limbs([
638                732262946680281,
639                1674412764227063,
640                2182456405662809,
641                1350894754474250,
642                558458873295247,
643            ]),
644            xy2d: FieldElement51::from_limbs([
645                2103305098582922,
646                1960809151316468,
647                715134605001343,
648                1454892949167181,
649                40827143824949,
650            ]),
651        },
652        AffineNielsPoint {
653            y_plus_x: FieldElement51::from_limbs([
654                1239289043050193,
655                1744654158124578,
656                758702410031698,
657                4048562808759936,
658                2253402870349013,
659            ]),
660            y_minus_x: FieldElement51::from_limbs([
661                2232056027107988,
662                987343914584615,
663                2115594492994461,
664                1819598072792159,
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6032                2022432361201842,
6033                1088816090685051,
6034                1977843398539868,
6035                1854834215890724,
6036                564238862029357,
6037            ]),
6038            xy2d: FieldElement51::from_limbs([
6039                938868489100585,
6040                1100285072929025,
6041                1017806255688848,
6042                1957262154788833,
6043                152787950560442,
6044            ]),
6045        },
6046        AffineNielsPoint {
6047            y_plus_x: FieldElement51::from_limbs([
6048                3119119231364171,
6049                2872271776627789,
6050                2477832016990963,
6051                2593801257642876,
6052                1761675818237335,
6053            ]),
6054            y_minus_x: FieldElement51::from_limbs([
6055                1295072362439987,
6056                931227904689414,
6057                1355731432641687,
6058                922235735834035,
6059                892227229410209,
6060            ]),
6061            xy2d: FieldElement51::from_limbs([
6062                1680989767906154,
6063                535362787031440,
6064                2136691276706570,
6065                1942228485381244,
6066                1267350086882274,
6067            ]),
6068        },
6069        AffineNielsPoint {
6070            y_plus_x: FieldElement51::from_limbs([
6071                2617818047455756,
6072                2684460443440843,
6073                2378209521329782,
6074                1973842949591661,
6075                2897427157127624,
6076            ]),
6077            y_minus_x: FieldElement51::from_limbs([
6078                535509430575217,
6079                546885533737322,
6080                1524675609547799,
6081                2138095752851703,
6082                1260738089896827,
6083            ]),
6084            xy2d: FieldElement51::from_limbs([
6085                1159906385590467,
6086                2198530004321610,
6087                714559485023225,
6088                81880727882151,
6089                1484020820037082,
6090            ]),
6091        },
6092        AffineNielsPoint {
6093            y_plus_x: FieldElement51::from_limbs([
6094                1377485731340769,
6095                2046328105512000,
6096                1802058637158797,
6097                2313945950453421,
6098                1356993908853900,
6099            ]),
6100            y_minus_x: FieldElement51::from_limbs([
6101                2013612215646735,
6102                1830770575920375,
6103                536135310219832,
6104                609272325580394,
6105                270684344495013,
6106            ]),
6107            xy2d: FieldElement51::from_limbs([
6108                1237542585982777,
6109                2228682050256790,
6110                1385281931622824,
6111                593183794882890,
6112                493654978552689,
6113            ]),
6114        },
6115    ]),
6116    LookupTable([
6117        AffineNielsPoint {
6118            y_plus_x: FieldElement51::from_limbs([
6119                2299141301692989,
6120                1891414891220256,
6121                983894663308928,
6122                2427961581972066,
6123                3378060928864955,
6124            ]),
6125            y_minus_x: FieldElement51::from_limbs([
6126                1694030170963455,
6127                502038567066200,
6128                1691160065225467,
6129                949628319562187,
6130                275110186693066,
6131            ]),
6132            xy2d: FieldElement51::from_limbs([
6133                1124515748676336,
6134                1661673816593408,
6135                1499640319059718,
6136                1584929449166988,
6137                558148594103306,
6138            ]),
6139        },
6140        AffineNielsPoint {
6141            y_plus_x: FieldElement51::from_limbs([
6142                1784525599998356,
6143                1619698033617383,
6144                2097300287550715,
6145                2510065271789004,
6146                1905684794832757,
6147            ]),
6148            y_minus_x: FieldElement51::from_limbs([
6149                1288941072872766,
6150                931787902039402,
6151                190731008859042,
6152                2006859954667190,
6153                1005931482221702,
6154            ]),
6155            xy2d: FieldElement51::from_limbs([
6156                1465551264822703,
6157                152905080555927,
6158                680334307368453,
6159                173227184634745,
6160                666407097159852,
6161            ]),
6162        },
6163        AffineNielsPoint {
6164            y_plus_x: FieldElement51::from_limbs([
6165                2111017076203943,
6166                3630560299479595,
6167                1248583954016455,
6168                3604089008549670,
6169                1895180776543895,
6170            ]),
6171            y_minus_x: FieldElement51::from_limbs([
6172                171348223915638,
6173                662766099800389,
6174                462338943760497,
6175                466917763340314,
6176                656911292869115,
6177            ]),
6178            xy2d: FieldElement51::from_limbs([
6179                488623681976577,
6180                866497561541722,
6181                1708105560937768,
6182                1673781214218839,
6183                1506146329818807,
6184            ]),
6185        },
6186        AffineNielsPoint {
6187            y_plus_x: FieldElement51::from_limbs([
6188                2412225278142205,
6189                950394373239688,
6190                2682296937026182,
6191                711676555398831,
6192                320964687779005,
6193            ]),
6194            y_minus_x: FieldElement51::from_limbs([
6195                988979367990485,
6196                1359729327576302,
6197                1301834257246029,
6198                294141160829308,
6199                29348272277475,
6200            ]),
6201            xy2d: FieldElement51::from_limbs([
6202                1434382743317910,
6203                100082049942065,
6204                221102347892623,
6205                186982837860588,
6206                1305765053501834,
6207            ]),
6208        },
6209        AffineNielsPoint {
6210            y_plus_x: FieldElement51::from_limbs([
6211                2205916462268190,
6212                2751663643476068,
6213                961960554686615,
6214                2409862576442233,
6215                1841471168298304,
6216            ]),
6217            y_minus_x: FieldElement51::from_limbs([
6218                1191737341426592,
6219                1847042034978363,
6220                1382213545049056,
6221                1039952395710448,
6222                788812858896859,
6223            ]),
6224            xy2d: FieldElement51::from_limbs([
6225                1346965964571152,
6226                1291881610839830,
6227                2142916164336056,
6228                786821641205979,
6229                1571709146321039,
6230            ]),
6231        },
6232        AffineNielsPoint {
6233            y_plus_x: FieldElement51::from_limbs([
6234                787164375951248,
6235                2454669019058437,
6236                3608390234717387,
6237                1431233331032509,
6238                786341368775957,
6239            ]),
6240            y_minus_x: FieldElement51::from_limbs([
6241                492448143532951,
6242                304105152670757,
6243                1761767168301056,
6244                233782684697790,
6245                1981295323106089,
6246            ]),
6247            xy2d: FieldElement51::from_limbs([
6248                665807507761866,
6249                1343384868355425,
6250                895831046139653,
6251                439338948736892,
6252                1986828765695105,
6253            ]),
6254        },
6255        AffineNielsPoint {
6256            y_plus_x: FieldElement51::from_limbs([
6257                3007896024559801,
6258                1721699973539148,
6259                2510565115413133,
6260                1390588532210644,
6261                1212530909934781,
6262            ]),
6263            y_minus_x: FieldElement51::from_limbs([
6264                852891097972275,
6265                1816988871354562,
6266                1543772755726524,
6267                1174710635522444,
6268                202129090724628,
6269            ]),
6270            xy2d: FieldElement51::from_limbs([
6271                1205281565824323,
6272                22430498399418,
6273                992947814485516,
6274                1392458699738672,
6275                688441466734558,
6276            ]),
6277        },
6278        AffineNielsPoint {
6279            y_plus_x: FieldElement51::from_limbs([
6280                3302427242100220,
6281                1955849529137134,
6282                2171162376368357,
6283                2343545681983462,
6284                447733118757825,
6285            ]),
6286            y_minus_x: FieldElement51::from_limbs([
6287                1287181461435438,
6288                622722465530711,
6289                880952150571872,
6290                741035693459198,
6291                311565274989772,
6292            ]),
6293            xy2d: FieldElement51::from_limbs([
6294                1003649078149734,
6295                545233927396469,
6296                1849786171789880,
6297                1318943684880434,
6298                280345687170552,
6299            ]),
6300        },
6301    ]),
6302]);
6303
6304/// Odd multiples of the basepoint `[B, 3B, 5B, 7B, 9B, 11B, 13B, 15B, ..., 127B]`.
6305#[cfg(feature = "precomputed-tables")]
6306#[allow(dead_code)]
6307pub(crate) const AFFINE_ODD_MULTIPLES_OF_BASEPOINT: NafLookupTable8<AffineNielsPoint> =
6308    NafLookupTable8([
6309        AffineNielsPoint {
6310            y_plus_x: FieldElement51::from_limbs([
6311                3540182452943730,
6312                2497478415033846,
6313                2521227595762870,
6314                1462984067271729,
6315                2389212253076811,
6316            ]),
6317            y_minus_x: FieldElement51::from_limbs([
6318                62697248952638,
6319                204681361388450,
6320                631292143396476,
6321                338455783676468,
6322                1213667448819585,
6323            ]),
6324            xy2d: FieldElement51::from_limbs([
6325                301289933810280,
6326                1259582250014073,
6327                1422107436869536,
6328                796239922652654,
6329                1953934009299142,
6330            ]),
6331        },
6332        AffineNielsPoint {
6333            y_plus_x: FieldElement51::from_limbs([
6334                1601611775252272,
6335                1720807796594148,
6336                1132070835939856,
6337                3512254832574799,
6338                2147779492816910,
6339            ]),
6340            y_minus_x: FieldElement51::from_limbs([
6341                316559037616741,
6342                2177824224946892,
6343                1459442586438991,
6344                1461528397712656,
6345                751590696113597,
6346            ]),
6347            xy2d: FieldElement51::from_limbs([
6348                1850748884277385,
6349                1200145853858453,
6350                1068094770532492,
6351                672251375690438,
6352                1586055907191707,
6353            ]),
6354        },
6355        AffineNielsPoint {
6356            y_plus_x: FieldElement51::from_limbs([
6357                769950342298400,
6358                2384754244604994,
6359                3095885746880802,
6360                3225892188161580,
6361                2977876099231263,
6362            ]),
6363            y_minus_x: FieldElement51::from_limbs([
6364                425251763115706,
6365                608463272472562,
6366                442562545713235,
6367                837766094556764,
6368                374555092627893,
6369            ]),
6370            xy2d: FieldElement51::from_limbs([
6371                1086255230780037,
6372                274979815921559,
6373                1960002765731872,
6374                929474102396301,
6375                1190409889297339,
6376            ]),
6377        },
6378        AffineNielsPoint {
6379            y_plus_x: FieldElement51::from_limbs([
6380                2916800678241215,
6381                2065379846933858,
6382                2622030924071124,
6383                2602788184473875,
6384                1233371373142984,
6385            ]),
6386            y_minus_x: FieldElement51::from_limbs([
6387                2019367628972465,
6388                676711900706637,
6389                110710997811333,
6390                1108646842542025,
6391                517791959672113,
6392            ]),
6393            xy2d: FieldElement51::from_limbs([
6394                965130719900578,
6395                247011430587952,
6396                526356006571389,
6397                91986625355052,
6398                2157223321444601,
6399            ]),
6400        },
6401        AffineNielsPoint {
6402            y_plus_x: FieldElement51::from_limbs([
6403                1802695059464988,
6404                1664899123557221,
6405                2845359304426105,
6406                2160434469266658,
6407                3179370264440279,
6408            ]),
6409            y_minus_x: FieldElement51::from_limbs([
6410                1725674970513508,
6411                1933645953859181,
6412                1542344539275782,
6413                1767788773573747,
6414                1297447965928905,
6415            ]),
6416            xy2d: FieldElement51::from_limbs([
6417                1381809363726107,
6418                1430341051343062,
6419                2061843536018959,
6420                1551778050872521,
6421                2036394857967624,
6422            ]),
6423        },
6424        AffineNielsPoint {
6425            y_plus_x: FieldElement51::from_limbs([
6426                4222693909998302,
6427                2779866139518454,
6428                1619374932191226,
6429                2207306624415883,
6430                1169170329061080,
6431            ]),
6432            y_minus_x: FieldElement51::from_limbs([
6433                2070390218572616,
6434                1458919061857835,
6435                624171843017421,
6436                1055332792707765,
6437                433987520732508,
6438            ]),
6439            xy2d: FieldElement51::from_limbs([
6440                893653801273833,
6441                1168026499324677,
6442                1242553501121234,
6443                1306366254304474,
6444                1086752658510815,
6445            ]),
6446        },
6447        AffineNielsPoint {
6448            y_plus_x: FieldElement51::from_limbs([
6449                2465253816303469,
6450                3191571337672685,
6451                1159882208056013,
6452                2569188183312765,
6453                621213314200686,
6454            ]),
6455            y_minus_x: FieldElement51::from_limbs([
6456                1971678598905747,
6457                338026507889165,
6458                762398079972271,
6459                655096486107477,
6460                42299032696322,
6461            ]),
6462            xy2d: FieldElement51::from_limbs([
6463                177130678690680,
6464                1754759263300204,
6465                1864311296286618,
6466                1180675631479880,
6467                1292726903152791,
6468            ]),
6469        },
6470        AffineNielsPoint {
6471            y_plus_x: FieldElement51::from_limbs([
6472                1913163449625248,
6473                2712579013977241,
6474                2193883288642313,
6475                1008900146920800,
6476                1721983679009502,
6477            ]),
6478            y_minus_x: FieldElement51::from_limbs([
6479                1070401523076875,
6480                1272492007800961,
6481                1910153608563310,
6482                2075579521696771,
6483                1191169788841221,
6484            ]),
6485            xy2d: FieldElement51::from_limbs([
6486                692896803108118,
6487                500174642072499,
6488                2068223309439677,
6489                1162190621851337,
6490                1426986007309901,
6491            ]),
6492        },
6493        AffineNielsPoint {
6494            y_plus_x: FieldElement51::from_limbs([
6495                1819621230288238,
6496                2735700366193240,
6497                1755134670739586,
6498                3080648199451191,
6499                4172807995775876,
6500            ]),
6501            y_minus_x: FieldElement51::from_limbs([
6502                992069868904071,
6503                799011518185730,
6504                1777586403832768,
6505                1134820506145684,
6506                1999461475558530,
6507            ]),
6508            xy2d: FieldElement51::from_limbs([
6509                425204543703124,
6510                2040469794090382,
6511                1651690622153809,
6512                1500530168597569,
6513                1253908377065966,
6514            ]),
6515        },
6516        AffineNielsPoint {
6517            y_plus_x: FieldElement51::from_limbs([
6518                2105824306960939,
6519                1387520302709358,
6520                3633176580451016,
6521                2211816663841753,
6522                1629085891776489,
6523            ]),
6524            y_minus_x: FieldElement51::from_limbs([
6525                1485201376284999,
6526                1022406647424656,
6527                504181009209019,
6528                962621520820995,
6529                590876713147230,
6530            ]),
6531            xy2d: FieldElement51::from_limbs([
6532                265873406365287,
6533                1192742653492898,
6534                88553098803050,
6535                525037770869640,
6536                1266933811251234,
6537            ]),
6538        },
6539        AffineNielsPoint {
6540            y_plus_x: FieldElement51::from_limbs([
6541                3552316659826612,
6542                1254279525791875,
6543                1609927932077699,
6544                3578654071679972,
6545                3750681296069893,
6546            ]),
6547            y_minus_x: FieldElement51::from_limbs([
6548                37186803519861,
6549                1404297334376301,
6550                578519728836650,
6551                1740727951192592,
6552                2095534282477028,
6553            ]),
6554            xy2d: FieldElement51::from_limbs([
6555                833234263154399,
6556                2023862470013762,
6557                1854137933982069,
6558                853924318090959,
6559                1589812702805850,
6560            ]),
6561        },
6562        AffineNielsPoint {
6563            y_plus_x: FieldElement51::from_limbs([
6564                3679150557957763,
6565                1319179453661745,
6566                497496853611112,
6567                2665464286942351,
6568                1208137952365560,
6569            ]),
6570            y_minus_x: FieldElement51::from_limbs([
6571                1654513078530905,
6572                907489875842908,
6573                126098711296368,
6574                1726320004173677,
6575                28269495058173,
6576            ]),
6577            xy2d: FieldElement51::from_limbs([
6578                114436686957443,
6579                532739313025996,
6580                115428841215897,
6581                2191499400074366,
6582                370280402676434,
6583            ]),
6584        },
6585        AffineNielsPoint {
6586            y_plus_x: FieldElement51::from_limbs([
6587                1111146849833253,
6588                2016430049079759,
6589                1860522747477948,
6590                3537164738290194,
6591                4137142824844184,
6592            ]),
6593            y_minus_x: FieldElement51::from_limbs([
6594                429069864577128,
6595                975327637149449,
6596                237881983565075,
6597                1654761232378630,
6598                2122527599091807,
6599            ]),
6600            xy2d: FieldElement51::from_limbs([
6601                2093793463548278,
6602                754827233241879,
6603                1420389751719629,
6604                1829952782588138,
6605                2011865756773717,
6606            ]),
6607        },
6608        AffineNielsPoint {
6609            y_plus_x: FieldElement51::from_limbs([
6610                676293365438898,
6611                2850296017886344,
6612                1205350322490195,
6613                2763699392265669,
6614                2133931188538142,
6615            ]),
6616            y_minus_x: FieldElement51::from_limbs([
6617                48340340349120,
6618                1299261101494832,
6619                1137329686775218,
6620                1534848106674340,
6621                1351662218216799,
6622            ]),
6623            xy2d: FieldElement51::from_limbs([
6624                1904520614137939,
6625                1590301001714014,
6626                215781420985270,
6627                2043534301034629,
6628                1970888949300424,
6629            ]),
6630        },
6631        AffineNielsPoint {
6632            y_plus_x: FieldElement51::from_limbs([
6633                2365217962409710,
6634                2061307169694064,
6635                1887478590157603,
6636                2169639621284316,
6637                2373810867477200,
6638            ]),
6639            y_minus_x: FieldElement51::from_limbs([
6640                1020052624656948,
6641                1260412094216707,
6642                366721640607121,
6643                585331442306596,
6644                345876457758061,
6645            ]),
6646            xy2d: FieldElement51::from_limbs([
6647                975390299880933,
6648                1066555195234642,
6649                12651997758352,
6650                1184252205433068,
6651                1058378155074223,
6652            ]),
6653        },
6654        AffineNielsPoint {
6655            y_plus_x: FieldElement51::from_limbs([
6656                1431537716602643,
6657                2024827957433813,
6658                3746434518400495,
6659                1087794891033550,
6660                2156817571680455,
6661            ]),
6662            y_minus_x: FieldElement51::from_limbs([
6663                929288033346881,
6664                255179964546973,
6665                711057989588035,
6666                208899572612840,
6667                185348357387383,
6668            ]),
6669            xy2d: FieldElement51::from_limbs([
6670                823689746424808,
6671                47266130989546,
6672                209403309368097,
6673                1100966895202707,
6674                710792075292719,
6675            ]),
6676        },
6677        AffineNielsPoint {
6678            y_plus_x: FieldElement51::from_limbs([
6679                2311213117823762,
6680                3296668540922318,
6681                2004276520649823,
6682                1861500579441125,
6683                3148029033359833,
6684            ]),
6685            y_minus_x: FieldElement51::from_limbs([
6686                1563693677475261,
6687                1843782073741194,
6688                1950700654453170,
6689                911540858113949,
6690                2085151496302359,
6691            ]),
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curve25519_dalek/backend/serial/u64/constants.rs

curve25519_dalek/backend/serial/u64/
constants.rs
