ark-curves-cherry-picked/bls12_381/src/fields/tests.rs
bls12_381/src/fields/tests.rsRaw
1use ark_algebra_test_templates::*;
2use ark_ec::AdditiveGroup;
3use ark_ff::{
4 biginteger::{BigInt, BigInteger, BigInteger384},
5 fields::{FftField, Field, Fp12Config, Fp2Config, Fp6Config, PrimeField},
6 One, UniformRand, Zero,
7};
8use ark_std::{
9 cmp::Ordering,
10 ops::{AddAssign, MulAssign, SubAssign},
11 vec,
12};
13
14use crate::{Fq, Fq12, Fq12Config, Fq2, Fq2Config, Fq6, Fq6Config, Fr};
15
16test_field!(fr; Fr; mont_prime_field);
17test_field!(fq; Fq; mont_prime_field);
18test_field!(fq2; Fq2);
19test_field!(fq6; Fq6);
20test_field!(fq12; Fq12);
21
22#[test]
23fn test_negative_one() {
24 let neg_one = Fq::new_unchecked(BigInt::new([
25 0x43f5fffffffcaaae,
26 0x32b7fff2ed47fffd,
27 0x7e83a49a2e99d69,
28 0xeca8f3318332bb7a,
29 0xef148d1ea0f4c069,
30 0x40ab3263eff0206,
31 ]));
32 assert_eq!(neg_one, -Fq::one());
33}
34
35#[test]
36fn test_frob_coeffs() {
37 let nqr = -Fq::one();
38
39 assert_eq!(Fq2Config::FROBENIUS_COEFF_FP2_C1[0], Fq::one());
40 assert_eq!(
41 Fq2Config::FROBENIUS_COEFF_FP2_C1[1],
42 nqr.pow([
43 0xdcff7fffffffd555,
44 0xf55ffff58a9ffff,
45 0xb39869507b587b12,
46 0xb23ba5c279c2895f,
47 0x258dd3db21a5d66b,
48 0xd0088f51cbff34d,
49 ])
50 );
51
52 let nqr = Fq2::new(Fq::one(), Fq::one());
53
54 assert_eq!(Fq6Config::FROBENIUS_COEFF_FP6_C1[0], Fq2::one());
55 assert_eq!(
56 Fq6Config::FROBENIUS_COEFF_FP6_C1[1],
57 nqr.pow([
58 0x9354ffffffffe38e,
59 0xa395554e5c6aaaa,
60 0xcd104635a790520c,
61 0xcc27c3d6fbd7063f,
62 0x190937e76bc3e447,
63 0x8ab05f8bdd54cde,
64 ])
65 );
66 assert_eq!(
67 Fq6Config::FROBENIUS_COEFF_FP6_C1[2],
68 nqr.pow([
69 0xb78e0000097b2f68,
70 0xd44f23b47cbd64e3,
71 0x5cb9668120b069a9,
72 0xccea85f9bf7b3d16,
73 0xdba2c8d7adb356d,
74 0x9cd75ded75d7429,
75 0xfc65c31103284fab,
76 0xc58cb9a9b249ee24,
77 0xccf734c3118a2e9a,
78 0xa0f4304c5a256ce6,
79 0xc3f0d2f8e0ba61f8,
80 0xe167e192ebca97,
81 ])
82 );
83 assert_eq!(
84 Fq6Config::FROBENIUS_COEFF_FP6_C1[3],
85 nqr.pow([
86 0xdbc6fcd6f35b9e06,
87 0x997dead10becd6aa,
88 0x9dbbd24c17206460,
89 0x72b97acc6057c45e,
90 0xf8e9a230bf0c628e,
91 0x647ccb1885c63a7,
92 0xce80264fc55bf6ee,
93 0x94d8d716c3939fc4,
94 0xad78f0eb77ee6ee1,
95 0xd6fe49bfe57dc5f9,
96 0x2656d6c15c63647,
97 0xdf6282f111fa903,
98 0x1bdba63e0632b4bb,
99 0x6883597bcaa505eb,
100 0xa56d4ec90c34a982,
101 0x7e4c42823bbe90b2,
102 0xf64728aa6dcb0f20,
103 0x16e57e16ef152f,
104 ])
105 );
106 assert_eq!(
107 Fq6Config::FROBENIUS_COEFF_FP6_C1[4],
108 nqr.pow([
109 0x4649add3c71c6d90,
110 0x43caa6528972a865,
111 0xcda8445bbaaa0fbb,
112 0xc93dea665662aa66,
113 0x2863bc891834481d,
114 0x51a0c3f5d4ccbed8,
115 0x9210e660f90ccae9,
116 0xe2bd6836c546d65e,
117 0xf223abbaa7cf778b,
118 0xd4f10b222cf11680,
119 0xd540f5eff4a1962e,
120 0xa123a1f140b56526,
121 0x31ace500636a59f6,
122 0x3a82bc8c8dfa57a9,
123 0x648c511e217fc1f8,
124 0x36c17ffd53a4558f,
125 0x881bef5fd684eefd,
126 0x5d648dbdc5dbb522,
127 0x8fd07bf06e5e59b8,
128 0x8ddec8a9acaa4b51,
129 0x4cc1f8688e2def26,
130 0xa74e63cb492c03de,
131 0x57c968173d1349bb,
132 0x253674e02a866,
133 ])
134 );
135 assert_eq!(
136 Fq6Config::FROBENIUS_COEFF_FP6_C1[5],
137 nqr.pow([
138 0xf896f792732eb2be,
139 0x49c86a6d1dc593a1,
140 0xe5b31e94581f91c3,
141 0xe3da5cc0a6b20d7f,
142 0x822caef950e0bfed,
143 0x317ed950b9ee67cd,
144 0xffd664016ee3f6cd,
145 0x77d991c88810b122,
146 0x62e72e635e698264,
147 0x905e1a1a2d22814a,
148 0xf5b7ab3a3f33d981,
149 0x175871b0bc0e25dd,
150 0x1e2e9a63df5c3772,
151 0xe888b1f7445b149d,
152 0x9551c19e5e7e2c24,
153 0xecf21939a3d2d6be,
154 0xd830dbfdab72dbd4,
155 0x7b34af8d622d40c0,
156 0x3df6d20a45671242,
157 0xaf86bee30e21d98,
158 0x41064c1534e5df5d,
159 0xf5f6cabd3164c609,
160 0xa5d14bdf2b7ee65,
161 0xa718c069defc9138,
162 0xdb1447e770e3110e,
163 0xc1b164a9e90af491,
164 0x7180441f9d251602,
165 0x1fd3a5e6a9a893e,
166 0x1e17b779d54d5db,
167 0x3c7afafe3174,
168 ])
169 );
170
171 assert_eq!(Fq6Config::FROBENIUS_COEFF_FP6_C2[0], Fq2::one());
172 assert_eq!(
173 Fq6Config::FROBENIUS_COEFF_FP6_C2[1],
174 nqr.pow([
175 0x26a9ffffffffc71c,
176 0x1472aaa9cb8d5555,
177 0x9a208c6b4f20a418,
178 0x984f87adf7ae0c7f,
179 0x32126fced787c88f,
180 0x11560bf17baa99bc,
181 ])
182 );
183 assert_eq!(
184 Fq6Config::FROBENIUS_COEFF_FP6_C2[2],
185 nqr.pow([
186 0x6f1c000012f65ed0,
187 0xa89e4768f97ac9c7,
188 0xb972cd024160d353,
189 0x99d50bf37ef67a2c,
190 0x1b74591af5b66adb,
191 0x139aebbdaebae852,
192 0xf8cb862206509f56,
193 0x8b1973536493dc49,
194 0x99ee698623145d35,
195 0x41e86098b44ad9cd,
196 0x87e1a5f1c174c3f1,
197 0x1c2cfc325d7952f,
198 ])
199 );
200 assert_eq!(
201 Fq6Config::FROBENIUS_COEFF_FP6_C2[3],
202 nqr.pow([
203 0xb78df9ade6b73c0c,
204 0x32fbd5a217d9ad55,
205 0x3b77a4982e40c8c1,
206 0xe572f598c0af88bd,
207 0xf1d344617e18c51c,
208 0xc8f996310b8c74f,
209 0x9d004c9f8ab7eddc,
210 0x29b1ae2d87273f89,
211 0x5af1e1d6efdcddc3,
212 0xadfc937fcafb8bf3,
213 0x4cadad82b8c6c8f,
214 0x1bec505e223f5206,
215 0x37b74c7c0c656976,
216 0xd106b2f7954a0bd6,
217 0x4ada9d9218695304,
218 0xfc988504777d2165,
219 0xec8e5154db961e40,
220 0x2dcafc2dde2a5f,
221 ])
222 );
223 assert_eq!(
224 Fq6Config::FROBENIUS_COEFF_FP6_C2[4],
225 nqr.pow([
226 0x8c935ba78e38db20,
227 0x87954ca512e550ca,
228 0x9b5088b775541f76,
229 0x927bd4ccacc554cd,
230 0x50c779123068903b,
231 0xa34187eba9997db0,
232 0x2421ccc1f21995d2,
233 0xc57ad06d8a8dacbd,
234 0xe44757754f9eef17,
235 0xa9e2164459e22d01,
236 0xaa81ebdfe9432c5d,
237 0x424743e2816aca4d,
238 0x6359ca00c6d4b3ed,
239 0x750579191bf4af52,
240 0xc918a23c42ff83f0,
241 0x6d82fffaa748ab1e,
242 0x1037debfad09ddfa,
243 0xbac91b7b8bb76a45,
244 0x1fa0f7e0dcbcb370,
245 0x1bbd9153595496a3,
246 0x9983f0d11c5bde4d,
247 0x4e9cc796925807bc,
248 0xaf92d02e7a269377,
249 0x4a6ce9c0550cc,
250 ])
251 );
252 assert_eq!(
253 Fq6Config::FROBENIUS_COEFF_FP6_C2[5],
254 nqr.pow([
255 0xf12def24e65d657c,
256 0x9390d4da3b8b2743,
257 0xcb663d28b03f2386,
258 0xc7b4b9814d641aff,
259 0x4595df2a1c17fdb,
260 0x62fdb2a173dccf9b,
261 0xffacc802ddc7ed9a,
262 0xefb3239110216245,
263 0xc5ce5cc6bcd304c8,
264 0x20bc34345a450294,
265 0xeb6f56747e67b303,
266 0x2eb0e361781c4bbb,
267 0x3c5d34c7beb86ee4,
268 0xd11163ee88b6293a,
269 0x2aa3833cbcfc5849,
270 0xd9e4327347a5ad7d,
271 0xb061b7fb56e5b7a9,
272 0xf6695f1ac45a8181,
273 0x7beda4148ace2484,
274 0x15f0d7dc61c43b30,
275 0x820c982a69cbbeba,
276 0xebed957a62c98c12,
277 0x14ba297be56fdccb,
278 0x4e3180d3bdf92270,
279 0xb6288fcee1c6221d,
280 0x8362c953d215e923,
281 0xe300883f3a4a2c05,
282 0x3fa74bcd535127c,
283 0x3c2f6ef3aa9abb6,
284 0x78f5f5fc62e8,
285 ])
286 );
287
288 assert_eq!(Fq12Config::FROBENIUS_COEFF_FP12_C1[0], Fq2::one());
289 assert_eq!(
290 Fq12Config::FROBENIUS_COEFF_FP12_C1[1],
291 nqr.pow([
292 0x49aa7ffffffff1c7,
293 0x51caaaa72e35555,
294 0xe688231ad3c82906,
295 0xe613e1eb7deb831f,
296 0xc849bf3b5e1f223,
297 0x45582fc5eeaa66f,
298 ])
299 );
300 assert_eq!(
301 Fq12Config::FROBENIUS_COEFF_FP12_C1[2],
302 nqr.pow([
303 0xdbc7000004bd97b4,
304 0xea2791da3e5eb271,
305 0x2e5cb340905834d4,
306 0xe67542fcdfbd9e8b,
307 0x86dd1646bd6d9ab6,
308 0x84e6baef6baeba14,
309 0x7e32e188819427d5,
310 0x62c65cd4d924f712,
311 0x667b9a6188c5174d,
312 0x507a18262d12b673,
313 0xe1f8697c705d30fc,
314 0x70b3f0c975e54b,
315 ])
316 );
317 assert_eq!(
318 Fq12Config::FROBENIUS_COEFF_FP12_C1[3],
319 nqr.pow(vec![
320 0x6de37e6b79adcf03,
321 0x4cbef56885f66b55,
322 0x4edde9260b903230,
323 0x395cbd66302be22f,
324 0xfc74d1185f863147,
325 0x323e658c42e31d3,
326 0x67401327e2adfb77,
327 0xca6c6b8b61c9cfe2,
328 0xd6bc7875bbf73770,
329 0xeb7f24dff2bee2fc,
330 0x8132b6b60ae31b23,
331 0x86fb1417888fd481,
332 0x8dedd31f03195a5d,
333 0x3441acbde55282f5,
334 0x52b6a764861a54c1,
335 0x3f2621411ddf4859,
336 0xfb23945536e58790,
337 0xb72bf0b778a97,
338 ])
339 );
340 assert_eq!(
341 Fq12Config::FROBENIUS_COEFF_FP12_C1[4],
342 nqr.pow(vec![
343 0xa324d6e9e38e36c8,
344 0xa1e5532944b95432,
345 0x66d4222ddd5507dd,
346 0xe49ef5332b315533,
347 0x1431de448c1a240e,
348 0xa8d061faea665f6c,
349 0x490873307c866574,
350 0xf15eb41b62a36b2f,
351 0x7911d5dd53e7bbc5,
352 0x6a78859116788b40,
353 0x6aa07af7fa50cb17,
354 0x5091d0f8a05ab293,
355 0x98d6728031b52cfb,
356 0x1d415e4646fd2bd4,
357 0xb246288f10bfe0fc,
358 0x9b60bffea9d22ac7,
359 0x440df7afeb42777e,
360 0x2eb246dee2edda91,
361 0xc7e83df8372f2cdc,
362 0x46ef6454d65525a8,
363 0x2660fc344716f793,
364 0xd3a731e5a49601ef,
365 0x2be4b40b9e89a4dd,
366 0x129b3a7015433,
367 ])
368 );
369 assert_eq!(
370 Fq12Config::FROBENIUS_COEFF_FP12_C1[5],
371 nqr.pow(vec![
372 0xfc4b7bc93997595f,
373 0xa4e435368ee2c9d0,
374 0xf2d98f4a2c0fc8e1,
375 0xf1ed2e60535906bf,
376 0xc116577ca8705ff6,
377 0x98bf6ca85cf733e6,
378 0x7feb3200b771fb66,
379 0x3becc8e444085891,
380 0x31739731af34c132,
381 0xc82f0d0d169140a5,
382 0xfadbd59d1f99ecc0,
383 0xbac38d85e0712ee,
384 0x8f174d31efae1bb9,
385 0x744458fba22d8a4e,
386 0x4aa8e0cf2f3f1612,
387 0x76790c9cd1e96b5f,
388 0x6c186dfed5b96dea,
389 0x3d9a57c6b116a060,
390 0x1efb690522b38921,
391 0x857c35f718710ecc,
392 0xa083260a9a72efae,
393 0xfafb655e98b26304,
394 0x52e8a5ef95bf732,
395 0x538c6034ef7e489c,
396 0xed8a23f3b8718887,
397 0x60d8b254f4857a48,
398 0x38c0220fce928b01,
399 0x80fe9d2f354d449f,
400 0xf0bdbbceaa6aed,
401 0x1e3d7d7f18ba,
402 ])
403 );
404 assert_eq!(
405 Fq12Config::FROBENIUS_COEFF_FP12_C1[6],
406 nqr.pow(vec![
407 0x21219610a012ba3c,
408 0xa5c19ad35375325,
409 0x4e9df1e497674396,
410 0xfb05b717c991c6ef,
411 0x4a1265bca93a32f2,
412 0xd875ff2a7bdc1f66,
413 0xc6d8754736c771b2,
414 0x2d80c759ba5a2ae7,
415 0x138a20df4b03cc1a,
416 0xc22d07fe68e93024,
417 0xd1dc474d3b433133,
418 0xc22aa5e75044e5c,
419 0xf657c6fbf9c17ebf,
420 0xc591a794a58660d,
421 0x2261850ee1453281,
422 0xd17d3bd3b7f5efb4,
423 0xf00cec8ec507d01,
424 0x2a6a775657a00ae6,
425 0x5f098a12ff470719,
426 0x409d194e7b5c5afa,
427 0x1d66478e982af5b,
428 0xda425a5b5e01ca3f,
429 0xf77e4f78747e903c,
430 0x177d49f73732c6fc,
431 0xa9618fecabe0e1f4,
432 0xba5337eac90bd080,
433 0x66fececdbc35d4e7,
434 0xa4cd583203d9206f,
435 0x98391632ceeca596,
436 0x4946b76e1236ad3f,
437 0xa0dec64e60e711a1,
438 0xfcb41ed3605013,
439 0x8ca8f9692ae1e3a9,
440 0xd3078bfc28cc1baf,
441 0xf0536f764e982f82,
442 0x3125f1a2656,
443 ])
444 );
445 assert_eq!(
446 Fq12Config::FROBENIUS_COEFF_FP12_C1[7],
447 nqr.pow(vec![
448 0x742754a1f22fdb,
449 0x2a1955c2dec3a702,
450 0x9747b28c796d134e,
451 0xc113a0411f59db79,
452 0x3bb0fa929853bfc1,
453 0x28c3c25f8f6fb487,
454 0xbc2b6c99d3045b34,
455 0x98fb67d6badde1fd,
456 0x48841d76a24d2073,
457 0xd49891145fe93ae6,
458 0xc772b9c8e74d4099,
459 0xccf4e7b9907755bb,
460 0x9cf47b25d42fd908,
461 0x5616a0c347fc445d,
462 0xff93b7a7ad1b8a6d,
463 0xac2099256b78a77a,
464 0x7804a95b02892e1c,
465 0x5cf59ca7bfd69776,
466 0xa7023502acd3c866,
467 0xc76f4982fcf8f37,
468 0x51862a5a57ac986e,
469 0x38b80ed72b1b1023,
470 0x4a291812066a61e1,
471 0xcd8a685eff45631,
472 0x3f40f708764e4fa5,
473 0x8aa0441891285092,
474 0x9eff60d71cdf0a9,
475 0x4fdd9d56517e2bfa,
476 0x1f3c80d74a28bc85,
477 0x24617417c064b648,
478 0x7ddda1e4385d5088,
479 0xf9e132b11dd32a16,
480 0xcc957cb8ef66ab99,
481 0xd4f206d37cb752c5,
482 0x40de343f28ad616b,
483 0x8d1f24379068f0e3,
484 0x6f31d7947ea21137,
485 0x27311f9c32184061,
486 0x9eea0664cc78ce5f,
487 0x7d4151f6fea9a0da,
488 0x454096fa75bd571a,
489 0x4fe0f20ecb,
490 ])
491 );
492 assert_eq!(
493 Fq12Config::FROBENIUS_COEFF_FP12_C1[8],
494 nqr.pow(vec![
495 0x802f5720d0b25710,
496 0x6714f0a258b85c7c,
497 0x31394c90afdf16e,
498 0xe9d2b0c64f957b19,
499 0xe67c0d9c5e7903ee,
500 0x3156fdc5443ea8ef,
501 0x7c4c50524d88c892,
502 0xc99dc8990c0ad244,
503 0xd37ababf3649a896,
504 0x76fe4b838ff7a20c,
505 0xcf69ee2cec728db3,
506 0xb83535548e5f41,
507 0x371147684ccb0c23,
508 0x194f6f4fa500db52,
509 0xc4571dc78a4c5374,
510 0xe4d46d479999ca97,
511 0x76b6785a615a151c,
512 0xcceb8bcea7eaf8c1,
513 0x80d87a6fbe5ae687,
514 0x6a97ddddb85ce85,
515 0xd783958f26034204,
516 0x7144506f2e2e8590,
517 0x948693d377aef166,
518 0x8364621ed6f96056,
519 0xf021777c4c09ee2d,
520 0xc6cf5e746ecd50b,
521 0xa2337b7aa22743df,
522 0xae753f8bbacab39c,
523 0xfc782a9e34d3c1cc,
524 0x21b827324fe494d9,
525 0x5692ce350ed03b38,
526 0xf323a2b3cd0481b0,
527 0xe859c97a4ccad2e3,
528 0x48434b70381e4503,
529 0x46042d62e4132ed8,
530 0x48c4d6f56122e2f2,
531 0xf87711ab9f5c1af7,
532 0xb14b7a054759b469,
533 0x8eb0a96993ffa9aa,
534 0x9b21fb6fc58b760c,
535 0xf3abdd115d2e7d25,
536 0xf7beac3d4d12409c,
537 0x40a5585cce69bf03,
538 0x697881e1ba22d5a8,
539 0x3d6c04e6ad373fd9,
540 0x849871bf627be886,
541 0x550f4b9b71b28ef9,
542 0x81d2e0d78,
543 ])
544 );
545 assert_eq!(
546 Fq12Config::FROBENIUS_COEFF_FP12_C1[9],
547 nqr.pow(vec![
548 0x4af4accf7de0b977,
549 0x742485e21805b4ee,
550 0xee388fbc4ac36dec,
551 0x1e199da57ad178a,
552 0xc27c12b292c6726a,
553 0x162e6ed84505b5e8,
554 0xe191683f336e09df,
555 0x17deb7e8d1e0fce6,
556 0xd944f19ad06f5836,
557 0x4c5f5e59f6276026,
558 0xf1ba9c7c148a38a8,
559 0xd205fe2dba72b326,
560 0x9a2cf2a4c289824e,
561 0x4f47ad512c39e24d,
562 0xc5894d984000ea09,
563 0x2974c03ff7cf01fa,
564 0xfcd243b48cb99a22,
565 0x2b5150c9313ac1e8,
566 0x9089f37c7fc80eda,
567 0x989540cc9a7aea56,
568 0x1ab1d4e337e63018,
569 0x42b546c30d357e43,
570 0x1c6abc04f76233d9,
571 0x78b3b8d88bf73e47,
572 0x151c4e4c45dc68e6,
573 0x519a79c4f54397ed,
574 0x93f5b51535a127c5,
575 0x5fc51b6f52fa153e,
576 0x2e0504f2d4a965c3,
577 0xc85bd3a3da52bffe,
578 0x98c60957a46a89ef,
579 0x48c03b5976b91cae,
580 0xc6598040a0a61438,
581 0xbf0b49dc255953af,
582 0xb78dff905b628ab4,
583 0x68140b797ba74ab8,
584 0x116cf037991d1143,
585 0x2f7fe82e58acb0b8,
586 0xc20bf7a8f7be5d45,
587 0x86c2905c338d5709,
588 0xff13a3ae6c8ace3d,
589 0xb6f95e2282d08337,
590 0xd49f7b313e9cbf29,
591 0xf794517193a1ce8c,
592 0x39641fecb596a874,
593 0x411c4c4edf462fb3,
594 0x3f8cd55c10cf25b4,
595 0x2bdd7ea165e860b6,
596 0xacd7d2cef4caa193,
597 0x6558a1d09a05f96,
598 0x1f52b5f5b546fc20,
599 0x4ee22a5a8c250c12,
600 0xd3a63a54a205b6b3,
601 0xd2ff5be8,
602 ])
603 );
604 assert_eq!(
605 Fq12Config::FROBENIUS_COEFF_FP12_C1[10],
606 nqr.pow(vec![
607 0xe5953a4f96cdda44,
608 0x336b2d734cbc32bb,
609 0x3f79bfe3cd7410e,
610 0x267ae19aaa0f0332,
611 0x85a9c4db78d5c749,
612 0x90996b046b5dc7d8,
613 0x8945eae9820afc6a,
614 0x2644ddea2b036bd,
615 0x39898e35ac2e3819,
616 0x2574eab095659ab9,
617 0x65953d51ac5ea798,
618 0xc6b8c7afe6752466,
619 0x40e9e993e9286544,
620 0x7e0ad34ad9700ea0,
621 0xac1015eba2c69222,
622 0x24f057a19239b5d8,
623 0x2043b48c8a3767eb,
624 0x1117c124a75d7ff4,
625 0x433cfd1a09fb3ce7,
626 0x25b087ce4bcf7fb,
627 0xbcee0dc53a3e5bdb,
628 0xbffda040cf028735,
629 0xf7cf103a25512acc,
630 0x31d4ecda673130b9,
631 0xea0906dab18461e6,
632 0x5a40585a5ac3050d,
633 0x803358fc14fd0eda,
634 0x3678ca654eada770,
635 0x7b91a1293a45e33e,
636 0xcd5e5b8ea8530e43,
637 0x21ae563ab34da266,
638 0xecb00dad60df8894,
639 0x77fe53e652facfef,
640 0x9b7d1ad0b00244ec,
641 0xe695df5ca73f801,
642 0x23cdb21feeab0149,
643 0x14de113e7ea810d9,
644 0x52600cd958dac7e7,
645 0xc83392c14667e488,
646 0x9f808444bc1717fc,
647 0x56facb4bcf7c788f,
648 0x8bcad53245fc3ca0,
649 0xdef661e83f27d81c,
650 0x37d4ebcac9ad87e5,
651 0x6fe8b24f5cdb9324,
652 0xee08a26c1197654c,
653 0xc98b22f65f237e9a,
654 0xf54873a908ed3401,
655 0x6e1cb951d41f3f3,
656 0x290b2250a54e8df6,
657 0x7f36d51eb1db669e,
658 0xb08c7ed81a6ee43e,
659 0x95e1c90fb092f680,
660 0x429e4afd0e8b820,
661 0x2c14a83ee87d715c,
662 0xf37267575cfc8af5,
663 0xb99e9afeda3c2c30,
664 0x8f0f69da75792d5a,
665 0x35074a85a533c73,
666 0x156ed119,
667 ])
668 );
669 assert_eq!(
670 Fq12Config::FROBENIUS_COEFF_FP12_C1[11],
671 nqr.pow(vec![
672 0x107db680942de533,
673 0x6262b24d2052393b,
674 0x6136df824159ebc,
675 0xedb052c9970c5deb,
676 0xca813aea916c3777,
677 0xf49dacb9d76c1788,
678 0x624941bd372933bb,
679 0xa5e60c2520638331,
680 0xb38b661683411074,
681 0x1d2c9af4c43d962b,
682 0x17d807a0f14aa830,
683 0x6e6581a51012c108,
684 0x668a537e5b35e6f5,
685 0x6c396cf3782dca5d,
686 0x33b679d1bff536ed,
687 0x736cce41805d90aa,
688 0x8a562f369eb680bf,
689 0x9f61aa208a11ded8,
690 0x43dd89dd94d20f35,
691 0xcf84c6610575c10a,
692 0x9f318d49cf2fe8e6,
693 0xbbc6e5f25a6e434e,
694 0x6528c433d11d987b,
695 0xffced71cc48c0e8a,
696 0x4cbb1474f4cb2a26,
697 0x66a035c0b28b7231,
698 0xa6f2875faa1a82ae,
699 0xdd1ea3deff818b02,
700 0xe0cfdf0dcdecf701,
701 0x9aefa231f2f6d23,
702 0xfb251297efa06746,
703 0x5a40d367df985538,
704 0x1ea31d69ab506fed,
705 0xc64ea8280e89a73f,
706 0x969acf9f2d4496f4,
707 0xe84c9181ee60c52c,
708 0xc60f27fc19fc6ca4,
709 0x760b33d850154048,
710 0x84f69080f66c8457,
711 0xc0192ba0fabf640e,
712 0xd2c338765c23a3a8,
713 0xa7838c20f02cec6c,
714 0xb7cf01d020572877,
715 0xd63ffaeba0be200a,
716 0xf7492baeb5f041ac,
717 0x8602c5212170d117,
718 0xad9b2e83a5a42068,
719 0x2461829b3ba1083e,
720 0x7c34650da5295273,
721 0xdc824ba800a8265a,
722 0xd18d9b47836af7b2,
723 0x3af78945c58cbf4d,
724 0x7ed9575b8596906c,
725 0x6d0c133895009a66,
726 0x53bc1247ea349fe1,
727 0x6b3063078d41aa7a,
728 0x6184acd8cd880b33,
729 0x76f4d15503fd1b96,
730 0x7a9afd61eef25746,
731 0xce974aadece60609,
732 0x88ca59546a8ceafd,
733 0x6d29391c41a0ac07,
734 0x443843a60e0f46a6,
735 0xa1590f62fd2602c7,
736 0x536d5b15b514373f,
737 0x22d582b,
738 ])
739 );
740}
741
742#[test]
743fn test_fq_repr_from() {
744 assert_eq!(BigInt::from(100u64), BigInt::new([100, 0, 0, 0, 0, 0]));
745}
746
747#[test]
748fn test_fq_repr_is_odd() {
749 assert!(!BigInteger384::from(0u64).is_odd());
750 assert!(BigInteger384::from(0u64).is_even());
751 assert!(BigInteger384::from(1u64).is_odd());
752 assert!(!BigInteger384::from(1u64).is_even());
753 assert!(!BigInteger384::from(324834872u64).is_odd());
754 assert!(BigInteger384::from(324834872u64).is_even());
755 assert!(BigInteger384::from(324834873u64).is_odd());
756 assert!(!BigInteger384::from(324834873u64).is_even());
757}
758
759#[test]
760fn test_fq_repr_is_zero() {
761 assert!(BigInteger384::from(0u64).is_zero());
762 assert!(!BigInteger384::from(1u64).is_zero());
763 assert!(!BigInt::new([0, 0, 0, 0, 1, 0]).is_zero());
764}
765
766#[test]
767fn test_fq_repr_div2() {
768 let mut a = BigInt::new([
769 0x8b0ad39f8dd7482a,
770 0x147221c9a7178b69,
771 0x54764cb08d8a6aa0,
772 0x8519d708e1d83041,
773 0x41f82777bd13fdb,
774 0xf43944578f9b771b,
775 ]);
776 a.div2();
777 assert_eq!(
778 a,
779 BigInt::new([
780 0xc58569cfc6eba415,
781 0xa3910e4d38bc5b4,
782 0xaa3b265846c53550,
783 0xc28ceb8470ec1820,
784 0x820fc13bbde89fed,
785 0x7a1ca22bc7cdbb8d,
786 ])
787 );
788 for _ in 0..10 {
789 a.div2();
790 }
791 assert_eq!(
792 a,
793 BigInt::new([
794 0x6d31615a73f1bae9,
795 0x54028e443934e2f1,
796 0x82a8ec99611b14d,
797 0xfb70a33ae11c3b06,
798 0xe36083f04eef7a27,
799 0x1e87288af1f36e,
800 ])
801 );
802 for _ in 0..300 {
803 a.div2();
804 }
805 assert_eq!(
806 a,
807 BigInt::new([0x7288af1f36ee3608, 0x1e8, 0x0, 0x0, 0x0, 0x0])
808 );
809 for _ in 0..50 {
810 a.div2();
811 }
812 assert_eq!(a, BigInt::new([0x7a1ca2, 0x0, 0x0, 0x0, 0x0, 0x0]));
813 for _ in 0..22 {
814 a.div2();
815 }
816 assert_eq!(a, BigInt::new([0x1, 0x0, 0x0, 0x0, 0x0, 0x0]));
817 a.div2();
818 assert!(a.is_zero());
819}
820
821#[test]
822fn test_fq_repr_divn() {
823 let mut a = BigInt::new([
824 0xaa5cdd6172847ffd,
825 0x43242c06aed55287,
826 0x9ddd5b312f3dd104,
827 0xc5541fd48046b7e7,
828 0x16080cf4071e0b05,
829 0x1225f2901aea514e,
830 ]);
831 a.divn(0);
832 assert_eq!(
833 a,
834 BigInt::new([
835 0xaa5cdd6172847ffd,
836 0x43242c06aed55287,
837 0x9ddd5b312f3dd104,
838 0xc5541fd48046b7e7,
839 0x16080cf4071e0b05,
840 0x1225f2901aea514e,
841 ])
842 );
843 a.divn(1);
844 assert_eq!(
845 a,
846 BigInt::new([
847 0xd52e6eb0b9423ffe,
848 0x21921603576aa943,
849 0xceeead98979ee882,
850 0xe2aa0fea40235bf3,
851 0xb04067a038f0582,
852 0x912f9480d7528a7,
853 ])
854 );
855 a.divn(50);
856 assert_eq!(
857 a,
858 BigInt::new([
859 0x8580d5daaa50f54b,
860 0xab6625e7ba208864,
861 0x83fa9008d6fcf3bb,
862 0x19e80e3c160b8aa,
863 0xbe52035d4a29c2c1,
864 0x244,
865 ])
866 );
867 a.divn(130);
868 assert_eq!(
869 a,
870 BigInt::new([
871 0xa0fea40235bf3cee,
872 0x4067a038f0582e2a,
873 0x2f9480d7528a70b0,
874 0x91,
875 0x0,
876 0x0,
877 ])
878 );
879 a.divn(64);
880 assert_eq!(
881 a,
882 BigInt::new([0x4067a038f0582e2a, 0x2f9480d7528a70b0, 0x91, 0x0, 0x0, 0x0])
883 );
884}
885
886#[test]
887fn test_fq_repr_mul2() {
888 let mut a = BigInteger384::from(23712937547u64);
889 a.mul2();
890 assert_eq!(a, BigInt::new([0xb0acd6c96, 0x0, 0x0, 0x0, 0x0, 0x0]));
891 for _ in 0..60 {
892 a.mul2();
893 }
894 assert_eq!(
895 a,
896 BigInt::new([0x6000000000000000, 0xb0acd6c9, 0x0, 0x0, 0x0, 0x0])
897 );
898 for _ in 0..300 {
899 a.mul2();
900 }
901 assert_eq!(
902 a,
903 BigInt::new([0x0, 0x0, 0x0, 0x0, 0x0, 0xcd6c960000000000])
904 );
905 for _ in 0..17 {
906 a.mul2();
907 }
908 assert_eq!(
909 a,
910 BigInt::new([0x0, 0x0, 0x0, 0x0, 0x0, 0x2c00000000000000])
911 );
912 for _ in 0..6 {
913 a.mul2();
914 }
915 assert!(a.is_zero());
916}
917
918#[test]
919fn test_fq_repr_num_bits() {
920 let mut a = BigInteger384::from(0u64);
921 assert_eq!(0, a.num_bits());
922 a = BigInteger384::from(1u64);
923 for i in 1..385 {
924 assert_eq!(i, a.num_bits());
925 a.mul2();
926 }
927 assert_eq!(0, a.num_bits());
928}
929
930#[test]
931fn test_fq_repr_sub_noborrow() {
932 let mut rng = ark_std::test_rng();
933
934 let mut t = BigInt::new([
935 0x827a4a08041ebd9,
936 0x3c239f3dcc8f0d6b,
937 0x9ab46a912d555364,
938 0x196936b17b43910b,
939 0xad0eb3948a5c34fd,
940 0xd56f7b5ab8b5ce8,
941 ]);
942 t.sub_with_borrow(&BigInt::new([
943 0xc7867917187ca02b,
944 0x5d75679d4911ffef,
945 0x8c5b3e48b1a71c15,
946 0x6a427ae846fd66aa,
947 0x7a37e7265ee1eaf9,
948 0x7c0577a26f59d5,
949 ]));
950 assert!(
951 t == BigInt::new([
952 0x40a12b8967c54bae,
953 0xdeae37a0837d0d7b,
954 0xe592c487bae374e,
955 0xaf26bbc934462a61,
956 0x32d6cc6e2b7a4a03,
957 0xcdaf23e091c0313,
958 ])
959 );
960
961 for _ in 0..1000 {
962 let mut a = BigInteger384::rand(&mut rng);
963 a.0[5] >>= 30;
964 let mut b = a;
965 for _ in 0..10 {
966 b.mul2();
967 }
968 let mut c = b;
969 for _ in 0..10 {
970 c.mul2();
971 }
972
973 assert!(a < b);
974 assert!(b < c);
975
976 let mut csub_ba = c;
977 csub_ba.sub_with_borrow(&b);
978 csub_ba.sub_with_borrow(&a);
979
980 let mut csub_ab = c;
981 csub_ab.sub_with_borrow(&a);
982 csub_ab.sub_with_borrow(&b);
983
984 assert_eq!(csub_ab, csub_ba);
985 }
986
987 // Subtracting q+1 from q should produce -1 (mod 2**384)
988 let mut qplusone = BigInt::new([
989 0xb9feffffffffaaab,
990 0x1eabfffeb153ffff,
991 0x6730d2a0f6b0f624,
992 0x64774b84f38512bf,
993 0x4b1ba7b6434bacd7,
994 0x1a0111ea397fe69a,
995 ]);
996 qplusone.sub_with_borrow(&BigInt::new([
997 0xb9feffffffffaaac,
998 0x1eabfffeb153ffff,
999 0x6730d2a0f6b0f624,
1000 0x64774b84f38512bf,
1001 0x4b1ba7b6434bacd7,
1002 0x1a0111ea397fe69a,
1003 ]));
1004 assert_eq!(
1005 qplusone,
1006 BigInt::new([
1007 0xffffffffffffffff,
1008 0xffffffffffffffff,
1009 0xffffffffffffffff,
1010 0xffffffffffffffff,
1011 0xffffffffffffffff,
1012 0xffffffffffffffff,
1013 ])
1014 );
1015}
1016
1017#[test]
1018fn test_fq_repr_add_nocarry() {
1019 let mut rng = ark_std::test_rng();
1020
1021 let mut t = BigInt::new([
1022 0x827a4a08041ebd9,
1023 0x3c239f3dcc8f0d6b,
1024 0x9ab46a912d555364,
1025 0x196936b17b43910b,
1026 0xad0eb3948a5c34fd,
1027 0xd56f7b5ab8b5ce8,
1028 ]);
1029 t.add_with_carry(&BigInt::new([
1030 0xc7867917187ca02b,
1031 0x5d75679d4911ffef,
1032 0x8c5b3e48b1a71c15,
1033 0x6a427ae846fd66aa,
1034 0x7a37e7265ee1eaf9,
1035 0x7c0577a26f59d5,
1036 ]));
1037 assert!(
1038 t == BigInt::new([
1039 0xcfae1db798be8c04,
1040 0x999906db15a10d5a,
1041 0x270fa8d9defc6f79,
1042 0x83abb199c240f7b6,
1043 0x27469abae93e1ff6,
1044 0xdd2fd2d4dfab6be,
1045 ])
1046 );
1047
1048 // Test for the associativity of addition.
1049 for _ in 0..1000 {
1050 let mut a = BigInteger384::rand(&mut rng);
1051 let mut b = BigInteger384::rand(&mut rng);
1052 let mut c = BigInteger384::rand(&mut rng);
1053
1054 // Unset the first few bits, so that overflow won't occur.
1055 a.0[5] >>= 3;
1056 b.0[5] >>= 3;
1057 c.0[5] >>= 3;
1058
1059 let mut abc = a;
1060 abc.add_with_carry(&b);
1061 abc.add_with_carry(&c);
1062
1063 let mut acb = a;
1064 acb.add_with_carry(&c);
1065 acb.add_with_carry(&b);
1066
1067 let mut bac = b;
1068 bac.add_with_carry(&a);
1069 bac.add_with_carry(&c);
1070
1071 let mut bca = b;
1072 bca.add_with_carry(&c);
1073 bca.add_with_carry(&a);
1074
1075 let mut cab = c;
1076 cab.add_with_carry(&a);
1077 cab.add_with_carry(&b);
1078
1079 let mut cba = c;
1080 cba.add_with_carry(&b);
1081 cba.add_with_carry(&a);
1082
1083 assert_eq!(abc, acb);
1084 assert_eq!(abc, bac);
1085 assert_eq!(abc, bca);
1086 assert_eq!(abc, cab);
1087 assert_eq!(abc, cba);
1088 }
1089
1090 // Adding 1 to (2^384 - 1) should produce zero
1091 let mut x = BigInt::new([
1092 0xffffffffffffffff,
1093 0xffffffffffffffff,
1094 0xffffffffffffffff,
1095 0xffffffffffffffff,
1096 0xffffffffffffffff,
1097 0xffffffffffffffff,
1098 ]);
1099 x.add_with_carry(&BigInteger384::from(1u64));
1100 assert!(x.is_zero());
1101}
1102
1103#[test]
1104fn test_fq2_sqrt() {
1105 // 1 has a sqrt in the base field
1106 let fq2_sqrt = Fq2::new(Fq::one(), Fq::zero()).sqrt().unwrap();
1107 assert_eq!(fq2_sqrt.c0, Fq::one());
1108 assert_eq!(fq2_sqrt.c1, Fq::zero());
1109
1110 // -1 has no sqrt in the base field, but should be valid in Fq2
1111 let fq2_sqrt = Fq2::new(-Fq::one(), Fq::zero()).sqrt().unwrap();
1112 assert_eq!(fq2_sqrt.c0, Fq::zero());
1113 assert_eq!(fq2_sqrt.c1, Fq::one());
1114}
1115
1116#[test]
1117fn test_fq_num_bits() {
1118 assert_eq!(Fq::MODULUS_BIT_SIZE, 381);
1119}
1120
1121#[test]
1122fn test_fq_root_of_unity() {
1123 assert_eq!(Fq::TWO_ADICITY, 1);
1124 assert_eq!(Fq::GENERATOR, Fq::from(BigInteger384::from(2u64)));
1125 assert_eq!(
1126 Fq::GENERATOR.pow([
1127 0xdcff7fffffffd555,
1128 0xf55ffff58a9ffff,
1129 0xb39869507b587b12,
1130 0xb23ba5c279c2895f,
1131 0x258dd3db21a5d66b,
1132 0xd0088f51cbff34d,
1133 ]),
1134 Fq::TWO_ADIC_ROOT_OF_UNITY
1135 );
1136 assert_eq!(
1137 Fq::TWO_ADIC_ROOT_OF_UNITY.pow([1 << Fq::TWO_ADICITY]),
1138 Fq::one()
1139 );
1140 assert!(Fq::GENERATOR.sqrt().is_none());
1141}
1142
1143// #[test]
1144// fn fq_field_tests() {
1145// ::tests::field::random_field_tests::<Fq>();
1146// ::tests::field::random_sqrt_tests::<Fq>();
1147// ::tests::field::random_frobenius_tests::<Fq, _>(Fq::char(), 13);
1148// ::tests::field::from_str_tests::<Fq>();
1149// }
1150
1151#[test]
1152fn test_fq_ordering() {
1153 // BigInteger384's ordering is well-tested, but we still need to make sure the
1154 // Fq elements aren't being compared in Montgomery form.
1155 for i in 0..100u64 {
1156 assert!(Fq::from(BigInteger384::from(i + 1)) > Fq::from(BigInteger384::from(i)));
1157 }
1158}
1159
1160// #[test]
1161// fn fq_repr_tests() {
1162// ::tests::repr::random_repr_tests::<BigInteger384>();
1163// }
1164
1165#[test]
1166fn test_fq_legendre() {
1167 use ark_ff::fields::LegendreSymbol::*;
1168
1169 assert_eq!(QuadraticResidue, Fq::one().legendre());
1170 assert_eq!(Zero, Fq::zero().legendre());
1171
1172 assert_eq!(
1173 QuadraticNonResidue,
1174 Fq::from(BigInteger384::from(2u64)).legendre()
1175 );
1176 assert_eq!(
1177 QuadraticResidue,
1178 Fq::from(BigInteger384::from(4u64)).legendre()
1179 );
1180
1181 let e = BigInt::new([
1182 0x52a112f249778642,
1183 0xd0bedb989b7991f,
1184 0xdad3b6681aa63c05,
1185 0xf2efc0bb4721b283,
1186 0x6057a98f18c24733,
1187 0x1022c2fd122889e4,
1188 ]);
1189 assert_eq!(QuadraticNonResidue, Fq::from(e).legendre());
1190 let e = BigInt::new([
1191 0x6dae594e53a96c74,
1192 0x19b16ca9ba64b37b,
1193 0x5c764661a59bfc68,
1194 0xaa346e9b31c60a,
1195 0x346059f9d87a9fa9,
1196 0x1d61ac6bfd5c88b,
1197 ]);
1198 assert_eq!(QuadraticResidue, Fq::from(e).legendre());
1199}
1200
1201#[test]
1202fn test_fq2_ordering() {
1203 let mut a = Fq2::new(Fq::zero(), Fq::zero());
1204
1205 let mut b = a.clone();
1206
1207 assert!(a.cmp(&b) == Ordering::Equal);
1208 b.c0.add_assign(&Fq::one());
1209 assert!(a.cmp(&b) == Ordering::Less);
1210 a.c0.add_assign(&Fq::one());
1211 assert!(a.cmp(&b) == Ordering::Equal);
1212 b.c1.add_assign(&Fq::one());
1213 assert!(a.cmp(&b) == Ordering::Less);
1214 a.c0.add_assign(&Fq::one());
1215 assert!(a.cmp(&b) == Ordering::Less);
1216 a.c1.add_assign(&Fq::one());
1217 assert!(a.cmp(&b) == Ordering::Greater);
1218 b.c0.add_assign(&Fq::one());
1219 assert!(a.cmp(&b) == Ordering::Equal);
1220}
1221
1222#[test]
1223fn test_fq2_basics() {
1224 assert_eq!(Fq2::new(Fq::zero(), Fq::zero(),), Fq2::zero());
1225 assert_eq!(Fq2::new(Fq::one(), Fq::zero(),), Fq2::one());
1226 assert!(Fq2::zero().is_zero());
1227 assert!(!Fq2::one().is_zero());
1228 assert!(!Fq2::new(Fq::zero(), Fq::one(),).is_zero());
1229}
1230
1231#[test]
1232fn test_fq2_squaring() {
1233 let a = Fq2::new(Fq::one(), Fq::one()).square(); // u + 1
1234 assert_eq!(
1235 a,
1236 Fq2::new(Fq::zero(), Fq::from(BigInteger384::from(2u64)),)
1237 ); // 2u
1238
1239 let a = Fq2::new(Fq::zero(), Fq::one()).square(); // u
1240 assert_eq!(a, {
1241 let neg1 = -Fq::one();
1242 Fq2::new(neg1, Fq::zero())
1243 }); // -1
1244
1245 let mut a = Fq2::new(
1246 Fq::from(BigInt::new([
1247 0x9c2c6309bbf8b598,
1248 0x4eef5c946536f602,
1249 0x90e34aab6fb6a6bd,
1250 0xf7f295a94e58ae7c,
1251 0x41b76dcc1c3fbe5e,
1252 0x7080c5fa1d8e042,
1253 ])),
1254 Fq::from(BigInt::new([
1255 0x38f473b3c870a4ab,
1256 0x6ad3291177c8c7e5,
1257 0xdac5a4c911a4353e,
1258 0xbfb99020604137a0,
1259 0xfc58a7b7be815407,
1260 0x10d1615e75250a21,
1261 ])),
1262 );
1263 a.square_in_place();
1264 assert_eq!(
1265 a,
1266 Fq2::new(
1267 Fq::from(BigInt::new([
1268 0xf262c28c538bcf68,
1269 0xb9f2a66eae1073ba,
1270 0xdc46ab8fad67ae0,
1271 0xcb674157618da176,
1272 0x4cf17b5893c3d327,
1273 0x7eac81369c43361,
1274 ])),
1275 Fq::from(BigInt::new([
1276 0xc1579cf58e980cf8,
1277 0xa23eb7e12dd54d98,
1278 0xe75138bce4cec7aa,
1279 0x38d0d7275a9689e1,
1280 0x739c983042779a65,
1281 0x1542a61c8a8db994,
1282 ])),
1283 )
1284 );
1285}
1286
1287#[test]
1288fn test_fq2_mul() {
1289 let mut a = Fq2::new(
1290 Fq::from(BigInt::new([
1291 0x85c9f989e1461f03,
1292 0xa2e33c333449a1d6,
1293 0x41e461154a7354a3,
1294 0x9ee53e7e84d7532e,
1295 0x1c202d8ed97afb45,
1296 0x51d3f9253e2516f,
1297 ])),
1298 Fq::from(BigInt::new([
1299 0xa7348a8b511aedcf,
1300 0x143c215d8176b319,
1301 0x4cc48081c09b8903,
1302 0x9533e4a9a5158be,
1303 0x7a5e1ecb676d65f9,
1304 0x180c3ee46656b008,
1305 ])),
1306 );
1307 a.mul_assign(&Fq2::new(
1308 Fq::from(BigInt::new([
1309 0xe21f9169805f537e,
1310 0xfc87e62e179c285d,
1311 0x27ece175be07a531,
1312 0xcd460f9f0c23e430,
1313 0x6c9110292bfa409,
1314 0x2c93a72eb8af83e,
1315 ])),
1316 Fq::from(BigInt::new([
1317 0x4b1c3f936d8992d4,
1318 0x1d2a72916dba4c8a,
1319 0x8871c508658d1e5f,
1320 0x57a06d3135a752ae,
1321 0x634cd3c6c565096d,
1322 0x19e17334d4e93558,
1323 ])),
1324 ));
1325 assert_eq!(
1326 a,
1327 Fq2::new(
1328 Fq::from(BigInt::new([
1329 0x95b5127e6360c7e4,
1330 0xde29c31a19a6937e,
1331 0xf61a96dacf5a39bc,
1332 0x5511fe4d84ee5f78,
1333 0x5310a202d92f9963,
1334 0x1751afbe166e5399,
1335 ])),
1336 Fq::from(BigInt::new([
1337 0x84af0e1bd630117a,
1338 0x6c63cd4da2c2aa7,
1339 0x5ba6e5430e883d40,
1340 0xc975106579c275ee,
1341 0x33a9ac82ce4c5083,
1342 0x1ef1a36c201589d,
1343 ])),
1344 )
1345 );
1346}
1347
1348#[test]
1349fn test_fq2_inverse() {
1350 assert!(Fq2::zero().inverse().is_none());
1351
1352 let a = Fq2::new(
1353 Fq::from(BigInt::new([
1354 0x85c9f989e1461f03,
1355 0xa2e33c333449a1d6,
1356 0x41e461154a7354a3,
1357 0x9ee53e7e84d7532e,
1358 0x1c202d8ed97afb45,
1359 0x51d3f9253e2516f,
1360 ])),
1361 Fq::from(BigInt::new([
1362 0xa7348a8b511aedcf,
1363 0x143c215d8176b319,
1364 0x4cc48081c09b8903,
1365 0x9533e4a9a5158be,
1366 0x7a5e1ecb676d65f9,
1367 0x180c3ee46656b008,
1368 ])),
1369 );
1370 let a = a.inverse().unwrap();
1371 assert_eq!(
1372 a,
1373 Fq2::new(
1374 Fq::from(BigInt::new([
1375 0x70300f9bcb9e594,
1376 0xe5ecda5fdafddbb2,
1377 0x64bef617d2915a8f,
1378 0xdfba703293941c30,
1379 0xa6c3d8f9586f2636,
1380 0x1351ef01941b70c4,
1381 ])),
1382 Fq::from(BigInt::new([
1383 0x8c39fd76a8312cb4,
1384 0x15d7b6b95defbff0,
1385 0x947143f89faedee9,
1386 0xcbf651a0f367afb2,
1387 0xdf4e54f0d3ef15a6,
1388 0x103bdf241afb0019,
1389 ])),
1390 )
1391 );
1392}
1393
1394#[test]
1395fn test_fq2_addition() {
1396 let mut a = Fq2::new(
1397 Fq::from(BigInt::new([
1398 0x2d0078036923ffc7,
1399 0x11e59ea221a3b6d2,
1400 0x8b1a52e0a90f59ed,
1401 0xb966ce3bc2108b13,
1402 0xccc649c4b9532bf3,
1403 0xf8d295b2ded9dc,
1404 ])),
1405 Fq::from(BigInt::new([
1406 0x977df6efcdaee0db,
1407 0x946ae52d684fa7ed,
1408 0xbe203411c66fb3a5,
1409 0xb3f8afc0ee248cad,
1410 0x4e464dea5bcfd41e,
1411 0x12d1137b8a6a837,
1412 ])),
1413 );
1414 a.add_assign(&Fq2::new(
1415 Fq::from(BigInt::new([
1416 0x619a02d78dc70ef2,
1417 0xb93adfc9119e33e8,
1418 0x4bf0b99a9f0dca12,
1419 0x3b88899a42a6318f,
1420 0x986a4a62fa82a49d,
1421 0x13ce433fa26027f5,
1422 ])),
1423 Fq::from(BigInt::new([
1424 0x66323bf80b58b9b9,
1425 0xa1379b6facf6e596,
1426 0x402aef1fb797e32f,
1427 0x2236f55246d0d44d,
1428 0x4c8c1800eb104566,
1429 0x11d6e20e986c2085,
1430 ])),
1431 ));
1432 assert_eq!(
1433 a,
1434 Fq2::new(
1435 Fq::from(BigInt::new([
1436 0x8e9a7adaf6eb0eb9,
1437 0xcb207e6b3341eaba,
1438 0xd70b0c7b481d23ff,
1439 0xf4ef57d604b6bca2,
1440 0x65309427b3d5d090,
1441 0x14c715d5553f01d2,
1442 ])),
1443 Fq::from(BigInt::new([
1444 0xfdb032e7d9079a94,
1445 0x35a2809d15468d83,
1446 0xfe4b23317e0796d5,
1447 0xd62fa51334f560fa,
1448 0x9ad265eb46e01984,
1449 0x1303f3465112c8bc,
1450 ])),
1451 )
1452 );
1453}
1454
1455#[test]
1456fn test_fq2_subtraction() {
1457 let mut a = Fq2::new(
1458 Fq::from(BigInt::new([
1459 0x2d0078036923ffc7,
1460 0x11e59ea221a3b6d2,
1461 0x8b1a52e0a90f59ed,
1462 0xb966ce3bc2108b13,
1463 0xccc649c4b9532bf3,
1464 0xf8d295b2ded9dc,
1465 ])),
1466 Fq::from(BigInt::new([
1467 0x977df6efcdaee0db,
1468 0x946ae52d684fa7ed,
1469 0xbe203411c66fb3a5,
1470 0xb3f8afc0ee248cad,
1471 0x4e464dea5bcfd41e,
1472 0x12d1137b8a6a837,
1473 ])),
1474 );
1475 a.sub_assign(&Fq2::new(
1476 Fq::from(BigInt::new([
1477 0x619a02d78dc70ef2,
1478 0xb93adfc9119e33e8,
1479 0x4bf0b99a9f0dca12,
1480 0x3b88899a42a6318f,
1481 0x986a4a62fa82a49d,
1482 0x13ce433fa26027f5,
1483 ])),
1484 Fq::from(BigInt::new([
1485 0x66323bf80b58b9b9,
1486 0xa1379b6facf6e596,
1487 0x402aef1fb797e32f,
1488 0x2236f55246d0d44d,
1489 0x4c8c1800eb104566,
1490 0x11d6e20e986c2085,
1491 ])),
1492 ));
1493 assert_eq!(
1494 a,
1495 Fq2::new(
1496 Fq::from(BigInt::new([
1497 0x8565752bdb5c9b80,
1498 0x7756bed7c15982e9,
1499 0xa65a6be700b285fe,
1500 0xe255902672ef6c43,
1501 0x7f77a718021c342d,
1502 0x72ba14049fe9881,
1503 ])),
1504 Fq::from(BigInt::new([
1505 0xeb4abaf7c255d1cd,
1506 0x11df49bc6cacc256,
1507 0xe52617930588c69a,
1508 0xf63905f39ad8cb1f,
1509 0x4cd5dd9fb40b3b8f,
1510 0x957411359ba6e4c,
1511 ])),
1512 )
1513 );
1514}
1515
1516#[test]
1517fn test_fq2_negation() {
1518 let mut a = Fq2::new(
1519 Fq::from(BigInt::new([
1520 0x2d0078036923ffc7,
1521 0x11e59ea221a3b6d2,
1522 0x8b1a52e0a90f59ed,
1523 0xb966ce3bc2108b13,
1524 0xccc649c4b9532bf3,
1525 0xf8d295b2ded9dc,
1526 ])),
1527 Fq::from(BigInt::new([
1528 0x977df6efcdaee0db,
1529 0x946ae52d684fa7ed,
1530 0xbe203411c66fb3a5,
1531 0xb3f8afc0ee248cad,
1532 0x4e464dea5bcfd41e,
1533 0x12d1137b8a6a837,
1534 ])),
1535 );
1536 a = -a;
1537 assert_eq!(
1538 a,
1539 Fq2::new(
1540 Fq::from(BigInt::new([
1541 0x8cfe87fc96dbaae4,
1542 0xcc6615c8fb0492d,
1543 0xdc167fc04da19c37,
1544 0xab107d49317487ab,
1545 0x7e555df189f880e3,
1546 0x19083f5486a10cbd,
1547 ])),
1548 Fq::from(BigInt::new([
1549 0x228109103250c9d0,
1550 0x8a411ad149045812,
1551 0xa9109e8f3041427e,
1552 0xb07e9bc405608611,
1553 0xfcd559cbe77bd8b8,
1554 0x18d400b280d93e62,
1555 ])),
1556 )
1557 );
1558}
1559
1560#[test]
1561fn test_fq2_doubling() {
1562 let mut a = Fq2::new(
1563 Fq::from(BigInt::new([
1564 0x2d0078036923ffc7,
1565 0x11e59ea221a3b6d2,
1566 0x8b1a52e0a90f59ed,
1567 0xb966ce3bc2108b13,
1568 0xccc649c4b9532bf3,
1569 0xf8d295b2ded9dc,
1570 ])),
1571 Fq::from(BigInt::new([
1572 0x977df6efcdaee0db,
1573 0x946ae52d684fa7ed,
1574 0xbe203411c66fb3a5,
1575 0xb3f8afc0ee248cad,
1576 0x4e464dea5bcfd41e,
1577 0x12d1137b8a6a837,
1578 ])),
1579 );
1580 a.double_in_place();
1581 assert_eq!(
1582 a,
1583 Fq2::new(
1584 Fq::from(BigInt::new([
1585 0x5a00f006d247ff8e,
1586 0x23cb3d4443476da4,
1587 0x1634a5c1521eb3da,
1588 0x72cd9c7784211627,
1589 0x998c938972a657e7,
1590 0x1f1a52b65bdb3b9,
1591 ])),
1592 Fq::from(BigInt::new([
1593 0x2efbeddf9b5dc1b6,
1594 0x28d5ca5ad09f4fdb,
1595 0x7c4068238cdf674b,
1596 0x67f15f81dc49195b,
1597 0x9c8c9bd4b79fa83d,
1598 0x25a226f714d506e,
1599 ])),
1600 )
1601 );
1602}
1603
1604#[test]
1605fn test_fq2_frobenius_map_in_place() {
1606 let mut a = Fq2::new(
1607 Fq::from(BigInt::new([
1608 0x2d0078036923ffc7,
1609 0x11e59ea221a3b6d2,
1610 0x8b1a52e0a90f59ed,
1611 0xb966ce3bc2108b13,
1612 0xccc649c4b9532bf3,
1613 0xf8d295b2ded9dc,
1614 ])),
1615 Fq::from(BigInt::new([
1616 0x977df6efcdaee0db,
1617 0x946ae52d684fa7ed,
1618 0xbe203411c66fb3a5,
1619 0xb3f8afc0ee248cad,
1620 0x4e464dea5bcfd41e,
1621 0x12d1137b8a6a837,
1622 ])),
1623 );
1624 a.frobenius_map_in_place(0);
1625 assert_eq!(
1626 a,
1627 Fq2::new(
1628 Fq::from(BigInt::new([
1629 0x2d0078036923ffc7,
1630 0x11e59ea221a3b6d2,
1631 0x8b1a52e0a90f59ed,
1632 0xb966ce3bc2108b13,
1633 0xccc649c4b9532bf3,
1634 0xf8d295b2ded9dc,
1635 ])),
1636 Fq::from(BigInt::new([
1637 0x977df6efcdaee0db,
1638 0x946ae52d684fa7ed,
1639 0xbe203411c66fb3a5,
1640 0xb3f8afc0ee248cad,
1641 0x4e464dea5bcfd41e,
1642 0x12d1137b8a6a837,
1643 ])),
1644 )
1645 );
1646 a.frobenius_map_in_place(1);
1647 assert_eq!(
1648 a,
1649 Fq2::new(
1650 Fq::from(BigInt::new([
1651 0x2d0078036923ffc7,
1652 0x11e59ea221a3b6d2,
1653 0x8b1a52e0a90f59ed,
1654 0xb966ce3bc2108b13,
1655 0xccc649c4b9532bf3,
1656 0xf8d295b2ded9dc,
1657 ])),
1658 Fq::from(BigInt::new([
1659 0x228109103250c9d0,
1660 0x8a411ad149045812,
1661 0xa9109e8f3041427e,
1662 0xb07e9bc405608611,
1663 0xfcd559cbe77bd8b8,
1664 0x18d400b280d93e62,
1665 ])),
1666 )
1667 );
1668 a.frobenius_map_in_place(1);
1669 assert_eq!(
1670 a,
1671 Fq2::new(
1672 Fq::from(BigInt::new([
1673 0x2d0078036923ffc7,
1674 0x11e59ea221a3b6d2,
1675 0x8b1a52e0a90f59ed,
1676 0xb966ce3bc2108b13,
1677 0xccc649c4b9532bf3,
1678 0xf8d295b2ded9dc,
1679 ])),
1680 Fq::from(BigInt::new([
1681 0x977df6efcdaee0db,
1682 0x946ae52d684fa7ed,
1683 0xbe203411c66fb3a5,
1684 0xb3f8afc0ee248cad,
1685 0x4e464dea5bcfd41e,
1686 0x12d1137b8a6a837,
1687 ])),
1688 )
1689 );
1690 a.frobenius_map_in_place(2);
1691 assert_eq!(
1692 a,
1693 Fq2::new(
1694 Fq::from(BigInt::new([
1695 0x2d0078036923ffc7,
1696 0x11e59ea221a3b6d2,
1697 0x8b1a52e0a90f59ed,
1698 0xb966ce3bc2108b13,
1699 0xccc649c4b9532bf3,
1700 0xf8d295b2ded9dc,
1701 ])),
1702 Fq::from(BigInt::new([
1703 0x977df6efcdaee0db,
1704 0x946ae52d684fa7ed,
1705 0xbe203411c66fb3a5,
1706 0xb3f8afc0ee248cad,
1707 0x4e464dea5bcfd41e,
1708 0x12d1137b8a6a837,
1709 ])),
1710 )
1711 );
1712}
1713
1714#[test]
1715fn test_fq2_legendre() {
1716 use ark_ff::fields::LegendreSymbol::*;
1717
1718 assert_eq!(Zero, Fq2::zero().legendre());
1719 // i^2 = -1
1720 let mut m1 = -Fq2::one();
1721 assert_eq!(QuadraticResidue, m1.legendre());
1722 Fq6Config::mul_fp2_by_nonresidue_in_place(&mut m1);
1723 assert_eq!(QuadraticNonResidue, m1.legendre());
1724}
1725
1726#[test]
1727fn test_fq2_mul_nonresidue() {
1728 let mut rng = ark_std::test_rng();
1729
1730 let nqr = Fq2::new(Fq::one(), Fq::one());
1731
1732 for _ in 0..1000 {
1733 let mut a = Fq2::rand(&mut rng);
1734 let mut b = a;
1735 Fq6Config::mul_fp2_by_nonresidue_in_place(&mut a);
1736 b.mul_assign(&nqr);
1737
1738 assert_eq!(a, b);
1739 }
1740}
1741
1742#[test]
1743fn test_fq6_mul_nonresidue() {
1744 let mut rng = ark_std::test_rng();
1745
1746 let nqr = Fq6::new(Fq2::zero(), Fq2::one(), Fq2::zero());
1747
1748 for _ in 0..1000 {
1749 let mut a = Fq6::rand(&mut rng);
1750 let mut b = a;
1751 Fq12Config::mul_fp6_by_nonresidue_in_place(&mut a);
1752 b.mul_assign(&nqr);
1753
1754 assert_eq!(a, b);
1755 }
1756}
1757
1758#[test]
1759fn test_fq6_mul_by_1() {
1760 let mut rng = ark_std::test_rng();
1761
1762 for _ in 0..1000 {
1763 let c1 = Fq2::rand(&mut rng);
1764 let mut a = Fq6::rand(&mut rng);
1765 let mut b = a;
1766
1767 a.mul_by_1(&c1);
1768 b.mul_assign(&Fq6::new(Fq2::zero(), c1, Fq2::zero()));
1769
1770 assert_eq!(a, b);
1771 }
1772}
1773
1774#[test]
1775fn test_fq6_mul_by_01() {
1776 let mut rng = ark_std::test_rng();
1777
1778 for _ in 0..1000 {
1779 let c0 = Fq2::rand(&mut rng);
1780 let c1 = Fq2::rand(&mut rng);
1781 let mut a = Fq6::rand(&mut rng);
1782 let mut b = a;
1783
1784 a.mul_by_01(&c0, &c1);
1785 b.mul_assign(&Fq6::new(c0, c1, Fq2::zero()));
1786
1787 assert_eq!(a, b);
1788 }
1789}
1790
1791#[test]
1792fn test_fq12_mul_by_014() {
1793 let mut rng = ark_std::test_rng();
1794
1795 for _ in 0..1000 {
1796 let c0 = Fq2::rand(&mut rng);
1797 let c1 = Fq2::rand(&mut rng);
1798 let c5 = Fq2::rand(&mut rng);
1799 let mut a = Fq12::rand(&mut rng);
1800 let mut b = a;
1801
1802 a.mul_by_014(&c0, &c1, &c5);
1803 b.mul_assign(&Fq12::new(
1804 Fq6::new(c0, c1, Fq2::zero()),
1805 Fq6::new(Fq2::zero(), c5, Fq2::zero()),
1806 ));
1807
1808 assert_eq!(a, b);
1809 }
1810}