Barretenberg
The ZK-SNARK library at the core of Aztec
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fq12.test.cpp
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1#include "fq12.hpp"
2#include <gtest/gtest.h>
3
4using namespace bb;
5
6TEST(fq12, AddCheckAgainstConstants)
7{
8 fq12 a = { { { { 0xe5090b4f4ae647a8, 0xf5d4801f152fdf6c, 0xcdb69d33dba7f562, 0x228f26abab7d6687 },
9 { 0xc27a82b14db8404f, 0xcbf9354b3655de9b, 0xa57fd51d8df378ad, 0x2e3fc75bde967502 } },
10 { { 0x68313cbef88a5759, 0x5b133f7951386452, 0x39e7dc61e0a99225, 0xd431d506584ef0c },
11 { 0xe1cb4e7cdde02d54, 0x77850ffc86025996, 0x32f2ac7001b781bc, 0x161e5d998a9ca841 } },
12 { { 0x6a19408ab0b98992, 0xdf60d135d3ca1b8e, 0xc2c4fb314a6fb787, 0x6dad3e4fcdc4109 },
13 { 0xf19bf45ccc4fa4c7, 0x772e75432f1a1b7d, 0xf5fdbc43092cb02b, 0x1e8b68995e7650a4 } } },
14 { { { 0xbb590c3f964679e8, 0x7cc101ff81317c47, 0xf0795826878a3d87, 0x2fa65099a1bb9d0a },
15 { 0x366de96875edef88, 0xb912fe4346bce97f, 0x9021ce3f941f43ee, 0x1df070ec2d40307e } },
16 { { 0x2f374251a079ed16, 0x781ed5eba2c32177, 0x46f730607db6faaa, 0x17059595d4861d63 },
17 { 0xffac861b22b6af3c, 0x2d42efdd21ffbfa, 0xcc63ae5632de7dc4, 0x303860faf42e67d4 } },
18 { { 0x83ee1b92ac44538, 0x2ad45ea546f39c5e, 0x983243f0954f3d85, 0x2cda1dee8630e07d },
19 { 0xdf1ea9591f4f9acc, 0x967ee067573afba1, 0x43b75fdd61c3a0f9, 0x7a3fcd3793426e2 } } } };
20 fq12 b = { { { { 0x245aaeeeca2e8585, 0xdf288bfa5a851ba8, 0x735d09b2b32bea1e, 0x28086604acb87f71 },
21 { 0x997ea2f96d830756, 0xc59e9aed4c05f014, 0xf47897613190565a, 0x25e98544dc2c8831 } },
22 { { 0x3a03ed7df625906d, 0x85650c015c4c8d83, 0x40acaeaff65a8f65, 0x1a7c84a9f7b973ca },
23 { 0xc30774c5f550ab0a, 0x6cab91e0a92ca253, 0xef9a802117ecb2e6, 0x11fe101c5c74dd84 } },
24 { { 0x4fc81f6d823665, 0x474c3b6df0c616ae, 0xcfc039d881f4dbc5, 0x13f25378fc4b7321 },
25 { 0x48be6e134dfb42e1, 0x13242e5605a54db6, 0x3a3ac4c510c6d51d, 0x1d828e5782e808c7 } } },
26 { { { 0x4d5aaa2e6bf2f6ce, 0x77b940cf8467d6bd, 0x3db11f4ecb5d955f, 0x26c0713713247292 },
27 { 0x189f56d466889ee9, 0x71c8f6408d8cc0, 0x3ce56be0a825f633, 0x1dda277a21fc4a5 } },
28 { { 0x3385740320b58676, 0x22acfbf39a2b78ea, 0xcbc2d6fbc8b3627e, 0x153c7d04d6a74399 },
29 { 0x6e34eb6dd8178662, 0x80cb55dc8f40d064, 0xeb7ec75be44cb60c, 0x2b2ab9ce7d0e325b } },
30 { { 0xa12ef4f30cba6dcc, 0x2a75211f0179f708, 0x805c5f02cea31575, 0x33b07ab9f23b37f },
31 { 0xdfc83826a0a99b10, 0x44e813c27143ff65, 0x44006acae2a0f4b2, 0xda7d72fd6d6b8be } } } };
32 fq12 expected = { { { { 0xcd432e273c97cfe6, 0x3d7ba18807433087, 0x88c361300d528724, 0x1a333e3d770445cf },
33 { 0x1fd89993e2be4a5e, 0xfa1665a719ea0423, 0xe1a826c83e0276aa, 0x23c4fe2dd9915d0a } },
34 { { 0xa2352a3ceeafe7c6, 0xe0784b7aad84f1d5, 0x7a948b11d704218a, 0x27bfa1fa5d3e62d6 },
35 { 0xa4d2c342d330d85e, 0xe430a1dd2f2efbea, 0x228d2c9119a434a2, 0x281c6db5e71185c6 } },
36 { { 0x6a6908aa1e3bbff7, 0x26ad0ca3c490323c, 0x92853509cc64934d, 0x1acd275df927b42b },
37 { 0xfe39d65941cdea61, 0xf2d13907cc4d9ea6, 0x77e83b5198722cea, 0xba9a87e002cb942 } } },
38 { { { 0xcc932a5729bc736f, 0x5cf8d83d9d278877, 0x75da31bed1667a89, 0x2602735dd3ae6f73 },
39 { 0x4f0d403cdc768e71, 0xb984c739874a763f, 0xcd073a203c453a21, 0x1fce1363cf5ff523 } },
40 { { 0x62bcb654c12f738c, 0x9acbd1df3cee9a61, 0x12ba075c466a5d28, 0x2c42129aab2d60fd },
41 { 0x31c0e57222513857, 0xec1e1a48f8ef01d2, 0xff922ffb95a9db72, 0x2afecc56900afa06 } },
42 { { 0xa96dd6ac377eb304, 0x55497fc4486d9366, 0x188ea2f363f252fa, 0x3015259a255493fd },
43 { 0xbee6e17fbff935dc, 0xdb66f429c87efb07, 0x87b7caa8446495ab, 0x154bd403500adfa0 } } } };
44 fq12 result = a + b;
45 EXPECT_EQ(result, expected);
46}
47
48TEST(fq12, SubCheckAgainstConstants)
49{
50 fq12 a = { { { { 0xf828470cae144505, 0xe05f8f664caae877, 0x27b46814f04c96a3, 0x49d8f97c040a1a2 },
51 { 0x3651629333fd6d1, 0xf7c08d56035cb892, 0x7fd937c7d75b567f, 0x11aac5d9567d8c7e } },
52 { { 0xd47a8bb08e4a676f, 0x4e8ec845cea67faa, 0xb643308828d68eca, 0xd707220f70bb972 },
53 { 0xbde9a346a4e047e2, 0xe591795a7234509, 0x25f51ea67778b6a7, 0x1ae4992ae87a5275 } },
54 { { 0x3a18d8e1bb596051, 0x98a5e65ed32f9a9d, 0xaa7e1d1c2f37f724, 0x1c49e3f27295d2ad },
55 { 0x474045a3fc2d57bf, 0x97589ff46e5fb00d, 0x61d9e3d73384db69, 0x131a19f4298c9de2 } } },
56 { { { 0x706133429743b32, 0x1e6447ce7c8339f8, 0x298b9e4c899c0bd7, 0xafa684968b50282 },
57 { 0xcc455561541a8cee, 0xfdf2f5fc63431236, 0xe07e5b31b4d6b6e5, 0x1be630fe3cb76f18 } },
58 { { 0xd43cd3daf76a5feb, 0x435676c0cb9e6de0, 0x4a33cda2a7256295, 0xf72cd4603cc9157 },
59 { 0xe459117a2159f829, 0x79e9077fdc67694d, 0x2e9455f7048f57c9, 0x2db6d0e0acacbefd } },
60 { { 0x3de184f574e6a906, 0xa76c351979057c33, 0xaddd00ad7f01ef80, 0x27ee592a59c8bc64 },
61 { 0x51a52b09f0ce135d, 0xac3d8564b56af445, 0x84991dd9a2667ea5, 0x21d842ca48429246 } } } };
62 fq12 b = { { { { 0x93d4916d22adcba0, 0x683e80bb29e3ec60, 0x388f10e59e129cfb, 0x19e09f077f0675ce },
63 { 0xf1a9f3b587b1e349, 0xd6a6887757b799b0, 0x95d9dee7828e0465, 0x6aff335face1944 } },
64 { { 0x6b756aa7799e83d1, 0x6369ec6364c2929d, 0xaa05da6983b0c4a3, 0x13adec60e10fddb5 },
65 { 0x138177f49f63310, 0x2d4da5c584a5becb, 0x807fc7d23a607feb, 0x1e6357a0ab0d3670 } },
66 { { 0xab12964a122cf1b6, 0x99ef88e109b9d21a, 0x32215e4c634251b1, 0x24717e2ca7747434 },
67 { 0x3cd50c8d4c4095d2, 0x18b12fa8ddc10828, 0xe5bb788ac1476aa6, 0x2d91a0bc1e3f42b3 } } },
68 { { { 0x237a667d2dd96f73, 0xfefb62c91bee98ef, 0xe49892737da80da0, 0x28df2b3a12aeeac3 },
69 { 0x5fb1f89589c428df, 0x6de7c766737bec95, 0xa70a6430b61b7bbc, 0x2cf8498d167b3c80 } },
70 { { 0xa26a8dab924ff949, 0xdbbe720bad96b613, 0x8b1af40cdfc70a62, 0x1d75af668d1a5e75 },
71 { 0x9b716b611633cb21, 0xf5495a0ba4b827da, 0xfa13f0e39a7c4d80, 0x1efa635ab063db6f } },
72 { { 0x3d6d5d0a4a1add14, 0x8168927ff59bd9aa, 0xc7ca1b1129a41303, 0x2541c1d8afe4a234 },
73 { 0xbea0fc047742181b, 0x302f7d5a9e270655, 0x83259d4a1a636c93, 0x231cc5a6fecd70ff } } } };
74 fq12 expected = { { { { 0xa07441b663e376ac, 0xfa2793c8b38c6a4, 0xa7759ce5d3bb5206, 0x1b213f03226bcbfd },
75 { 0x11bb2273ab8df388, 0x211a04deaba51ee1, 0xe9ff58e054cd521a, 0xafad2a35baf7339 } },
76 { { 0xa525ad1fed28e0e5, 0x82a64673d255b79a, 0xc48d9bd526a72284, 0x2a26d432f72d7be6 },
77 { 0xf8d217de33671219, 0x788cdc618aef50cb, 0x5dc59c8abe998f19, 0x2ce58ffd1e9ebc2e } },
78 { { 0xcb26ceae81a96be2, 0x9637c80f31e7930f, 0x30ad04864d76fdd0, 0x283cb438ac52fea3 },
79 { 0x468bc52d8869bf34, 0x1628dadcf9107272, 0x346eb102f3bec921, 0x15ecc7aaec7efb58 } } },
80 { { { 0x1fac38cdd417c906, 0xb6ea4f96c9066b96, 0xfd43518f8d755693, 0x127f8b823737b7e7 },
81 { 0xa8b3e8e2a2d36156, 0x278c99275838f02e, 0xf1c43cb7803c9387, 0x1f5235e4076dd2c1 } },
82 { { 0x6df2d2463d9763e9, 0xff196f468679825a, 0x77691f4c48dfb08f, 0x22616c5257e3d30b },
83 { 0x48e7a6190b262d08, 0x849fad7437af4173, 0x348065136a130a48, 0xebc6d85fc48e38d } },
84 { { 0x7427eb2acbcbf2, 0x2603a2998369a289, 0xe612e59c555ddc7d, 0x2ac9751a9e41a2f },
85 { 0xcf24bb1c5208f889, 0x138f729b7fb5b87c, 0xb9c3c64609846a70, 0x2f1fcb962aa6c170 } } } };
86 fq12 result = a - b;
87 EXPECT_EQ(result, expected);
88}
89
90TEST(fq12, MulCheckAgainstConstants)
91{
92
93#if defined(__SIZEOF_INT128__) && !defined(__wasm__)
94 fq12 a = { { { { 0xd43e9f8be859502b, 0x26a42a1a95cee1ef, 0x3d63c085c1892b32, 0x2e5beaf431211a76 },
95 { 0x5f32ad7cee215ff5, 0xce967fda9424120e, 0x10ea4e52628bac33, 0x51b85ee9671b7f3 } },
96 { { 0x95f8e84e0ff94a83, 0x6c6fb2cf3c73b30a, 0x28e8e13841f714a8, 0x2a3412f681e31b4d },
97 { 0xcd03b28cdc6fcc09, 0xf7ee307ef2077412, 0xbc9d525a4ffd0836, 0x2d4f5f6e688bf0dd } },
98 { { 0xb1908010bcb66716, 0xbd23aa28e73d7e20, 0xfc3464edca7f2034, 0x18df61620d6a3cc1 },
99 { 0x56720acb51310603, 0x9a77e402b6e5a115, 0xe35197b7788364cd, 0x2e6e4007d35342d7 } } },
100 { { { 0x33ec11b94eac5710, 0x73c9dcd8bdea426d, 0xeeb51979ffe73f42, 0x9cc4ada6e7c8b3c },
101 { 0xcfa8f5fe99105971, 0x32f56cb5227e01fa, 0xfcbf8257d846eaa6, 0x6d61581ae78a315 } },
102 { { 0x242e46e642ade123, 0xc5de69ea316cbe0f, 0x63085993f3770f26, 0x9d2ffea4b8e13e1 },
103 { 0x13eddc3b1cf3d2f1, 0xb79750aed7439222, 0x6615c429a49c7b6e, 0x243e8df9e6214e9c } },
104 { { 0x82c1aefce33671b, 0x46d36904f9839aaa, 0x37f089bd51cd0269, 0x207b0fbf328c0c1b },
105 { 0x408aa3eafba634f9, 0x7dfc25c916d2a990, 0xb9b9afe508057cb2, 0x10045453df51156b } } } };
106 fq12 b = { { { { 0xc544906e527a4dbb, 0x3b08eba65d831ce2, 0xf44924359d69ef21, 0xeb24efb0d86c18d },
107 { 0x762256ecff65aa30, 0xcc5d8240a745dd40, 0xc9ae36345a8d3a7, 0x23aae88e4c37875c } },
108 { { 0xdcbd0dbc20d6245f, 0x54f64b8ceeebe3e9, 0xc2f8d8dcd678c88e, 0x908df13ed6053d1 },
109 { 0x4923d2490485825a, 0xf1a9109e0b644eb5, 0x429d1b8bacc163f6, 0x15013536538d4f45 } },
110 { { 0x659fa4d073b4406, 0x222fce98d820bc19, 0x68e5ba5f6a6b0185, 0x2a76a4a0a34f20b2 },
111 { 0xfa94b15348a564dd, 0x28f6070c9cc9d3e6, 0x2d51cbd531b80d38, 0x90238942d0598dd } } },
112 { { { 0x774b857008f9eb46, 0xaa79c6612b259dd3, 0xaaf7799629c36c25, 0x199674aa3fc4dc4 },
113 { 0x521ed8b0f4029e01, 0xb5cef10d7e9082a7, 0x22a2dbf23ddbfdc7, 0x10ed71ea96a11df8 } },
114 { { 0xfcc59d9a0a13d0da, 0x406533bb1dec3d99, 0x6b8aa2d76bcc954b, 0x217785904ce22f1a },
115 { 0xa65e26fd5fc187af, 0xf09cff1136f9ef97, 0xecbb91eec77033ef, 0x1e24cd13205cc6a1 } },
116 { { 0xcbdde8b25e2f3316, 0x92ace6648cdee119, 0x2578759b6d80407b, 0x73b0d667c920360 },
117 { 0x37012fc28dfb6150, 0xbbbe148fa2b455ba, 0x3e40c8247f10d3b5, 0x2659914dcf14d694 } } } };
118 fq12 expected = { { { { 0x90705f5d2661c46a, 0x8359404686aca366, 0xf1746b64a8e7726f, 0x8f5986313948a97 },
119 { 0x27bede3683dfbbee, 0x7b848bc1f4e2538f, 0xf00da00ebe5a4978, 0x2d936f521ae05a79 } },
120 { { 0x43be456f10e7479, 0xa213a8ec67a82f12, 0x1ab6e831782ea23c, 0x22b9ad870683188 },
121 { 0xc62073ee2256503b, 0x5b2c57b0384c5915, 0xc62b200365d81355, 0x77e010f605b0fa0 } },
122 { { 0x1ef104ada95be821, 0x25519a0c57a40a9d, 0x729f93a79a60faea, 0x15f0ba49c2ffc141 },
123 { 0x9f0e325fa9e3aae5, 0xc2b6acd6f85edf02, 0xc490de65594e8f0, 0x2a5589155f78b7d6 } } },
124 { { { 0x3d974df017795d21, 0x11abc3064ac33706, 0xbfdcf2eed81ed0d0, 0x2c880426e5fc3264 },
125 { 0x44db12fb914f9b11, 0xe5e47f8a30738ef4, 0x7088a7a22dfb33c3, 0x1a992c655dc96df9 } },
126 { { 0x911391f2830c808f, 0x304ef4bf1ba305f9, 0xe449bc05ed945fa1, 0x27443aad475e4349 },
127 { 0xeaf256aa7a6b49b5, 0xeaa1b56258e3194e, 0xde3b531fd4fe961b, 0x26a0b5c35ce4be53 } },
128 { { 0x1f7661fa7dd7d68c, 0x71c1360fdb272200, 0x3fdb8fcc1dbfd160, 0x1ba330295e24399b },
129 { 0x5c93a291c6579918, 0x6536baab9e09bc80, 0x93ad9959edff4c64, 0x138af9a14abfeb1e } } } };
130#else
131 fq12 a = { { { { 0x7c0386cfac84570eUL, 0x135ac6487c86816dUL, 0x130fe55503fd0b4dUL, 0x1fbc2d0fc05289e4UL },
132 { 0x31f40b593ab506cbUL, 0xc4bbb9e4b2ce224UL, 0xf458f928ccf17d61UL, 0x1243d27a2aa21de4UL } },
133 { { 0x67ae435929fa99e3UL, 0x93501c918a76046dUL, 0xaca4ccc8963e432eUL, 0x2bee18b27c27853eUL },
134 { 0xd0c6730507d0d015UL, 0xd41cfd656c0a9059UL, 0xb292659d53fa0444UL, 0x2e8f0ac98edef6fdUL } },
135 { { 0x700740aa0efd0e50UL, 0x2c5e9c0660931b42UL, 0x188425137ce80beUL, 0x15a745139a2d95a4UL },
136 { 0xc270eebcc77b120eUL, 0x8dd2034c9f5e661dUL, 0xd0cacb8be3443ebbUL, 0x2206cf8406979618UL } } },
137 { { { 0x14beeea0c29cf256UL, 0xec331baf4a9d8e57UL, 0x84c18cf8f3dfd61cUL, 0x172f849c8867a6a3UL },
138 { 0x49c8f77c0173904UL, 0xa7ec5eadf91525UL, 0xb6af342102d7f350UL, 0x1931766a4a4de218UL } },
139 { { 0x1d05943f42ce34b6UL, 0x2ec4bdddbaed0295UL, 0xf29903765d9d2a7UL, 0x180626982a98bb32UL },
140 { 0x16cef1562b3f9cbfUL, 0x564982ca86391192UL, 0x338241cef0f07d6eUL, 0x2eceb2ea88b46fcdUL } },
141 { { 0x16d7e01a042c1c8dUL, 0x6ccf62b19f1db7abUL, 0xdf7b7fb19a040d7bUL, 0x17278879d86f5ffaUL },
142 { 0xb80f047affe4ba5aUL, 0xd4768f74c5e34883UL, 0x413437ff1a222a7UL, 0x1c9f79ff1e326bd6UL } } } };
143 fq12 b = { { { { 0x8b6d20fcb2e4cfe1UL, 0xd90b5af04637d61UL, 0xe5213491fb1c8ddUL, 0x22c31d57c6199047UL },
144 { 0x5d5e4792797a849fUL, 0xef0fb5048682755eUL, 0x4262903127b8490UL, 0x1c5a05774b7b87c2UL } },
145 { { 0x6afefb11e053997dUL, 0xa9425cc6d3438879UL, 0xc589bf0a479257f6UL, 0x2f265a3f46125967UL },
146 { 0x16d32bf792576ea5UL, 0x838faa5f1ec28d7dUL, 0xf78fe731049b021dUL, 0x2b0eaaf50224c689UL } },
147 { { 0x37aff72139bcccfcUL, 0xb3d22b3397a55baeUL, 0xf3efabf7233a8667UL, 0x3dbff83c87691bcUL },
148 { 0x25f36df6da3ba93dUL, 0x2939ccbc8f01881dUL, 0x10a81e15af7aed31UL, 0x2e518a473abafad5UL } } },
149 { { { 0xad5021ea46c06b79UL, 0xb7b76193fc41efe1UL, 0xa69eed0eb6ec2c57UL, 0x2c89ae19e58186bUL },
150 { 0xae75112332f4de13UL, 0x374e8d70552ca0d8UL, 0x68e87f702af0ecf1UL, 0x95ede632701dd39UL } },
151 { { 0x6de7a94aa7bc5726UL, 0x7874ee4c3c04b1cUL, 0x9a6e5d3e5875115dUL, 0x651f42a42021fb7UL },
152 { 0x555a79f9e6ea299bUL, 0xd504f95c1ecbea79UL, 0xe97d114d516cef0bUL, 0x2d27cfdd54e9f124UL } },
153 { { 0x8b3ae5f063f26da4UL, 0xf797224bfa14f904UL, 0xcdcd9c93aa02adfbUL, 0x25d073040d79eb5dUL },
154 { 0xf84a169b376e11UL, 0xac1f29c1236def7cUL, 0xc84235bd3c78d593UL, 0x11668081e4c22e74UL } } } };
155 fq12 expected = {
156 { { { 0xe1692f3291c79addUL, 0x75a0f3f9cb5b780fUL, 0x94fc10049567941cUL, 0x2cbd84240c99322dUL },
157 { 0xec0b5c231d51cf6eUL, 0xaf66fb345ef4b557UL, 0x684bd6749e20d417UL, 0x6acb8ccf83a8a5aUL } },
158 { { 0x4b5bfec7495191d9UL, 0xaaf3b2fb8c9417b3UL, 0x9e8cc0788452ef36UL, 0x150f0c9b2bd490d9UL },
159 { 0xd38c4d68e8d61244UL, 0x7854bc167c3f883UL, 0xe422e992b4fd0935UL, 0x2e2ee820869b7371UL } },
160 { { 0x9458ec7554a72a3eUL, 0x611f6d973e483feaUL, 0x3f8ea4f8370c8826UL, 0x189afef00f4165e6UL },
161 { 0x8a57858c6746a623UL, 0x5c2f5d8907db836eUL, 0x18aa628b09f8cc39UL, 0x301cdc8e2edb165bUL } } },
162 { { { 0xe339df6c6902f315UL, 0xbcf4e508382eec7UL, 0x1a86782e58331768UL, 0x15a3a1d93ce727deUL },
163 { 0x9d3911edc9a69069UL, 0xacf7dd9e1ee36b27UL, 0xd3c0532725cf9a45UL, 0x1c7c570ac4e21c68UL } },
164 { { 0x434490153d5b55f1UL, 0x3e3b2fb04143f767UL, 0x8960b1eb0cea5302UL, 0x2ebbac70edefc529UL },
165 { 0x7f1d271429347ab1UL, 0x88934417e9466212UL, 0xc7939527fa312259UL, 0x1a4b0f339ebf2668UL } },
166 { { 0xb48265b482310282UL, 0x910d43c20ce40215UL, 0x5cd12ae9ce1f579UL, 0xd588117ef09f079UL },
167 { 0xc0edc126a51743acUL, 0x8cc656a2dbe2116cUL, 0xd1efe6afadd96829UL, 0x2cab86c6c9a9e1ddUL } } }
168 };
169#endif
170
171 fq12 result = a * b;
172 EXPECT_EQ(result, expected);
173}
174
175TEST(fq12, SparseMulCheckAgainstConstants)
176{
177 fq12::ell_coeffs ell;
178
179#if defined(__SIZEOF_INT128__) && !defined(__wasm__)
180 fq12 a = { { { { 0x472e65066d5d00e3, 0xd35147f048cc3b15, 0xb7a9aafbfc298c58, 0x3905463add8c9a2f },
181 { 0xdec4ece2f569ec88, 0x9a081a157e39b6ed, 0xfc51bb6b4b3880c0, 0x2ddceafb16a16476 } },
182 { { 0x275d05338f5b9a3, 0x727afc5b10a7333f, 0x3b0d7f3e9ebb8e6a, 0x3ab5c561cd99c099 },
183 { 0x8f2117ff5147917e, 0xcdfaf8cb263e1cd8, 0xa85a504fa7513d5, 0x3dcaf9e370d20258 } },
184 { { 0xe4106e3fc1e7ac34, 0xe3c36cb15b7c1892, 0x67070534f096dcbf, 0x1e3ef02da60028c3 },
185 { 0xaa36989b7e7b0e01, 0xe6f6c3526615429f, 0xba6095c16e66a97e, 0x2fb7b3001a00e584 } } },
186 { { { 0x7d4600840fbb809a, 0x1d03db0ea4f77f8, 0xcdc35920853dbeb1, 0x4cff960c5f4a22be },
187 { 0x928ef2f332ca5cd6, 0xd383a99f620b8168, 0x8428902deeeba70, 0x5ada483adf652e4b } },
188 { { 0xe3aab2410014dec, 0x38a0846be949b16b, 0x3802c68bfc6acfd4, 0x339a198441966680 },
189 { 0xfedd77dcff33fbf0, 0x7f1b82292b1e21a9, 0x6e44e3633b491d67, 0x4fb2ff7c4f8f930a } },
190 { { 0xa87576a50f58782, 0x6782d190e626eb27, 0x81afbe31e6a0d5fb, 0x16cb22fe61b92953 },
191 { 0x8e9f5a1a369eb503, 0x832fb9ee9a0d227c, 0xc8f5e08b45c26436, 0x4429425509a037b5 } } } };
192 ell.o = { { 0x12a5b2fa59f772bb, 0x73a2a13dd93ccc34, 0x6a1c5c9ccb5f51d4, 0x277c679d506d92d1 },
193 { 0xf0b7bc6cefc16ce2, 0xcfe9a91168fb54c2, 0x10e0446d5b0f14f6, 0x17f4aa9fcfb33c6a } };
194 ell.w = { { 0x2b357e5761e1fc77, 0x76484af65df9a595, 0x628d4aa82f649b7b, 0x3f425d75614ba91b },
195 { 0xa255f54a6fb2dd82, 0x2ca7a56feb20097b, 0x4ab331e2d79b3f27, 0x5867650bd9f7ab81 } };
196 ell.vw = { { 0xf571d10252ecff6a, 0xb8c4b65b8d31eb37, 0x749c8ab2bf7b6542, 0x422b52a14c9f7d04 },
197 { 0x4898da2ca187c0e4, 0xbb8c29391de0d254, 0xfd5049b2c105803c, 0x3399dcb18d329a43 } };
198 fq12 expected = { { { { 0x79efc8e7c0a27aa8, 0x7ac24ff5ecc9394, 0xc58c40b6e363e70, 0x4470129dd36f0e70 },
199 { 0x23f2393725453587, 0xea302b084071681e, 0x95318e663b181b18, 0x14d9bc2cdaf7e1ed } },
200 { { 0x1992489299979a4f, 0xf1dd746fa4a5a4ce, 0x6e80aeabc7e819f, 0x4c12049b3a7e6963 },
201 { 0x4ce92c9594659c28, 0x238b100a24e4f48d, 0x751b6aa6b8745b74, 0x30a34c223cefc39d } },
202 { { 0x61a56c890121d480, 0x6295f67879d8981c, 0x5885afdee0fd190c, 0x1248b7bb4a120f1e },
203 { 0x65f95bd269873f97, 0x78e3f50db648e564, 0x4628092ce0179e07, 0xc9c8dac7963da4 } } },
204 { { { 0x46ffb362ea405947, 0x67cec8b42219ae95, 0x7b26e8192f3b7619, 0x21be4630d07e7743 },
205 { 0xef90217d55dfdf2b, 0xe1ad2fe98a4121de, 0xf36d24f03210fa31, 0x31b1f2a24ce3b3f3 } },
206 { { 0xbb9a983325c57c7c, 0x5b9384ca0a384860, 0x8da37d78d55d86de, 0x33097a924217f66f },
207 { 0x83d2ac92b96e3d59, 0xa86210b27499db4e, 0x2803a767a08e8df8, 0x3dcfb2cbf6cabfd4 } },
208 { { 0xcf8e0a5f6bbb085f, 0x4bd90884781a1a2c, 0xbfe17a10d901ed53, 0x3661cda6ad4d8742 },
209 { 0x464986de3c267aa3, 0xebe2b417b64ef133, 0x514763d3f8f819a8, 0x3c3fea7527bb962c } } } };
210#else
211 fq12 a = { { { { 0x35186180618f811dUL, 0x8474970501151c3fUL, 0x519b4c1ecd7fc593UL, 0x222970c125671fefUL },
212 { 0xcccd31b14e97e2aeUL, 0x7fd8c5a589e1212eUL, 0xf0cf420639e7bd1bUL, 0xfdc2dec705bc9fbUL } },
213 { { 0x61e53f02fc299bd6UL, 0xd229b9cc940256e9UL, 0x5c58ebc9e3eaf69UL, 0x27d5072c45da4cf6UL },
214 { 0x7f0d1c58556a9ca8UL, 0x132672ac75fbf500UL, 0x8429bc1b126cac1aUL, 0x29b2fa7aea7f447cUL } },
215 { { 0xba362462baeba3bUL, 0x39d2ad60af1109e1UL, 0x32eb7a127642090aUL, 0x306c332e09563554UL },
216 { 0xfee21cab983f1487UL, 0x862c82b11ce0ccdaUL, 0xfa5a47141e2b7c87UL, 0x1ad0e019fb1a4b89UL } } },
217 { { { 0xea64b40baf069b62UL, 0xa2c0e5b6e3b56f79UL, 0xb8bd866b5c7493d8UL, 0x2c5b6f1bed930fb3UL },
218 { 0x765e1522747d3b63UL, 0x85a1a4692f367e85UL, 0x8dd10f4c0507f088UL, 0x342af2e20635dfc3UL } },
219 { { 0xcb02c9793f901a12UL, 0xf4e0662d4a19469fUL, 0x85af8f425a2c3e18UL, 0x5f0c5464a358a7cUL },
220 { 0xa51286fbed1c0b94UL, 0x1d269f9c2ca7108fUL, 0x584e43551addb9edUL, 0x2200003433ddd8d4UL } },
221 { { 0xcb02b7f36f5e1917UL, 0xfc4f397a632869aUL, 0x6943b08b3d8691f1UL, 0x383c711053cc7feUL },
222 { 0x7e532f599e5b182cUL, 0x5bb8ecd54e157f4bUL, 0x70f0160a761156baUL, 0x33eacee27f7f6f8dUL } } } };
223 ell.o = { { 0x396824f9423c9e2aUL, 0x112f54f68c0af42aUL, 0x8b647f1044c7410dUL, 0x55cfbff2ea815f0UL },
224 { 0x910f584748dac517UL, 0x1c9fe3a800bfba17UL, 0x4f5477f9cb4e715eUL, 0x28b4bb3ec47f2ad0UL } };
225 ell.w = { { 0xc5795b43903afe81UL, 0x854f4d8204fb4206UL, 0xccce2acb2edc4871UL, 0x283b1e4618827cbdUL },
226 { 0xab5eec20ea0a4e2aUL, 0x41a2890bba394b74UL, 0x943671019c19dfb1UL, 0x1632db7439b726b5UL } };
227 ell.vw = { { 0x94c2987400a16253UL, 0xa5d9e5051b206145UL, 0x9e15a0b02eb2d09eUL, 0x249126ddc099b98cUL },
228 { 0x16c8aa8b705e7912UL, 0x5254ffd3dcfd63c7UL, 0x2f5ff41aed824b29UL, 0x5e92aefbdbc02f5UL } };
229 fq12 expected = {
230 { { { 0xac407cf40656cf85UL, 0x53c4e45c7d91d7bbUL, 0x24fc4059030b458dUL, 0xc608988d828a6acUL },
231 { 0x70a009bbaa4dd445UL, 0x9472f7a5c065ba98UL, 0x4a1e4282cf71e65cUL, 0x261f89c5ef771b94UL } },
232 { { 0x73edb5dcea89d202UL, 0xa467bd8e2e7b0a2dUL, 0xdd53bfb2448cf1b6UL, 0xea940f7541be43aUL },
233 { 0x19140fd77d13dc20UL, 0x8134af178e654002UL, 0x99649e06de6062d1UL, 0x7dfb5eb77c46e77UL } },
234 { { 0x6327000dfe5eb0acUL, 0x38add03e55bd84edUL, 0x6cf2b74e0d92fd29UL, 0x4634a06b3ee61d6UL },
235 { 0xbf2b7a4d30e7f2e0UL, 0x1c7ea1b6c91cac8cUL, 0xc501259c02f3c0efUL, 0x19391b58f2c7b488UL } } },
236 { { { 0xb52a6266ad4d64c6UL, 0xf4b9ee05496e6a85UL, 0x8df70576c6512b21UL, 0xf2a083ab58b24d9UL },
237 { 0x6df2accfac5c3c80UL, 0x4578ab0439eaea36UL, 0x639be73611f43a89UL, 0x29b485ed76427947UL } },
238 { { 0xb320f772d092e959UL, 0xeac1dc82d05defe2UL, 0xf216b293fa0477baUL, 0x244135793b992890UL },
239 { 0x153faec55a401808UL, 0x60096f964173c3bfUL, 0x33ea086fd59bf075UL, 0x2a4a178ba996f400UL } },
240 { { 0xb94e24cdde4a6b2bUL, 0xc46f7eadbbb4944aUL, 0xc935ba276b8e959dUL, 0x2e82fb20dfe802a3UL },
241 { 0xa03b844c89c4be8fUL, 0x679f46cfe0884ae4UL, 0x14b1dbb1644ebedbUL, 0x28b55b24a8e35f2fUL } } }
242 };
243#endif
244
245 a.self_sparse_mul(ell);
246 fq12 result = a;
247 EXPECT_EQ(result, expected);
248}
249
250TEST(fq12, SqrCheckAgainstConstants)
251{
252#if defined(__SIZEOF_INT128__) && !defined(__wasm__)
253 fq12 a = { { { { 0xef9d68a7df0715fd, 0xfda8aff4030523cf, 0xd09b1482069c0972, 0x252195422f351b07 },
254 { 0x3192057a31dec453, 0xe1c2dd8879191e47, 0xe90a8a00c9b29c5b, 0x1db75f06dff5dd5e } },
255 { { 0xdb01b2dbb451df8f, 0x42d8923147ae4171, 0xd1264f3077ab1733, 0x2fbabfe2fbc0c62f },
256 { 0xb942d7f55f2300c6, 0xd5f9c907303a4377, 0x4b738eb660419004, 0x105fd9e8561dde19 } },
257 { { 0xd75f00fb47a5933b, 0x90b2c7e3db87476f, 0xce6e2140c49dfe37, 0x204b393bab70c36a },
258 { 0xe6ccc13d4cb9f2a1, 0x647703faa348c685, 0xcffcc5fab2041de9, 0x26390187897069d4 } } },
259 { { { 0xf411e9d666eb1c62, 0x5e79344ceba3c66a, 0x7952b27642ac6fab, 0xd99ea6525d5b1d5 },
260 { 0x684ee7c0845405ab, 0xe7e0a59a8540a44, 0xa78c74e32cbffa52, 0x2701b3cc0496a1e5 } },
261 { { 0xf4efc2a5342a90f0, 0x34fe1ec2efba9bed, 0x6457f324257a5bf6, 0x154f629fd85e3e3f },
262 { 0x1fbea12685ae2c87, 0xe72f6e501b2c85fe, 0x2c3cb81d695bb3e1, 0x2328129a857763fc } },
263 { { 0x5260c233e0adaf77, 0x20a311f1c26ee1d9, 0x6084dae2715116bb, 0x19dc89569a2a6f66 },
264 { 0x246466b86cc89d2c, 0x126f819c3031f783, 0x4eaf2d505a6158d4, 0x1c3a124bbbcb851 } } } };
265 fq12 expected = { { { { 0x32705d7cf5a364e3, 0x446995889b6c9278, 0x68016f8f5e05c46c, 0x1538ea0aea917bf9 },
266 { 0x700b02b3212abeba, 0x97881851fbeb8379, 0x2b3772e40c72fa4c, 0x227d63d2149286d0 } },
267 { { 0x4d52012a7af91a46, 0x11d348c55c0f80a0, 0xc7404131a714a543, 0x1b3c367127d42ed5 },
268 { 0x470be7817ba24d95, 0xa24a051e930fd709, 0xa2ecfe1119e0114f, 0x121a2c6bf2023fa3 } },
269 { { 0x34d2687ca37c8f51, 0x45d98e94e67ce9eb, 0xf8cb2850c835c8fb, 0x5f862e96fbd08c6 },
270 { 0xb433ae036220b411, 0xabda439ed34d9e10, 0x172a87ec00dd4588, 0x22d963b58a394b03 } } },
271 { { { 0x47e81dbb3d96dd4a, 0x8f2374b381aec29b, 0x563d859a3117771a, 0x15304bf6eaf07eb5 },
272 { 0xdd7fdbda9b473d87, 0xb29690530d01ba9, 0x31e385e8cb4fe384, 0x156826e46c02f167 } },
273 { { 0xeece14a760655b9c, 0xaeba2fd6595006f3, 0x816376d423c9948a, 0x15949533f02c2dee },
274 { 0x19ea0ed62e5093c2, 0xcf288a69b5a24352, 0xa9bdc89dd4491b7d, 0x447edc7b33f3d1c } },
275 { { 0xceb417494bece8e, 0x7f3d84971a20d351, 0x31679ed74c101d91, 0x1bb2c06842073c0c },
276 { 0x6db2993066e5fd73, 0x2c08c9fd6c3b5483, 0x3b32d43ab22d6cea, 0x3df72d32906f5f0 } } } };
277#else
278 fq12 a = { { { { 0x509ff2d7952b00f8UL, 0x80f400de95f97cc0UL, 0xcbdc0724af60e599UL, 0x1acb4d80c9fc5d10UL },
279 { 0xbbd649942a91be1bUL, 0xf9c0c84462b1c06aUL, 0x735c138d99b9fc89UL, 0x1f7a0e55480cc8c4UL } },
280 { { 0x184564b253194647UL, 0x2665e8d5000a721UL, 0xd31174f546b93313UL, 0x1b327c76331660ecUL },
281 { 0xcf1585c76f7e33faUL, 0xd42af737f2d68572UL, 0x3b4f1daaf9248cf2UL, 0x28102c8df7cb8188UL } },
282 { { 0xfd34a1893271a08dUL, 0xa8bb3e8ddf935064UL, 0xaf2e701ff4238744UL, 0x112cb808f50649edUL },
283 { 0xfa6a796e73099831UL, 0xc33d172135fc08f1UL, 0xffc1f0839ae21c08UL, 0xd5487b930349686UL } } },
284 { { { 0xa138da16197ba208UL, 0x131b351230ea78f4UL, 0x67d421144983327fUL, 0x301ad90db1293961UL },
285 { 0x2aaf49d5664bf971UL, 0x41de301d76480c2UL, 0xf1b7cd92f25da91eUL, 0x266ad04894fb98a1UL } },
286 { { 0x5430ab66ae7c441eUL, 0x56b0046a411a6a05UL, 0x769a94899a38a9a8UL, 0x47009b2bb1105a4UL },
287 { 0x90e78ec3428acf7fUL, 0x494d36f303578d13UL, 0xf860c04788d78bd4UL, 0xbff46fe73771bc5UL } },
288 { { 0x4deef8f7b5691d29UL, 0x4ca2a905e4dc7c9UL, 0xd346bb2f908bf92dUL, 0x4e7f53251024a06UL },
289 { 0x506c4af6c096a839UL, 0xb66ec8f49dcd25d7UL, 0x1d956454caa9c224UL, 0x80fd62496656a00UL } } } };
290 fq12 expected = {
291 { { { 0x444065edd96c27eUL, 0x441edd1fb7593b4dUL, 0xebca21f0aba5b86aUL, 0x1a0f7150178bce4UL },
292 { 0xd6944c6d8a9a1326UL, 0xebe3e1c083a9070aUL, 0x90085ed26d41b187UL, 0x270dbc63380d166fUL } },
293 { { 0x6ff64bb4265979c2UL, 0x934f9a7229efd61bUL, 0xf2633f5fc77c71cdUL, 0x794a11250897c9UL },
294 { 0x4c16eb3426ead093UL, 0xc6b10f92e5172d17UL, 0x722cc34bab735deeUL, 0x2ef62e8e932612a9UL } },
295 { { 0xe5eb6b4fe61af24bUL, 0xf4ad92e89647ddbeUL, 0xf07438f58235164fUL, 0x2ddf71d5540c3861UL },
296 { 0x1f892a5ed0dbc0bfUL, 0xdea7e0ca077a8f66UL, 0x561aba1a7909c0acUL, 0x2296a5f0bb3fca3UL } } },
297 { { { 0xb33c0e27dc05cf5eUL, 0x9b5ac27c7f9f3fafUL, 0xb34ce34b0ddc0e33UL, 0x8d34950d591462UL },
298 { 0x6633d2139211d6feUL, 0x1c194cb263ca6182UL, 0x280ced1e54e99b63UL, 0x78892452fa76a9eUL } },
299 { { 0x8ffaebac35d5999eUL, 0x8e3226d773c7cac4UL, 0x180b0a89641fbc37UL, 0xd165c35b4cefb88UL },
300 { 0xc500c29819187db2UL, 0xb60e7813e364d528UL, 0xc718884d8620befeUL, 0x28351c10a5846341UL } },
301 { { 0x631e54f75f1002c2UL, 0x409714a9ec1a2c33UL, 0x374ef41466eb7b9bUL, 0xf4a88f46b6a3e97UL },
302 { 0x3e120ddf2bc5b3d2UL, 0x52166a8ab686fb53UL, 0xf5b9fbe942aaec8aUL, 0x1b25bd7f5e7b7db3UL } } }
303 };
304#endif
305
306 fq12 result = a.sqr();
307 EXPECT_EQ(result, expected);
308}
309
310TEST(fq12, FrobeniusMapThree)
311{
312#if defined(__SIZEOF_INT128__) && !defined(__wasm__)
313 fq12 a = { { { { 0x9a56f1e63b1f0db8, 0xd629a6c847f6cedd, 0x4a179c053a91458b, 0xa84c02b0b6d7470 },
314 { 0xffa3e17eab3609a1, 0x6a97b9cf5c3fe152, 0x8996248da177be9f, 0x113bd2d7f24591d } },
315 { { 0x572c4fd8a85cc3b, 0x48197102a98815e8, 0x3a1d00190e8ee460, 0x8c0a0ce9c093781 },
316 { 0x4e0e0e931a6c5239, 0xc2c764493f1ddc6e, 0x16612bee3c36cb07, 0x1c4bcafbc27e189d } },
317 { { 0x9c25202f11b4a225, 0x6183855884e1d9e4, 0x9bec1271f82069fd, 0x25c073771f7bdfd3 },
318 { 0x8369ec32ca273e66, 0x72abfd9ddb3c9580, 0x45c8c3900fa0972, 0xed4e39f24d881cc } } },
319 { { { 0xbe14c75a7ad8b8d, 0xa7f800a3617eb0cc, 0x8ac553d859ebfa82, 0x1bd48369b2897384 },
320 { 0xa87047cda886d4e4, 0xa10f79abb449eca1, 0xa91048654572ca4a, 0x11800c4140b84683 } },
321 { { 0xbdab137f3526b04c, 0xcdf528cca5ac1194, 0xcd0ff308caa11d1a, 0x13c37af89e7ad03c },
322 { 0x9014dab1a6705e3e, 0x70ed9bade13bc7b7, 0x83467e7a0e0db5f, 0x2edb100f286c3cc2 } },
323 { { 0xe786890dc3e92812, 0xaa840f633c4d0061, 0xd73779dc2e753e05, 0xb0cf45d93b45890 },
324 { 0x1dc2a49708e5d8f, 0x189d394aac19ff2e, 0x6c365b59d178d821, 0x4a15ee554b55690 } } } };
325 fq12 expected = { { { { 0x9a56f1e63b1f0db8, 0xd629a6c847f6cedd, 0x4a179c053a91458b, 0xa84c02b0b6d7470 },
326 { 0x3c7caa982d46f3a6, 0x2ce9b0c20c31e93a, 0x2eba2128e00999be, 0x2f509145620d470c } },
327 { { 0x8d1840c0a5e1beb1, 0x138909972699551, 0x6a2e46c29fc2e5e1, 0x2d5cc6154756f1f4 },
328 { 0x5c8d20bf46b48f23, 0x6f2cfc3bbdc5a317, 0xc528bbde6b995609, 0x24d37fc007b3c428 } },
329 { { 0xe1eea948d237426c, 0xe5c87a399cc972b1, 0x9747645c534da08a, 0x1e805d835ba889b4 },
330 { 0xdca7dd1573c013f7, 0x49a6b1b9c1877fe4, 0x352a43009f945986, 0x1136516f2fe27f7e } } },
331 { { { 0xf1591bdf82b9d577, 0x1ecfa28b5fe484a1, 0xe0e909e81b7b33de, 0x9a74f7ffc66975f },
332 { 0x9014340deeb7e8e0, 0xdf43f8e4e9470acf, 0x28e60662f1312e80, 0x17aadacec0d56c71 } },
333 { { 0xdb21cdcd8b4802fa, 0xb576311ef4863621, 0x28198e0757da3a32, 0x792df3cde67eb9a },
334 { 0x373dde8dfb6dceb3, 0xa0feac44ec583fb4, 0x257146bc7ad7d5c2, 0x1ee0a5c45a91938b } },
335 { { 0xf8c975188dd668a5, 0xfa38a6144e0c5451, 0x8ebdddc91016c224, 0x13fe7e09fe48aefb },
336 { 0x2ce375ffd1c12d33, 0xc2099e064cd9724d, 0x9c54b742a4d8bd59, 0x1c79d60ac5202c8c } } } };
337#else
338 fq12 a = { { { { 0xe21af43e50f3c756UL, 0x382c59a08c2f1c63UL, 0xf111de6049209f49UL, 0x2e3e2eb02684cd0eUL },
339 { 0xf47c2fd566c13420UL, 0x52f739eb87fc2a5fUL, 0x32c491b42ef7d3edUL, 0x2277a5afe48b23b1UL } },
340 { { 0x81b5e33f164894fdUL, 0xda70b7e26c9c83eUL, 0xaa0ea6914a55d235UL, 0x261e91951b2ecf56UL },
341 { 0x8777f8c814c07822UL, 0xb1d30aee8bbb4fdbUL, 0xd68096f26bc12a63UL, 0x226bdb647a45d0b3UL } },
342 { { 0xe196e3bdeadc85f8UL, 0xfc4ead6ed1903f55UL, 0x35fbc522dfecf6e5UL, 0x2ea7141ed2d4f68aUL },
343 { 0x5018998ba882e541UL, 0x1f2f49ebb929119UL, 0x10bf13b591b51304UL, 0x2715b1dab0519809UL } } },
344 { { { 0x41dfb519bce7a2a2UL, 0x57e69632d7d5db93UL, 0x63059436226719c0UL, 0x1382e9227bb12da2UL },
345 { 0x78a2f4b9c37bba73UL, 0x9f5fa1370c59e023UL, 0x36960dd11dca7d4eUL, 0x1bb2293869e6eeaaUL } },
346 { { 0xa7bb52bda67d2ce5UL, 0xd12b03267bae96bUL, 0x45ead6d4c0922699UL, 0x357633e5fd4e57bUL },
347 { 0xf6caeb876f66196eUL, 0x5c88f8b1ea233a64UL, 0x6d24d190eef310f6UL, 0x2fa0d06ea9b6d35dUL } },
348 { { 0x4bed4d1891ba154fUL, 0x2bf8026dae838260UL, 0xdcbd5388441e5626UL, 0xee0668e4e2fb0f6UL },
349 { 0x8723a4e98854ba0bUL, 0x4d22e9a149ea8618UL, 0x5dda9a16aa96fb0aUL, 0x2fef151f315f190UL } } } };
350 fq12 expected = {
351 { { { 0xe21af43e50f3c756UL, 0x382c59a08c2f1c63UL, 0xf111de6049209f49UL, 0x2e3e2eb02684cd0eUL },
352 { 0x47a45c4171bbc927UL, 0x448a30a5e075a02dUL, 0x858bb40252898470UL, 0xdeca8c2fca67c78UL } },
353 { { 0xd358397e360f2515UL, 0xfd6900b5784eb831UL, 0x64b0f2a74cb5b985UL, 0x303bdfa5683f19d3UL },
354 { 0xee96f5c48ada25b8UL, 0xb17d89d5ee0965adUL, 0x5d90f2b14f0a7867UL, 0x11089d3bd9d1812fUL } },
355 { { 0x8b4a37515d2483f4UL, 0xe2f2f3d7704a8333UL, 0x82a719484b992a0cUL, 0x8358f71dd30b350UL },
356 { 0xff959db32aa39cd3UL, 0xb246a2f8b40c4889UL, 0xb9d5613c61fc64c3UL, 0x127acef64f2e0dfbUL } } },
357 { { { 0xc2603367444cbf36UL, 0x4cebd20389e5d4eeUL, 0xcb3f9abc665e6992UL, 0x1290194e45a92b01UL },
358 { 0x7c9e4c6727aa44d7UL, 0x7e9de180a367babUL, 0x500cb6ac8f91a2a0UL, 0x1f7ac11ce8c52bb3UL } },
359 { { 0x3796fd3f2e8f6cddUL, 0xb93f0f07868dcf79UL, 0x69a0645a73c08c82UL, 0x665f5d67055274UL },
360 { 0x3530dff683f60cd4UL, 0x49b935416224237eUL, 0x47e3654d3cdfd104UL, 0x143e9791ba51ee22UL } },
361 { { 0xb8785e8bc743805UL, 0x9582592773c34113UL, 0x7ba82edd6f46c7deUL, 0xab7c56a5990bd53UL },
362 { 0x6224e65eff5bd762UL, 0x9a1a4290432e0bb7UL, 0x94f2017f7fff74a3UL, 0x282d3d44ce884ea4UL } } }
363 };
364#endif
365
366 fq12 result = a.frobenius_map_three();
367 EXPECT_EQ(result, expected);
368}
369
370TEST(fq12, FrobeniusMapTwo)
371{
372#if defined(__SIZEOF_INT128__) && !defined(__wasm__)
373 fq12 a = { { { { 0x52c2cc6e77bfe9bb, 0xd03d98cc3fd6d95, 0xfaeb6d6577aa9a30, 0x1ea38b81330e34df },
374 { 0x1f55d493000a14f3, 0x1db7ec50e2f5a356, 0xf3cfcc74b91481ae, 0x256fe76342b33dbb } },
375 { { 0xf3e95f622620a0f9, 0xe297badf08d73c22, 0x4df25d06ae059cfb, 0x16db699bc5bbddcb },
376 { 0xac821bca1b523880, 0x16e1c766941d5b3d, 0xcb1c3f0728eead67, 0x6a5bd44c11dc548 } },
377 { { 0xb6f165cba1492db7, 0x4b8dccf49d8ecb53, 0x4e9a8c3a5c91689f, 0x20ecb1ddd8c9db20 },
378 { 0xe7564097b01c2415, 0xf476520c5e9db5e6, 0xfe0ceb51798a245a, 0x2e9b3ec7fb7ad207 } } },
379 { { { 0xf6e41a9b92434e0f, 0xeac46c17d2196da2, 0x44ac37aaba7d0518, 0x180b934a2302bc95 },
380 { 0xe2f112f1202f2a60, 0xdc6b42ce5b35837a, 0xfcee96f99e45e6b, 0x16f32ea5beadafe6 } },
381 { { 0xf11a764f75cd1ed6, 0x5b8605f1e9098788, 0xea81f341743177be, 0x1cafbefd2f6c5fa2 },
382 { 0x17bee2a7f91295fe, 0xb6b9716d19e4bbbc, 0x2f2550ee4c7ac30, 0x262edd6f32297cd5 } },
383 { { 0x430e641e6e94258d, 0xb1755bba0763e432, 0x3db56777846ee870, 0x22afd677233812e3 },
384 { 0xf89461bd1d9c3fa3, 0x9e25f21b44ad86a4, 0xfd1ed29f62168344, 0x1b337ab64bd9b0af } } } };
385 fq12 expected = { { { { 0x52c2cc6e77bfe9bb, 0xd03d98cc3fd6d95, 0xfaeb6d6577aa9a30, 0x1ea38b81330e34df },
386 { 0x1f55d493000a14f3, 0x1db7ec50e2f5a356, 0xf3cfcc74b91481ae, 0x256fe76342b33dbb } },
387 { { 0x4d9bb69ca210d241, 0x42463a9de9a1298b, 0x6366c00ae6b366b2, 0x285cb81559b3c407 },
388 { 0x36f8a22587e7744b, 0xcba6fb2211505810, 0x357b875177bf4b97, 0x2da32e219de1632e } },
389 { { 0xb924dcf76fafea68, 0x430e02ed7ea41521, 0x29f4e4fcd758836c, 0x4839f24c2b447d },
390 { 0x7132411924f9b60d, 0xdd3d6a51478988d7, 0x98540139abbbd312, 0xc1409eeafe2aac } } },
391 { { { 0x222382f8f84c512c, 0x4b3f1d0eb307d6fd, 0x22f8fc60fe916c14, 0x1e63f42d2acbd109 },
392 { 0xf82d6103c6305cf4, 0x804b64f5caf58e7b, 0x69b8b37fa1383c9b, 0x2e74c0b9738bac8a } },
393 { { 0x4b0615c762afde71, 0x3bfb649f7f684304, 0xcdce52750d4fe09f, 0x13b48f75b1c54086 },
394 { 0x2461a96edf6a6749, 0xe0c7f9244e8d0ed1, 0xb55df0a79cb9ac2c, 0xa357103af082354 } },
395 { { 0xe1148c424a589341, 0x40ab0d25fb7fd0d1, 0x7909a54a9569db90, 0x99bde98bbc4352f },
396 { 0xfaa4fdcf224e38ee, 0x42b25f170bf5f577, 0xc13bf097c75be619, 0xbcb9923cbd60387 } } } };
397#else
398 fq12 a = { { { { 0xa5ce9c060e396dd4UL, 0xca5ede3c56c9dfa1UL, 0xf7283a6cd7385eb1UL, 0xc9b4f2cc9e618bcUL },
399 { 0x47ad703bb58adfb8UL, 0x82db8c7a94096d86UL, 0x3273057afe6fecfdUL, 0x249591a339c0b395UL } },
400 { { 0xf743b6ee14c147f7UL, 0x72621d5bfc3ca617UL, 0xf1978b242a1f7200UL, 0x58c9abd859356f7UL },
401 { 0x9fc148e808531ae4UL, 0x7e33428ce1e43d80UL, 0x8246ca0b17d04b6cUL, 0x13266ecc9ef22872UL } },
402 { { 0xef813b9466e4f00dUL, 0x41be0a62083cce0UL, 0xb4bbcf52f290d43cUL, 0x255bcc4ea029409dUL },
403 { 0xdef7a848a4ded44eUL, 0xcd9fc4819661004fUL, 0x28353ecc041c3066UL, 0x27a6a7890b897c1cUL } } },
404 { { { 0x569b1e1b9916eab7UL, 0x77f844752482d618UL, 0xc8d2dfa5b90c75a1UL, 0x2b91d0892e6f3036UL },
405 { 0xd83a28cd569274d7UL, 0xacd31b4648059115UL, 0x2d291841a5f79fffUL, 0x8853bfca3cd9a50UL } },
406 { { 0xe904f05380da0bc2UL, 0xc9a74003c930b32fUL, 0x5a9981596b16c136UL, 0x2eea5b92180eb16eUL },
407 { 0x18aea6c3fe1e03d1UL, 0xb8ac570097aafb8UL, 0x5e73d309f353e4f3UL, 0xc1004ae4756f68dUL } },
408 { { 0x370079d737c6ed86UL, 0x298c4ec1f2b51e25UL, 0xdfc6f1416cbf760bUL, 0x2d5c11050cbe98d1UL },
409 { 0x1462ea1f533b22a9UL, 0xb5262fc0a622613eUL, 0x6685b2cda9398a5cUL, 0x2fc6212886ea733aUL } } } };
410 fq12 expected = {
411 { { { 0xa5ce9c060e396dd4UL, 0xca5ede3c56c9dfa1UL, 0xf7283a6cd7385eb1UL, 0xc9b4f2cc9e618bcUL },
412 { 0x47ad703bb58adfb8UL, 0x82db8c7a94096d86UL, 0x3273057afe6fecfdUL, 0x249591a339c0b395UL } },
413 { { 0x9828994245688eeaUL, 0xe5a280f898969f11UL, 0xb4b0ecd3af49dcc6UL, 0x21670b00576e3cafUL },
414 { 0xd343da039e48db0eUL, 0xb3b4e737ecb54579UL, 0x1608becbcac11801UL, 0x8a492bd585ba0e3UL } },
415 { { 0x249b9eedf5fd4d00UL, 0x61c05dafd482a437UL, 0x3e9c9f9aeb106d88UL, 0x9073e4985688fa5UL },
416 { 0x264823249f36c1a0UL, 0xa7ad4a28f1311aeeUL, 0xa802735777a625bUL, 0x182813dd5fc55593UL } } },
417 { { { 0x91e56d561fc65bf4UL, 0x91c74e7a38170c9bUL, 0xf8da19ddb4129b39UL, 0x4a864abc1999de1UL },
418 { 0xf9dbb5cb6765f02eUL, 0x484221af215c12f1UL, 0x9dae4490f9df3878UL, 0x22d6e5b80da4cc69UL } },
419 { { 0x531b9bc357a2f185UL, 0xcdda2a8d9f41175dUL, 0x5db6c45d166a9726UL, 0x179f2e0c922eebbUL },
420 { 0x2371e552da5ef976UL, 0x8bf6a5215ef71ad5UL, 0x59dc72ac8e2d736aUL, 0x245449c499daa99cUL } },
421 { { 0xb9ce3fc038247876UL, 0x88592556fd4f5aecUL, 0xcf53070ba4335fd6UL, 0x1121fc66315ce4f4UL },
422 { 0xafbbe5445e5c30cfUL, 0x31c1f8e7a3a22522UL, 0x1d4c2afb60f35899UL, 0x26b4ff5552650fd4UL } } }
423 };
424#endif
425 fq12 result = a.frobenius_map_two();
426 EXPECT_EQ(result, expected);
427}
428
429TEST(fq12, FrobeniusMapOne)
430{
431
432#if defined(__SIZEOF_INT128__) && !defined(__wasm__)
433 fq12 a = { { { { 0x6c9edca7f0d6f6e, 0x7bb482de96b01e0, 0xb04fc4b2b2ea7e6, 0x4d9efc00ceb8323 },
434 { 0xb55c2222935ee583, 0x9c114ab89499b4da, 0x771cb5cabe1f458a, 0x1c3f0ac5303a5935 } },
435 { { 0x524feabf94af29ea, 0x95573536ab8b6ced, 0x524e16790930912c, 0x280d5af94a3424d0 },
436 { 0xb6bdb5285238031c, 0x961e21ab4b9f7945, 0xa99257ecdc41179e, 0x25e9db7f50b8546f } },
437 { { 0x8ca5a9882dc185c4, 0xa497430d9ad2eebf, 0x29ed717c08faa305, 0xda59ed41c4283dc },
438 { 0x175ebf044916d79d, 0x3ed791b6263d56f1, 0x5c7c8932a433f839, 0x285eee6d768929ed } } },
439 { { { 0x9195748c97fc7d6b, 0xa1da2592e5bde3bb, 0xe5f0358e5d6cd5b, 0xb890130084b6b73 },
440 { 0xb50d2c5ff65b68cd, 0xccefdc002bc84549, 0x732d99161ec379d5, 0x2c722b5ccbe40e2c } },
441 { { 0x1a3eaa24332c6fec, 0x8071b2dfdcbd55b9, 0x8fe8eb04d17c636a, 0x19a62bd610f3804d },
442 { 0x5e3a6b8238a14511, 0x70ef5efffc4e9e0e, 0x4e9b9a99caea296d, 0x28b9c9b70b4a747 } },
443 { { 0xc8f5f5664e3f17b4, 0x9e7b5d54d9e15481, 0xbd988b509f7d50b3, 0x101e343da280a34d },
444 { 0xbbb066284977a03, 0x264fc527ee8e520b, 0xacfa9508d9838c79, 0x191aa234984e211d } } } };
445 fq12 expected = { { { { 0x6c9edca7f0d6f6e, 0x7bb482de96b01e0, 0xb04fc4b2b2ea7e6, 0x4d9efc00ceb8323 },
446 { 0x86c469f4451e17c4, 0xfb701fd8d3d815b2, 0x41338febc36212d2, 0x142543adb0f746f4 } },
447 { { 0xf4f695f59ce42cc7, 0xfab5aeca9715cd7, 0x8b69eaaf2cd76201, 0x364198e07630ca1 },
448 { 0x3cfc0f380cf3ba4a, 0xa1b605c52d334134, 0x321851c92680ca6c, 0x1749c78adebf8a5 } },
449 { { 0xeb71d65e04f06a8e, 0x569282ba59fbff0c, 0x1fb36eb4c4a1775, 0x22e79a74ea6bc0e6 },
450 { 0xe14b43fe62621be8, 0x36134c26ff43c3be, 0x3bd5b11835a8d7ee, 0x2e3b0f601d37b2c9 } } },
451 { { { 0xbda31ec838b3068d, 0x4f5f85130ea53c9c, 0xdae0c5f1f50979a1, 0x22eb05e4599b8f58 },
452 { 0xac23aa05132e266c, 0x5f0aa178c3a8f897, 0xe63225d0708133b9, 0xeeed4318f7539dd } },
453 { { 0x4249d30a2f88f55d, 0x10a7f2448ad57e4f, 0x260e76b439322dff, 0x1cb7e78896fd543c },
454 { 0x6602e7e93a714d67, 0x7398f14acf72c7e0, 0x8028d203d5e4928, 0x7d1fad57418b580 } },
455 { { 0xcba1922169de670, 0xcd20689212638b5e, 0x8dbbc53af7639bbb, 0x57a19a043d38c39 },
456 { 0x2b2d3090bfb1118b, 0xa752e789e316e0c7, 0xc1c4d33385bc3e10, 0x2610936b5468ba45 } } } };
457#else
458 fq12 a = { { { { 0x24dc150b5836f5ebUL, 0x30e4c608f40adc59UL, 0x37aeb841e150f3a8UL, 0xa110ca8f9db83e4UL },
459 { 0x713a6ab73312e162UL, 0xdb0fd8d93b365d68UL, 0xedf1d282a8d07abeUL, 0x20d3d49231cde3bfUL } },
460 { { 0x2eaf1da09933840aUL, 0x47c1d410d5df0b52UL, 0x919bba97feef2c11UL, 0x177b677e677a55cdUL },
461 { 0xf888f6cf22cba791UL, 0xf820cd3640d260ebUL, 0x32742ec8e28152aeUL, 0x36fc6b21931e9e2UL } },
462 { { 0x779044381bcbd101UL, 0x3f5ba296ae5db8faUL, 0xc2dbbc1691c8456aUL, 0x12d18799d91da0dUL },
463 { 0xd089a63726293a6aUL, 0x77cd64002c1c4bcaUL, 0xd76a11cb5f5c0da6UL, 0x21add603f21af96eUL } } },
464 { { { 0x8dcabcf31424c06fUL, 0x16bac862dc9fed95UL, 0xc1ae831f305040e5UL, 0x1e6200dce1120d3dUL },
465 { 0xd1f5ad6845446895UL, 0x74526d8ca424b736UL, 0x849b3d172cc8381fUL, 0x12e88895f9e2a0d4UL } },
466 { { 0x85cc8318ddbe2910UL, 0x961fb2e5108e0e4fUL, 0x781905321776e776UL, 0x2e8093940b560716UL },
467 { 0x8b2ce4303baba4d9UL, 0x866a756e2161f73eUL, 0x1b230d82dbc3d550UL, 0x210f44fb356348c0UL } },
468 { { 0xc57933e5530111baUL, 0xe45d80ed27b8a6b4UL, 0x7feeb0f2e09ca2cbUL, 0x1fdb773784242816UL },
469 { 0xb5580ae30b1f6bf0UL, 0x51e1fbe74aad988dUL, 0x1a4e45b3185c094bUL, 0x1d0f5f64f6aa211aUL } } } };
470 fq12 expected = {
471 { { { 0x24dc150b5836f5ebUL, 0x30e4c608f40adc59UL, 0x37aeb841e150f3a8UL, 0xa110ca8f9db83e4UL },
472 { 0xcae6215fa56a1be5UL, 0xbc7191b82d3b6d24UL, 0xca5e7333d8b0dd9eUL, 0xf9079e0af63bc69UL } },
473 { { 0x2691a685eb8b9e52UL, 0xc66888725d4805e4UL, 0xfc9cca7897e98f66UL, 0xbba94db29fe53ddUL },
474 { 0x9f81e7019e774940UL, 0x36c0b8a5a6682687UL, 0x430a3924d0194d94UL, 0x2e938f15bd7f14a6UL } },
475 { { 0x74e35b32ad2905fUL, 0x35afc43add46aeedUL, 0xb0309a03e6a3fe42UL, 0x3f0424b1202b900UL },
476 { 0x1d98151eed9dceaeUL, 0x13f07d5ab22bb4fUL, 0xe14df7a387f2a2cfUL, 0x1ba0ba8d43259443UL } } },
477 { { { 0x4d7742f9a326103fUL, 0x4f500f51726e60e7UL, 0xcce27ad8fe9043c1UL, 0x45db038f7fc875bUL },
478 { 0x675053d4c95fe601UL, 0x8dc76ffbc91ef3feUL, 0x4b7246a3829a5be1UL, 0x2a53c42803e89a45UL } },
479 { { 0xef087aab854dca2UL, 0x6de4ca5802af8bfaUL, 0xcc29efb20b2d894dUL, 0x2fef6cff0a2d4495UL },
480 { 0x93ba40b513b8ba7dUL, 0x7d971482e420074aUL, 0x66c0477724426b3aUL, 0x849d2701d1e8f30UL } },
481 { { 0xe2e17ffe4a45d62bUL, 0xdd88d28e131c0c19UL, 0x8e87d63b67ef6e60UL, 0x1e1648afd6dca6b4UL },
482 { 0x867863dcd1ed7571UL, 0x1eb989092fbf511aUL, 0x38c3979e11e620f1UL, 0x846c4328f3ea4a5UL } } }
483 };
484#endif
485
486 fq12 result = a.frobenius_map_one();
487 EXPECT_EQ(result, expected);
488}
489
490TEST(fq12, FrobeniusMapSixIsConjugation)
491{
492 fq12 a = fq12::random_element();
493 fq12 result = a.frobenius_map_three().frobenius_map_three();
494 EXPECT_EQ(result.c0, a.c0);
495 EXPECT_EQ(result.c1, -a.c1);
496}
497
498TEST(fq12, UnitaryInverse)
499{
500 // Unitary elements can be obtained by taking a random element and raising it to the power
501 // (q^12 - 1) / (q^4 - q^2 + 1) = (q^2 + 1) (q^6 - 1)
502 // Note that q^4 - q^2 + 1 is the cyclotomic polynomial of degree 12 evaluated at q
503 fq12 unitary_input = fq12::random_element();
504 unitary_input = unitary_input.frobenius_map_two() * unitary_input;
505 unitary_input = unitary_input.frobenius_map_three().frobenius_map_three() * unitary_input.invert();
506 fq12 result = unitary_input.unitary_inverse();
507
508 EXPECT_EQ(unitary_input * result, fq12::one());
509 EXPECT_EQ(result.c0, unitary_input.c0);
510 EXPECT_EQ(result.c1, -unitary_input.c1);
511}
512
513TEST(fq12, FrobeniusCoefficients)
514{
515 fq2 frobenius_coeff_1{ Bn254Fq12Params::frobenius_coefficients_1 };
516 fq2 frobenius_coeff_2{ Bn254Fq12Params::frobenius_coefficients_2 };
517 fq2 frobenius_coeff_3{ Bn254Fq12Params::frobenius_coefficients_3 };
518
519 // \xi^{(q-1)/6}
520 fq2 expected_frobenius_coeff_1 = fq2{ 0x09, 0x01 }.pow((fq::modulus - 1) / 6);
521 // \xi^{(q^2-1)/6} = \xi^{(q-1)/6}^{q+1}
522 fq2 expected_frobenius_coeff_2 = expected_frobenius_coeff_1.pow(fq::modulus + 1);
523 // \xi^{(q^3-1)/6} = \xi^{(q-1)/6}^{q^2+q+1}
524 fq2 expected_frobenius_coeff_3 = expected_frobenius_coeff_1.pow(fq::modulus).pow(fq::modulus) *
525 expected_frobenius_coeff_1.pow(fq::modulus) * expected_frobenius_coeff_1;
526
527 EXPECT_EQ(frobenius_coeff_1, expected_frobenius_coeff_1);
528 EXPECT_EQ(frobenius_coeff_2, expected_frobenius_coeff_2);
529 EXPECT_EQ(frobenius_coeff_3, expected_frobenius_coeff_3);
530}
531
532TEST(fq12, SparseMul)
533{
534 fq12 a = fq12::random_element();
535 fq12::ell_coeffs ell;
536
537 ell.o = fq2::random_element();
538 ell.w = fq2::random_element();
539 ell.vw = fq2::random_element();
540
541 fq12 b{ fq6{ ell.o, fq2::zero(), fq2::zero() }, fq6{ ell.w, ell.vw, fq2::zero() } };
542 fq12 expected = a * b;
543
544 a.self_sparse_mul(ell);
545
546 EXPECT_EQ(a, expected);
547}
bb::field12::c1
base_field c1
Definition field12.hpp:48
bb::field12::frobenius_map_three
constexpr field12 frobenius_map_three() const
Definition field12.hpp:183
bb::field12::invert
constexpr field12 invert() const
Definition field12.hpp:172
bb::field12::random_element
static constexpr field12 random_element(numeric::RNG *engine=nullptr)
Definition field12.hpp:217
bb::field12::unitary_inverse
constexpr field12 unitary_inverse() const
Definition field12.hpp:209
bb::field12::one
static constexpr field12 one()
Definition field12.hpp:57
bb::field12::c0
base_field c0
Definition field12.hpp:47
bb::field12::frobenius_map_two
constexpr field12 frobenius_map_two() const
Definition field12.hpp:191
a
FF a
Definition field_gt.test.cpp:52
b
FF b
Definition field_gt.test.cpp:53
bb
Entry point for Barretenberg command-line interface.
Definition api.hpp:5
bb::TEST
TEST(BoomerangMegaCircuitBuilder, BasicCircuit)
Definition graph_description_megacircuitbuilder.test.cpp:22
bb::Bn254Fq12Params::frobenius_coefficients_2
static constexpr fq2 frobenius_coefficients_2
Definition fq12.hpp:59
bb::Bn254Fq12Params::frobenius_coefficients_3
static constexpr fq2 frobenius_coefficients_3
Definition fq12.hpp:64
bb::Bn254Fq12Params::frobenius_coefficients_1
static constexpr fq2 frobenius_coefficients_1
Definition fq12.hpp:54
bb::field12::ell_coeffs
Definition field12.hpp:50
bb::field12::ell_coeffs::w
quadratic_field w
Definition field12.hpp:52
bb::field12::ell_coeffs::vw
quadratic_field vw
Definition field12.hpp:53
bb::field12::ell_coeffs::o
quadratic_field o
Definition field12.hpp:51
bb::field2< fq, Bn254Fq2Params >::random_element
static field2 random_element(numeric::RNG *engine=nullptr)
Definition field2.hpp:201
bb::field2::pow
constexpr field2 pow(const uint256_t &exponent) const noexcept
Definition field2.hpp:127
bb::field< Bn254FqParams >::modulus
static constexpr uint256_t modulus
Definition field_declarations.hpp:234
bb::field::sqr
BB_INLINE constexpr field sqr() const noexcept
Definition field_impl.hpp:69