ark-curves-cherry-picked/bls12_381/src/fields/tests.rs
bls12_381/src/fields/tests.rsRaw
1use ark_algebra_test_templates::{
2 fields::*, generate_field_serialization_test, generate_field_test,
3};
4use ark_ff::{
5 biginteger::{BigInt, BigInteger, BigInteger384},
6 fields::{FftField, Field, Fp12Config, Fp2Config, Fp6Config, PrimeField, SquareRootField},
7 One, UniformRand, Zero,
8};
9use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
10use ark_std::{
11 cmp::Ordering,
12 ops::{AddAssign, MulAssign, SubAssign},
13 rand::Rng,
14 test_rng, vec,
15};
16
17use crate::{Fq, Fq12, Fq12Config, Fq2, Fq2Config, Fq6, Fq6Config, FqConfig, Fr, FrConfig};
18
19generate_field_test!(bls12_381; fq2; fq6; fq12; mont(6, 4); );
20generate_field_serialization_test!(bls12_381; fq2; fq6; fq12;);
21
22#[test]
23fn test_negative_one() {
24 let neg_one = Fq::new(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_neg_one() {
744 let o = -Fq::one();
745
746 let thing: [u64; 6] = [
747 0x43f5fffffffcaaae,
748 0x32b7fff2ed47fffd,
749 0x7e83a49a2e99d69,
750 0xeca8f3318332bb7a,
751 0xef148d1ea0f4c069,
752 0x40ab3263eff0206,
753 ];
754 let negative_one = Fq::new(BigInt::new(thing));
755
756 assert_eq!(negative_one, o);
757}
758
759#[test]
760fn test_fq_repr_from() {
761 assert_eq!(BigInt::from(100u64), BigInt::new([100, 0, 0, 0, 0, 0]));
762}
763
764#[test]
765fn test_fq_repr_is_odd() {
766 assert!(!BigInteger384::from(0u64).is_odd());
767 assert!(BigInteger384::from(0u64).is_even());
768 assert!(BigInteger384::from(1u64).is_odd());
769 assert!(!BigInteger384::from(1u64).is_even());
770 assert!(!BigInteger384::from(324834872u64).is_odd());
771 assert!(BigInteger384::from(324834872u64).is_even());
772 assert!(BigInteger384::from(324834873u64).is_odd());
773 assert!(!BigInteger384::from(324834873u64).is_even());
774}
775
776#[test]
777fn test_fq_repr_is_zero() {
778 assert!(BigInteger384::from(0u64).is_zero());
779 assert!(!BigInteger384::from(1u64).is_zero());
780 assert!(!BigInt::new([0, 0, 0, 0, 1, 0]).is_zero());
781}
782
783#[test]
784fn test_fq_repr_div2() {
785 let mut a = BigInt::new([
786 0x8b0ad39f8dd7482a,
787 0x147221c9a7178b69,
788 0x54764cb08d8a6aa0,
789 0x8519d708e1d83041,
790 0x41f82777bd13fdb,
791 0xf43944578f9b771b,
792 ]);
793 a.div2();
794 assert_eq!(
795 a,
796 BigInt::new([
797 0xc58569cfc6eba415,
798 0xa3910e4d38bc5b4,
799 0xaa3b265846c53550,
800 0xc28ceb8470ec1820,
801 0x820fc13bbde89fed,
802 0x7a1ca22bc7cdbb8d,
803 ])
804 );
805 for _ in 0..10 {
806 a.div2();
807 }
808 assert_eq!(
809 a,
810 BigInt::new([
811 0x6d31615a73f1bae9,
812 0x54028e443934e2f1,
813 0x82a8ec99611b14d,
814 0xfb70a33ae11c3b06,
815 0xe36083f04eef7a27,
816 0x1e87288af1f36e,
817 ])
818 );
819 for _ in 0..300 {
820 a.div2();
821 }
822 assert_eq!(
823 a,
824 BigInt::new([0x7288af1f36ee3608, 0x1e8, 0x0, 0x0, 0x0, 0x0])
825 );
826 for _ in 0..50 {
827 a.div2();
828 }
829 assert_eq!(a, BigInt::new([0x7a1ca2, 0x0, 0x0, 0x0, 0x0, 0x0]));
830 for _ in 0..22 {
831 a.div2();
832 }
833 assert_eq!(a, BigInt::new([0x1, 0x0, 0x0, 0x0, 0x0, 0x0]));
834 a.div2();
835 assert!(a.is_zero());
836}
837
838#[test]
839fn test_fq_repr_divn() {
840 let mut a = BigInt::new([
841 0xaa5cdd6172847ffd,
842 0x43242c06aed55287,
843 0x9ddd5b312f3dd104,
844 0xc5541fd48046b7e7,
845 0x16080cf4071e0b05,
846 0x1225f2901aea514e,
847 ]);
848 a.divn(0);
849 assert_eq!(
850 a,
851 BigInt::new([
852 0xaa5cdd6172847ffd,
853 0x43242c06aed55287,
854 0x9ddd5b312f3dd104,
855 0xc5541fd48046b7e7,
856 0x16080cf4071e0b05,
857 0x1225f2901aea514e,
858 ])
859 );
860 a.divn(1);
861 assert_eq!(
862 a,
863 BigInt::new([
864 0xd52e6eb0b9423ffe,
865 0x21921603576aa943,
866 0xceeead98979ee882,
867 0xe2aa0fea40235bf3,
868 0xb04067a038f0582,
869 0x912f9480d7528a7,
870 ])
871 );
872 a.divn(50);
873 assert_eq!(
874 a,
875 BigInt::new([
876 0x8580d5daaa50f54b,
877 0xab6625e7ba208864,
878 0x83fa9008d6fcf3bb,
879 0x19e80e3c160b8aa,
880 0xbe52035d4a29c2c1,
881 0x244,
882 ])
883 );
884 a.divn(130);
885 assert_eq!(
886 a,
887 BigInt::new([
888 0xa0fea40235bf3cee,
889 0x4067a038f0582e2a,
890 0x2f9480d7528a70b0,
891 0x91,
892 0x0,
893 0x0,
894 ])
895 );
896 a.divn(64);
897 assert_eq!(
898 a,
899 BigInt::new([0x4067a038f0582e2a, 0x2f9480d7528a70b0, 0x91, 0x0, 0x0, 0x0])
900 );
901}
902
903#[test]
904fn test_fq_repr_mul2() {
905 let mut a = BigInteger384::from(23712937547u64);
906 a.mul2();
907 assert_eq!(a, BigInt::new([0xb0acd6c96, 0x0, 0x0, 0x0, 0x0, 0x0]));
908 for _ in 0..60 {
909 a.mul2();
910 }
911 assert_eq!(
912 a,
913 BigInt::new([0x6000000000000000, 0xb0acd6c9, 0x0, 0x0, 0x0, 0x0])
914 );
915 for _ in 0..300 {
916 a.mul2();
917 }
918 assert_eq!(
919 a,
920 BigInt::new([0x0, 0x0, 0x0, 0x0, 0x0, 0xcd6c960000000000])
921 );
922 for _ in 0..17 {
923 a.mul2();
924 }
925 assert_eq!(
926 a,
927 BigInt::new([0x0, 0x0, 0x0, 0x0, 0x0, 0x2c00000000000000])
928 );
929 for _ in 0..6 {
930 a.mul2();
931 }
932 assert!(a.is_zero());
933}
934
935#[test]
936fn test_fq_repr_num_bits() {
937 let mut a = BigInteger384::from(0u64);
938 assert_eq!(0, a.num_bits());
939 a = BigInteger384::from(1u64);
940 for i in 1..385 {
941 assert_eq!(i, a.num_bits());
942 a.mul2();
943 }
944 assert_eq!(0, a.num_bits());
945}
946
947#[test]
948fn test_fq_repr_sub_noborrow() {
949 let mut rng = ark_std::test_rng();
950
951 let mut t = BigInt::new([
952 0x827a4a08041ebd9,
953 0x3c239f3dcc8f0d6b,
954 0x9ab46a912d555364,
955 0x196936b17b43910b,
956 0xad0eb3948a5c34fd,
957 0xd56f7b5ab8b5ce8,
958 ]);
959 t.sub_with_borrow(&BigInt::new([
960 0xc7867917187ca02b,
961 0x5d75679d4911ffef,
962 0x8c5b3e48b1a71c15,
963 0x6a427ae846fd66aa,
964 0x7a37e7265ee1eaf9,
965 0x7c0577a26f59d5,
966 ]));
967 assert!(
968 t == BigInt::new([
969 0x40a12b8967c54bae,
970 0xdeae37a0837d0d7b,
971 0xe592c487bae374e,
972 0xaf26bbc934462a61,
973 0x32d6cc6e2b7a4a03,
974 0xcdaf23e091c0313,
975 ])
976 );
977
978 for _ in 0..1000 {
979 let mut a = BigInteger384::rand(&mut rng);
980 a.0[5] >>= 30;
981 let mut b = a;
982 for _ in 0..10 {
983 b.mul2();
984 }
985 let mut c = b;
986 for _ in 0..10 {
987 c.mul2();
988 }
989
990 assert!(a < b);
991 assert!(b < c);
992
993 let mut csub_ba = c;
994 csub_ba.sub_with_borrow(&b);
995 csub_ba.sub_with_borrow(&a);
996
997 let mut csub_ab = c;
998 csub_ab.sub_with_borrow(&a);
999 csub_ab.sub_with_borrow(&b);
1000
1001 assert_eq!(csub_ab, csub_ba);
1002 }
1003
1004 // Subtracting q+1 from q should produce -1 (mod 2**384)
1005 let mut qplusone = BigInt::new([
1006 0xb9feffffffffaaab,
1007 0x1eabfffeb153ffff,
1008 0x6730d2a0f6b0f624,
1009 0x64774b84f38512bf,
1010 0x4b1ba7b6434bacd7,
1011 0x1a0111ea397fe69a,
1012 ]);
1013 qplusone.sub_with_borrow(&BigInt::new([
1014 0xb9feffffffffaaac,
1015 0x1eabfffeb153ffff,
1016 0x6730d2a0f6b0f624,
1017 0x64774b84f38512bf,
1018 0x4b1ba7b6434bacd7,
1019 0x1a0111ea397fe69a,
1020 ]));
1021 assert_eq!(
1022 qplusone,
1023 BigInt::new([
1024 0xffffffffffffffff,
1025 0xffffffffffffffff,
1026 0xffffffffffffffff,
1027 0xffffffffffffffff,
1028 0xffffffffffffffff,
1029 0xffffffffffffffff,
1030 ])
1031 );
1032}
1033
1034#[test]
1035fn test_fq_repr_add_nocarry() {
1036 let mut rng = ark_std::test_rng();
1037
1038 let mut t = BigInt::new([
1039 0x827a4a08041ebd9,
1040 0x3c239f3dcc8f0d6b,
1041 0x9ab46a912d555364,
1042 0x196936b17b43910b,
1043 0xad0eb3948a5c34fd,
1044 0xd56f7b5ab8b5ce8,
1045 ]);
1046 t.add_with_carry(&BigInt::new([
1047 0xc7867917187ca02b,
1048 0x5d75679d4911ffef,
1049 0x8c5b3e48b1a71c15,
1050 0x6a427ae846fd66aa,
1051 0x7a37e7265ee1eaf9,
1052 0x7c0577a26f59d5,
1053 ]));
1054 assert!(
1055 t == BigInt::new([
1056 0xcfae1db798be8c04,
1057 0x999906db15a10d5a,
1058 0x270fa8d9defc6f79,
1059 0x83abb199c240f7b6,
1060 0x27469abae93e1ff6,
1061 0xdd2fd2d4dfab6be,
1062 ])
1063 );
1064
1065 // Test for the associativity of addition.
1066 for _ in 0..1000 {
1067 let mut a = BigInteger384::rand(&mut rng);
1068 let mut b = BigInteger384::rand(&mut rng);
1069 let mut c = BigInteger384::rand(&mut rng);
1070
1071 // Unset the first few bits, so that overflow won't occur.
1072 a.0[5] >>= 3;
1073 b.0[5] >>= 3;
1074 c.0[5] >>= 3;
1075
1076 let mut abc = a;
1077 abc.add_with_carry(&b);
1078 abc.add_with_carry(&c);
1079
1080 let mut acb = a;
1081 acb.add_with_carry(&c);
1082 acb.add_with_carry(&b);
1083
1084 let mut bac = b;
1085 bac.add_with_carry(&a);
1086 bac.add_with_carry(&c);
1087
1088 let mut bca = b;
1089 bca.add_with_carry(&c);
1090 bca.add_with_carry(&a);
1091
1092 let mut cab = c;
1093 cab.add_with_carry(&a);
1094 cab.add_with_carry(&b);
1095
1096 let mut cba = c;
1097 cba.add_with_carry(&b);
1098 cba.add_with_carry(&a);
1099
1100 assert_eq!(abc, acb);
1101 assert_eq!(abc, bac);
1102 assert_eq!(abc, bca);
1103 assert_eq!(abc, cab);
1104 assert_eq!(abc, cba);
1105 }
1106
1107 // Adding 1 to (2^384 - 1) should produce zero
1108 let mut x = BigInt::new([
1109 0xffffffffffffffff,
1110 0xffffffffffffffff,
1111 0xffffffffffffffff,
1112 0xffffffffffffffff,
1113 0xffffffffffffffff,
1114 0xffffffffffffffff,
1115 ]);
1116 x.add_with_carry(&BigInteger384::from(1u64));
1117 assert!(x.is_zero());
1118}
1119
1120#[test]
1121fn test_fq2_sqrt() {
1122 // 1 has a sqrt in the base field
1123 let fq2_sqrt = Fq2::new(Fq::one(), Fq::zero()).sqrt().unwrap();
1124 assert_eq!(fq2_sqrt.c0, Fq::one());
1125 assert_eq!(fq2_sqrt.c1, Fq::zero());
1126
1127 // -1 has no sqrt in the base field, but should be valid in Fq2
1128 let fq2_sqrt = Fq2::new(-Fq::one(), Fq::zero()).sqrt().unwrap();
1129 assert_eq!(fq2_sqrt.c0, Fq::zero());
1130 assert_eq!(fq2_sqrt.c1, Fq::one());
1131}
1132
1133#[test]
1134fn test_fq_num_bits() {
1135 assert_eq!(Fq::MODULUS_BIT_SIZE, 381);
1136}
1137
1138#[test]
1139fn test_fq_root_of_unity() {
1140 assert_eq!(Fq::TWO_ADICITY, 1);
1141 assert_eq!(Fq::GENERATOR, Fq::from(BigInteger384::from(2u64)));
1142 assert_eq!(
1143 Fq::GENERATOR.pow([
1144 0xdcff7fffffffd555,
1145 0xf55ffff58a9ffff,
1146 0xb39869507b587b12,
1147 0xb23ba5c279c2895f,
1148 0x258dd3db21a5d66b,
1149 0xd0088f51cbff34d,
1150 ]),
1151 Fq::TWO_ADIC_ROOT_OF_UNITY
1152 );
1153 assert_eq!(
1154 Fq::TWO_ADIC_ROOT_OF_UNITY.pow([1 << Fq::TWO_ADICITY]),
1155 Fq::one()
1156 );
1157 assert!(Fq::GENERATOR.sqrt().is_none());
1158}
1159
1160// #[test]
1161// fn fq_field_tests() {
1162// ::tests::field::random_field_tests::<Fq>();
1163// ::tests::field::random_sqrt_tests::<Fq>();
1164// ::tests::field::random_frobenius_tests::<Fq, _>(Fq::char(), 13);
1165// ::tests::field::from_str_tests::<Fq>();
1166// }
1167
1168#[test]
1169fn test_fq_ordering() {
1170 // BigInteger384's ordering is well-tested, but we still need to make sure the
1171 // Fq elements aren't being compared in Montgomery form.
1172 for i in 0..100u64 {
1173 assert!(Fq::from(BigInteger384::from(i + 1)) > Fq::from(BigInteger384::from(i)));
1174 }
1175}
1176
1177// #[test]
1178// fn fq_repr_tests() {
1179// ::tests::repr::random_repr_tests::<BigInteger384>();
1180// }
1181
1182#[test]
1183fn test_fq_legendre() {
1184 use ark_ff::fields::LegendreSymbol::*;
1185
1186 assert_eq!(QuadraticResidue, Fq::one().legendre());
1187 assert_eq!(Zero, Fq::zero().legendre());
1188
1189 assert_eq!(
1190 QuadraticNonResidue,
1191 Fq::from(BigInteger384::from(2u64)).legendre()
1192 );
1193 assert_eq!(
1194 QuadraticResidue,
1195 Fq::from(BigInteger384::from(4u64)).legendre()
1196 );
1197
1198 let e = BigInt::new([
1199 0x52a112f249778642,
1200 0xd0bedb989b7991f,
1201 0xdad3b6681aa63c05,
1202 0xf2efc0bb4721b283,
1203 0x6057a98f18c24733,
1204 0x1022c2fd122889e4,
1205 ]);
1206 assert_eq!(QuadraticNonResidue, Fq::from(e).legendre());
1207 let e = BigInt::new([
1208 0x6dae594e53a96c74,
1209 0x19b16ca9ba64b37b,
1210 0x5c764661a59bfc68,
1211 0xaa346e9b31c60a,
1212 0x346059f9d87a9fa9,
1213 0x1d61ac6bfd5c88b,
1214 ]);
1215 assert_eq!(QuadraticResidue, Fq::from(e).legendre());
1216}
1217
1218#[test]
1219fn test_fq2_ordering() {
1220 let mut a = Fq2::new(Fq::zero(), Fq::zero());
1221
1222 let mut b = a.clone();
1223
1224 assert!(a.cmp(&b) == Ordering::Equal);
1225 b.c0.add_assign(&Fq::one());
1226 assert!(a.cmp(&b) == Ordering::Less);
1227 a.c0.add_assign(&Fq::one());
1228 assert!(a.cmp(&b) == Ordering::Equal);
1229 b.c1.add_assign(&Fq::one());
1230 assert!(a.cmp(&b) == Ordering::Less);
1231 a.c0.add_assign(&Fq::one());
1232 assert!(a.cmp(&b) == Ordering::Less);
1233 a.c1.add_assign(&Fq::one());
1234 assert!(a.cmp(&b) == Ordering::Greater);
1235 b.c0.add_assign(&Fq::one());
1236 assert!(a.cmp(&b) == Ordering::Equal);
1237}
1238
1239#[test]
1240fn test_fq2_basics() {
1241 assert_eq!(Fq2::new(Fq::zero(), Fq::zero(),), Fq2::zero());
1242 assert_eq!(Fq2::new(Fq::one(), Fq::zero(),), Fq2::one());
1243 assert!(Fq2::zero().is_zero());
1244 assert!(!Fq2::one().is_zero());
1245 assert!(!Fq2::new(Fq::zero(), Fq::one(),).is_zero());
1246}
1247
1248#[test]
1249fn test_fq2_squaring() {
1250 let a = Fq2::new(Fq::one(), Fq::one()).square(); // u + 1
1251 assert_eq!(
1252 a,
1253 Fq2::new(Fq::zero(), Fq::from(BigInteger384::from(2u64)),)
1254 ); // 2u
1255
1256 let a = Fq2::new(Fq::zero(), Fq::one()).square(); // u
1257 assert_eq!(a, {
1258 let neg1 = -Fq::one();
1259 Fq2::new(neg1, Fq::zero())
1260 }); // -1
1261
1262 let mut a = Fq2::new(
1263 Fq::from(BigInt::new([
1264 0x9c2c6309bbf8b598,
1265 0x4eef5c946536f602,
1266 0x90e34aab6fb6a6bd,
1267 0xf7f295a94e58ae7c,
1268 0x41b76dcc1c3fbe5e,
1269 0x7080c5fa1d8e042,
1270 ])),
1271 Fq::from(BigInt::new([
1272 0x38f473b3c870a4ab,
1273 0x6ad3291177c8c7e5,
1274 0xdac5a4c911a4353e,
1275 0xbfb99020604137a0,
1276 0xfc58a7b7be815407,
1277 0x10d1615e75250a21,
1278 ])),
1279 );
1280 a.square_in_place();
1281 assert_eq!(
1282 a,
1283 Fq2::new(
1284 Fq::from(BigInt::new([
1285 0xf262c28c538bcf68,
1286 0xb9f2a66eae1073ba,
1287 0xdc46ab8fad67ae0,
1288 0xcb674157618da176,
1289 0x4cf17b5893c3d327,
1290 0x7eac81369c43361,
1291 ])),
1292 Fq::from(BigInt::new([
1293 0xc1579cf58e980cf8,
1294 0xa23eb7e12dd54d98,
1295 0xe75138bce4cec7aa,
1296 0x38d0d7275a9689e1,
1297 0x739c983042779a65,
1298 0x1542a61c8a8db994,
1299 ])),
1300 )
1301 );
1302}
1303
1304#[test]
1305fn test_fq2_mul() {
1306 let mut a = Fq2::new(
1307 Fq::from(BigInt::new([
1308 0x85c9f989e1461f03,
1309 0xa2e33c333449a1d6,
1310 0x41e461154a7354a3,
1311 0x9ee53e7e84d7532e,
1312 0x1c202d8ed97afb45,
1313 0x51d3f9253e2516f,
1314 ])),
1315 Fq::from(BigInt::new([
1316 0xa7348a8b511aedcf,
1317 0x143c215d8176b319,
1318 0x4cc48081c09b8903,
1319 0x9533e4a9a5158be,
1320 0x7a5e1ecb676d65f9,
1321 0x180c3ee46656b008,
1322 ])),
1323 );
1324 a.mul_assign(&Fq2::new(
1325 Fq::from(BigInt::new([
1326 0xe21f9169805f537e,
1327 0xfc87e62e179c285d,
1328 0x27ece175be07a531,
1329 0xcd460f9f0c23e430,
1330 0x6c9110292bfa409,
1331 0x2c93a72eb8af83e,
1332 ])),
1333 Fq::from(BigInt::new([
1334 0x4b1c3f936d8992d4,
1335 0x1d2a72916dba4c8a,
1336 0x8871c508658d1e5f,
1337 0x57a06d3135a752ae,
1338 0x634cd3c6c565096d,
1339 0x19e17334d4e93558,
1340 ])),
1341 ));
1342 assert_eq!(
1343 a,
1344 Fq2::new(
1345 Fq::from(BigInt::new([
1346 0x95b5127e6360c7e4,
1347 0xde29c31a19a6937e,
1348 0xf61a96dacf5a39bc,
1349 0x5511fe4d84ee5f78,
1350 0x5310a202d92f9963,
1351 0x1751afbe166e5399,
1352 ])),
1353 Fq::from(BigInt::new([
1354 0x84af0e1bd630117a,
1355 0x6c63cd4da2c2aa7,
1356 0x5ba6e5430e883d40,
1357 0xc975106579c275ee,
1358 0x33a9ac82ce4c5083,
1359 0x1ef1a36c201589d,
1360 ])),
1361 )
1362 );
1363}
1364
1365#[test]
1366fn test_fq2_inverse() {
1367 assert!(Fq2::zero().inverse().is_none());
1368
1369 let a = Fq2::new(
1370 Fq::from(BigInt::new([
1371 0x85c9f989e1461f03,
1372 0xa2e33c333449a1d6,
1373 0x41e461154a7354a3,
1374 0x9ee53e7e84d7532e,
1375 0x1c202d8ed97afb45,
1376 0x51d3f9253e2516f,
1377 ])),
1378 Fq::from(BigInt::new([
1379 0xa7348a8b511aedcf,
1380 0x143c215d8176b319,
1381 0x4cc48081c09b8903,
1382 0x9533e4a9a5158be,
1383 0x7a5e1ecb676d65f9,
1384 0x180c3ee46656b008,
1385 ])),
1386 );
1387 let a = a.inverse().unwrap();
1388 assert_eq!(
1389 a,
1390 Fq2::new(
1391 Fq::from(BigInt::new([
1392 0x70300f9bcb9e594,
1393 0xe5ecda5fdafddbb2,
1394 0x64bef617d2915a8f,
1395 0xdfba703293941c30,
1396 0xa6c3d8f9586f2636,
1397 0x1351ef01941b70c4,
1398 ])),
1399 Fq::from(BigInt::new([
1400 0x8c39fd76a8312cb4,
1401 0x15d7b6b95defbff0,
1402 0x947143f89faedee9,
1403 0xcbf651a0f367afb2,
1404 0xdf4e54f0d3ef15a6,
1405 0x103bdf241afb0019,
1406 ])),
1407 )
1408 );
1409}
1410
1411#[test]
1412fn test_fq2_addition() {
1413 let mut a = Fq2::new(
1414 Fq::from(BigInt::new([
1415 0x2d0078036923ffc7,
1416 0x11e59ea221a3b6d2,
1417 0x8b1a52e0a90f59ed,
1418 0xb966ce3bc2108b13,
1419 0xccc649c4b9532bf3,
1420 0xf8d295b2ded9dc,
1421 ])),
1422 Fq::from(BigInt::new([
1423 0x977df6efcdaee0db,
1424 0x946ae52d684fa7ed,
1425 0xbe203411c66fb3a5,
1426 0xb3f8afc0ee248cad,
1427 0x4e464dea5bcfd41e,
1428 0x12d1137b8a6a837,
1429 ])),
1430 );
1431 a.add_assign(&Fq2::new(
1432 Fq::from(BigInt::new([
1433 0x619a02d78dc70ef2,
1434 0xb93adfc9119e33e8,
1435 0x4bf0b99a9f0dca12,
1436 0x3b88899a42a6318f,
1437 0x986a4a62fa82a49d,
1438 0x13ce433fa26027f5,
1439 ])),
1440 Fq::from(BigInt::new([
1441 0x66323bf80b58b9b9,
1442 0xa1379b6facf6e596,
1443 0x402aef1fb797e32f,
1444 0x2236f55246d0d44d,
1445 0x4c8c1800eb104566,
1446 0x11d6e20e986c2085,
1447 ])),
1448 ));
1449 assert_eq!(
1450 a,
1451 Fq2::new(
1452 Fq::from(BigInt::new([
1453 0x8e9a7adaf6eb0eb9,
1454 0xcb207e6b3341eaba,
1455 0xd70b0c7b481d23ff,
1456 0xf4ef57d604b6bca2,
1457 0x65309427b3d5d090,
1458 0x14c715d5553f01d2,
1459 ])),
1460 Fq::from(BigInt::new([
1461 0xfdb032e7d9079a94,
1462 0x35a2809d15468d83,
1463 0xfe4b23317e0796d5,
1464 0xd62fa51334f560fa,
1465 0x9ad265eb46e01984,
1466 0x1303f3465112c8bc,
1467 ])),
1468 )
1469 );
1470}
1471
1472#[test]
1473fn test_fq2_subtraction() {
1474 let mut a = Fq2::new(
1475 Fq::from(BigInt::new([
1476 0x2d0078036923ffc7,
1477 0x11e59ea221a3b6d2,
1478 0x8b1a52e0a90f59ed,
1479 0xb966ce3bc2108b13,
1480 0xccc649c4b9532bf3,
1481 0xf8d295b2ded9dc,
1482 ])),
1483 Fq::from(BigInt::new([
1484 0x977df6efcdaee0db,
1485 0x946ae52d684fa7ed,
1486 0xbe203411c66fb3a5,
1487 0xb3f8afc0ee248cad,
1488 0x4e464dea5bcfd41e,
1489 0x12d1137b8a6a837,
1490 ])),
1491 );
1492 a.sub_assign(&Fq2::new(
1493 Fq::from(BigInt::new([
1494 0x619a02d78dc70ef2,
1495 0xb93adfc9119e33e8,
1496 0x4bf0b99a9f0dca12,
1497 0x3b88899a42a6318f,
1498 0x986a4a62fa82a49d,
1499 0x13ce433fa26027f5,
1500 ])),
1501 Fq::from(BigInt::new([
1502 0x66323bf80b58b9b9,
1503 0xa1379b6facf6e596,
1504 0x402aef1fb797e32f,
1505 0x2236f55246d0d44d,
1506 0x4c8c1800eb104566,
1507 0x11d6e20e986c2085,
1508 ])),
1509 ));
1510 assert_eq!(
1511 a,
1512 Fq2::new(
1513 Fq::from(BigInt::new([
1514 0x8565752bdb5c9b80,
1515 0x7756bed7c15982e9,
1516 0xa65a6be700b285fe,
1517 0xe255902672ef6c43,
1518 0x7f77a718021c342d,
1519 0x72ba14049fe9881,
1520 ])),
1521 Fq::from(BigInt::new([
1522 0xeb4abaf7c255d1cd,
1523 0x11df49bc6cacc256,
1524 0xe52617930588c69a,
1525 0xf63905f39ad8cb1f,
1526 0x4cd5dd9fb40b3b8f,
1527 0x957411359ba6e4c,
1528 ])),
1529 )
1530 );
1531}
1532
1533#[test]
1534fn test_fq2_negation() {
1535 let mut a = Fq2::new(
1536 Fq::from(BigInt::new([
1537 0x2d0078036923ffc7,
1538 0x11e59ea221a3b6d2,
1539 0x8b1a52e0a90f59ed,
1540 0xb966ce3bc2108b13,
1541 0xccc649c4b9532bf3,
1542 0xf8d295b2ded9dc,
1543 ])),
1544 Fq::from(BigInt::new([
1545 0x977df6efcdaee0db,
1546 0x946ae52d684fa7ed,
1547 0xbe203411c66fb3a5,
1548 0xb3f8afc0ee248cad,
1549 0x4e464dea5bcfd41e,
1550 0x12d1137b8a6a837,
1551 ])),
1552 );
1553 a = -a;
1554 assert_eq!(
1555 a,
1556 Fq2::new(
1557 Fq::from(BigInt::new([
1558 0x8cfe87fc96dbaae4,
1559 0xcc6615c8fb0492d,
1560 0xdc167fc04da19c37,
1561 0xab107d49317487ab,
1562 0x7e555df189f880e3,
1563 0x19083f5486a10cbd,
1564 ])),
1565 Fq::from(BigInt::new([
1566 0x228109103250c9d0,
1567 0x8a411ad149045812,
1568 0xa9109e8f3041427e,
1569 0xb07e9bc405608611,
1570 0xfcd559cbe77bd8b8,
1571 0x18d400b280d93e62,
1572 ])),
1573 )
1574 );
1575}
1576
1577#[test]
1578fn test_fq2_doubling() {
1579 let mut a = Fq2::new(
1580 Fq::from(BigInt::new([
1581 0x2d0078036923ffc7,
1582 0x11e59ea221a3b6d2,
1583 0x8b1a52e0a90f59ed,
1584 0xb966ce3bc2108b13,
1585 0xccc649c4b9532bf3,
1586 0xf8d295b2ded9dc,
1587 ])),
1588 Fq::from(BigInt::new([
1589 0x977df6efcdaee0db,
1590 0x946ae52d684fa7ed,
1591 0xbe203411c66fb3a5,
1592 0xb3f8afc0ee248cad,
1593 0x4e464dea5bcfd41e,
1594 0x12d1137b8a6a837,
1595 ])),
1596 );
1597 a.double_in_place();
1598 assert_eq!(
1599 a,
1600 Fq2::new(
1601 Fq::from(BigInt::new([
1602 0x5a00f006d247ff8e,
1603 0x23cb3d4443476da4,
1604 0x1634a5c1521eb3da,
1605 0x72cd9c7784211627,
1606 0x998c938972a657e7,
1607 0x1f1a52b65bdb3b9,
1608 ])),
1609 Fq::from(BigInt::new([
1610 0x2efbeddf9b5dc1b6,
1611 0x28d5ca5ad09f4fdb,
1612 0x7c4068238cdf674b,
1613 0x67f15f81dc49195b,
1614 0x9c8c9bd4b79fa83d,
1615 0x25a226f714d506e,
1616 ])),
1617 )
1618 );
1619}
1620
1621#[test]
1622fn test_fq2_frobenius_map() {
1623 let mut a = Fq2::new(
1624 Fq::from(BigInt::new([
1625 0x2d0078036923ffc7,
1626 0x11e59ea221a3b6d2,
1627 0x8b1a52e0a90f59ed,
1628 0xb966ce3bc2108b13,
1629 0xccc649c4b9532bf3,
1630 0xf8d295b2ded9dc,
1631 ])),
1632 Fq::from(BigInt::new([
1633 0x977df6efcdaee0db,
1634 0x946ae52d684fa7ed,
1635 0xbe203411c66fb3a5,
1636 0xb3f8afc0ee248cad,
1637 0x4e464dea5bcfd41e,
1638 0x12d1137b8a6a837,
1639 ])),
1640 );
1641 a.frobenius_map(0);
1642 assert_eq!(
1643 a,
1644 Fq2::new(
1645 Fq::from(BigInt::new([
1646 0x2d0078036923ffc7,
1647 0x11e59ea221a3b6d2,
1648 0x8b1a52e0a90f59ed,
1649 0xb966ce3bc2108b13,
1650 0xccc649c4b9532bf3,
1651 0xf8d295b2ded9dc,
1652 ])),
1653 Fq::from(BigInt::new([
1654 0x977df6efcdaee0db,
1655 0x946ae52d684fa7ed,
1656 0xbe203411c66fb3a5,
1657 0xb3f8afc0ee248cad,
1658 0x4e464dea5bcfd41e,
1659 0x12d1137b8a6a837,
1660 ])),
1661 )
1662 );
1663 a.frobenius_map(1);
1664 assert_eq!(
1665 a,
1666 Fq2::new(
1667 Fq::from(BigInt::new([
1668 0x2d0078036923ffc7,
1669 0x11e59ea221a3b6d2,
1670 0x8b1a52e0a90f59ed,
1671 0xb966ce3bc2108b13,
1672 0xccc649c4b9532bf3,
1673 0xf8d295b2ded9dc,
1674 ])),
1675 Fq::from(BigInt::new([
1676 0x228109103250c9d0,
1677 0x8a411ad149045812,
1678 0xa9109e8f3041427e,
1679 0xb07e9bc405608611,
1680 0xfcd559cbe77bd8b8,
1681 0x18d400b280d93e62,
1682 ])),
1683 )
1684 );
1685 a.frobenius_map(1);
1686 assert_eq!(
1687 a,
1688 Fq2::new(
1689 Fq::from(BigInt::new([
1690 0x2d0078036923ffc7,
1691 0x11e59ea221a3b6d2,
1692 0x8b1a52e0a90f59ed,
1693 0xb966ce3bc2108b13,
1694 0xccc649c4b9532bf3,
1695 0xf8d295b2ded9dc,
1696 ])),
1697 Fq::from(BigInt::new([
1698 0x977df6efcdaee0db,
1699 0x946ae52d684fa7ed,
1700 0xbe203411c66fb3a5,
1701 0xb3f8afc0ee248cad,
1702 0x4e464dea5bcfd41e,
1703 0x12d1137b8a6a837,
1704 ])),
1705 )
1706 );
1707 a.frobenius_map(2);
1708 assert_eq!(
1709 a,
1710 Fq2::new(
1711 Fq::from(BigInt::new([
1712 0x2d0078036923ffc7,
1713 0x11e59ea221a3b6d2,
1714 0x8b1a52e0a90f59ed,
1715 0xb966ce3bc2108b13,
1716 0xccc649c4b9532bf3,
1717 0xf8d295b2ded9dc,
1718 ])),
1719 Fq::from(BigInt::new([
1720 0x977df6efcdaee0db,
1721 0x946ae52d684fa7ed,
1722 0xbe203411c66fb3a5,
1723 0xb3f8afc0ee248cad,
1724 0x4e464dea5bcfd41e,
1725 0x12d1137b8a6a837,
1726 ])),
1727 )
1728 );
1729}
1730
1731#[test]
1732fn test_fq2_legendre() {
1733 use ark_ff::fields::LegendreSymbol::*;
1734
1735 assert_eq!(Zero, Fq2::zero().legendre());
1736 // i^2 = -1
1737 let mut m1 = -Fq2::one();
1738 assert_eq!(QuadraticResidue, m1.legendre());
1739 m1 = Fq6Config::mul_fp2_by_nonresidue(&m1);
1740 assert_eq!(QuadraticNonResidue, m1.legendre());
1741}
1742
1743#[test]
1744fn test_fq2_mul_nonresidue() {
1745 let mut rng = ark_std::test_rng();
1746
1747 let nqr = Fq2::new(Fq::one(), Fq::one());
1748
1749 for _ in 0..1000 {
1750 let mut a = Fq2::rand(&mut rng);
1751 let mut b = a;
1752 a = Fq6Config::mul_fp2_by_nonresidue(&a);
1753 b.mul_assign(&nqr);
1754
1755 assert_eq!(a, b);
1756 }
1757}
1758
1759#[test]
1760fn test_fq6_mul_nonresidue() {
1761 let mut rng = ark_std::test_rng();
1762
1763 let nqr = Fq6::new(Fq2::zero(), Fq2::one(), Fq2::zero());
1764
1765 for _ in 0..1000 {
1766 let mut a = Fq6::rand(&mut rng);
1767 let mut b = a;
1768 a = Fq12Config::mul_fp6_by_nonresidue(&a);
1769 b.mul_assign(&nqr);
1770
1771 assert_eq!(a, b);
1772 }
1773}
1774
1775#[test]
1776fn test_fq6_mul_by_1() {
1777 let mut rng = ark_std::test_rng();
1778
1779 for _ in 0..1000 {
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_1(&c1);
1785 b.mul_assign(&Fq6::new(Fq2::zero(), c1, Fq2::zero()));
1786
1787 assert_eq!(a, b);
1788 }
1789}
1790
1791#[test]
1792fn test_fq6_mul_by_01() {
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 mut a = Fq6::rand(&mut rng);
1799 let mut b = a;
1800
1801 a.mul_by_01(&c0, &c1);
1802 b.mul_assign(&Fq6::new(c0, c1, Fq2::zero()));
1803
1804 assert_eq!(a, b);
1805 }
1806}
1807
1808#[test]
1809fn test_fq12_mul_by_014() {
1810 let mut rng = ark_std::test_rng();
1811
1812 for _ in 0..1000 {
1813 let c0 = Fq2::rand(&mut rng);
1814 let c1 = Fq2::rand(&mut rng);
1815 let c5 = Fq2::rand(&mut rng);
1816 let mut a = Fq12::rand(&mut rng);
1817 let mut b = a;
1818
1819 a.mul_by_014(&c0, &c1, &c5);
1820 b.mul_assign(&Fq12::new(
1821 Fq6::new(c0, c1, Fq2::zero()),
1822 Fq6::new(Fq2::zero(), c5, Fq2::zero()),
1823 ));
1824
1825 assert_eq!(a, b);
1826 }
1827}