--- /dev/null
+### Test cases for arithmetic mod 2^255 - 19. -*-conf-*-
+### Extracted from Catacomb.
+
+###--------------------------------------------------------------------------
+test add
+
+## Some load and store tests.
+x 0102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f20
+y 0000000000000000000000000000000000000000000000000000000000000000
+z 0102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f20
+
+x ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f
+y 0000000000000000000000000000000000000000000000000000000000000000
+z ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f
+
+x edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f
+y 00000000000000000000000000000000000000000000000000000000000000
+z 00
+
+## Random tests.
+x bb8cd45b6185ee8ca34c4d7560425fd5c2fc22871113c6427198e8f9439a8523
+y 98f16cc5e44b7228b7f3b6ed91930d68bba5071157d19259c48034d2817e30d5
+z 667e412146d160b55a400463f2d56c3d7ea22a9868e4589c35191dccc518b678
+
+x 8ef938a7b07a668c234c2c5bb65115b8e2e22a3703cda51c70e7a56a075d4f34
+y 1f3cd4bf4f768058c4de1aa5aeb90e227338e308c7a0a199050ca1c38d1e034c
+z c0350d6700f1e6e4e72a4700650b24da551b0e40ca6d47b675f3462e957b5200
+
+x 8b2c4678fd4f8b7254eea925e4da8d472db7f97d349d1b2134ced884b747ea7d
+y 58dca7954f843b7e4dc56b048903e7728df66ef6824f29932b2f568c995ddf2c
+z f608ee0d4dd4c6f0a1b3152a6dde74babaad6874b7ec44b45ffd2e1151a5c92a
+
+x 9cd64f0cf439bccd224f7a789396b9f888998d1ba9759c93a5d6a27f45db0e67
+y 12f724a127052612081e27e3915db9a540de9b64c566edc313914ad94424464e
+z c1cd74ad1b3fe2df2a6da15b25f4729ec97729806edc8957b967ed588aff5435
+
+x 82e59fa9703b2557303665fe24e3d46259da974d78155f05c6b8891f92fc808d
+y 98a073ec62baf1354b681a3c78d62df1698ed5077dbe2bd68ba4a6e0233e3447
+z 2d861396d3f5168d7b9e7f3a9db90254c3686d55f5d38adb515d3000b63ab554
+
+x 686ceca221d0f4c6d98287e97c506085064e7b172672b88ee555dd0308bfd309
+y 60adc3675be5e6c2921a74b5b8b24b0a26341a19567dae713a720786bc72df16
+z c819b00a7db5db896c9dfb9e3503ac8f2c8295307cef660020c8e489c431b320
+
+x a50a5b82d2451ed9a5844585712202a6dc0e0230501d57b8c00f4bd4771aed9e
+y 98d71b8b140aea02ad47d9b19e47d2a03257adc1d5c47611adc667652b78c87c
+z 63e2760de74f08dc52cc1e37106ad4460f66aff125e2cdc96dd6b239a392b51b
+
+x 1637e3eb4c5d173b8cba29bdb13b930f48ae0599e354819f8ae0cf70f0f7b61b
+y ffeef1767df70de7a4a75864c03935d7934c6cf5228b9c3000813ed0e55447e2
+z 2826d562ca542522316282217275c8e6dbfa718e06e01dd08a610e41d64cfe7d
+
+x 9e8bf571c45bc5f37c9126e70498698978903b94d9c6712baef91894ab924fda
+y 480f68f8ee644bfb64e3fa514eaf16aea6368da6813802c4c3e6ce8f6540dfa3
+z 0c9b5d6ab3c010efe1742139534780371fc7c83a5bff73ef71e0e72311d32e7e
+
+x df9bdbd478bd1ec1ff078cdc76f2a5fcdc52f0198ba412e0b5a10e664b175dad
+y 080bc47bd2fb2ba3be6a07a02162f76020479f2cc6469c6766df23acf9517896
+z 0da79f504bb94a64be72937c98549d5dfd998f4651ebae471c8132124569d543
+
+x b6dd223f5d8a3dc5dd6f7a0679173ff656303017a17f17f4086fd4ecd3a23020
+y 560d827aad23c26fddbfd16c3514a9b518a4586d6e3c5739860743662b14f4b4
+z 1feba4b90aaeff34bb2f4c73ae2be8ab6fd488840fbc6e2d8f761753ffb62455
+
+x 1d59691a670c40143ca7f7e693389ab64a911b17a2fe4368fba9097b40864162
+y cb42d3ba12a8b90ef1622ea09241d3157c515043040914356d6d99b95089fa07
+z e89b3cd579b4f9222d0a2687267a6dccc6e26b5aa607589d6817a334910f3c6a
+
+x 82b48877e9c8c18edb52db3e1417d894e572a8edd84335d93c642158f2a926e0
+y 93c6a39c1ef97f318c3b13bf8e77bea653b2eb130bdf43b00a0e0e40a362e819
+z 287b2c1408c241c0678eeefda28e963b39259401e422798947722f98950c0f7a
+
+x a6137481c5b9b8bcb3c87f3868c5f812da71aeb21c5ce18a508773120ea4f659
+y 812eacdc5a8eb2e8fde0c23a19c2e33466d754ab3109d28ff48fb41dab8066e2
+z 4d42205e20486ba5b1a942738187dc474049035e4e65b31a45172830b9245d3c
+
+x 598fb4096a7054e317e66bc9633d56dfcaeabc31a7bbc9da13074b242edeca09
+y 929b1bddd55c99b06b99a3ffbac5adc1d28823cb8354adcfea60b7a87fe32039
+z eb2ad0e63fcded93837f0fc91e0304a19d73e0fc2a1077aafe6702cdadc1eb42
+
+x c42183d915267e655409326b1b77a042d8918feefd75dd3d18551f398ef426e7
+y e3729a6110686ffa57d1c69284a60fb36173148a89b1810d04614f03c8f90084
+z cd941d3b268eed5facdaf8fd9f1db0f53905a47887275f4b1cb66e3c56ee276b
+
+x 67b8b7ea7e7f9f52d686f906589c919b293bff6d3127e7ac581dc1630af7bcc1
+y 99d18d2190ef0da148b843c014fea3efea59f9adbb28fa38407191fcc24e029c
+z 268a450c0f6fadf31e3f3dc76c9a358b1495f81bed4fe1e5988e5260cd45bf5d
+
+x bc3422b79e01234fefd3637a19bfb2dd0a83bf2071b27bf5389918a50e579294
+y b665dffe064aceffaabba94697cf27054d016427ebaf68858c5250cc5c1b770f
+z 859a01b6a54bf14e9a8f0dc1b08edae2578423485c62e47ac5eb68716b720924
+
+x d419cbfd5514d9cffa1765b9f273fd7492000a3d110586ed0b8137760a2e808e
+y bcb52f423917c074464b2078d1c3f883fb793b02411b8b13c08266d17658a499
+z b6cffa3f8f2b994441638531c437f6f88d7a453f52201101cc039e4781862428
+
+x 2f7eb8051d16a52b797e2618881bd0857eb205bf97e581e09680f86308f7e082
+y 9ceda63b29c3bfedbb6f3f0be2f3f2bd285bb9d21620c3edde69629b00b1c3cd
+z f16b5f4146d9641935ee65236a0fc343a70dbf91ae0545ce75ea5aff08a8a450
+
+###--------------------------------------------------------------------------
+test sub
+
+x dfb53b4ff67c742728c564d50ae20e3e3617804478a95e511d37ff4dcf04fa3f
+y 9bc2006bb07dcf7bf0b461e7599e3c3cbfcdf6b6f41fc1db2219767ce9c43bcd
+z 1ef33ae445ffa4ab371003eeb043d2017749898d83899d75fa1d89d1e53fbe72
+
+x 432ec65076c94af41e054a43f64fe4eecb23f50a303fd38e0172e4e846e67394
+y 3642c84c5f5fcd5a0f3f2e37114beb8e7b614c39d354f1b32fe7e9cc918da5c8
+z faebfd03176a7d990fc61b0ce504f95f50c2a8d15ceae1dad18afa1bb558ce4b
+
+x 1725a986c03d9d53346ab2064545ba90ab38191e19ded9ecc2f44d422ab04150
+y 11a20caef0239e4ffb5ab2f7d3576633a0d4a08c78a02f35765fafff5398c48b
+z f3829cd8cf19ff03390f000f71ed535d0b647891a03daab74c959e42d6177d44
+
+x ec5d5cdfc8183f9aa3d47634d16427c3a399e2166bfa4ddfecbc911e5f33ceba
+y 649f8e29c483765c4232c369fd0e50a0026eac306eb4bd6924e7b4d7d3f73e26
+z 9bbecdb50495c83d61a2b3cad355d722a12b36e6fc459075c8d5dc468b3b8f14
+
+x cc9927c331884612d8fab9a2262ad0db38f55e0cc587e45b972ea8b1f504450d
+y 30c5c9f8d5491a350051bbc6bb78e568d98061b43cb1797cd3d7454e8a7aa1bf
+z 76d45dca5b3e2cddd7a9fedb6ab1ea725f74fd5788d66adfc35662636b8aa34d
+
+x 662bc96da214e50f13e07a15b8e0b78f512c744a66975b2170ba28079ca7d03b
+y 84b072295dca0abef806ec5c1e594179dc5e9eb172c178af1902a42ea7a3728e
+z cf7a5644454ada511ad98eb89987761675cdd598f3d5e27156b884d8f4035e2d
+
+x ed6f947157492eccc5fb1d0542593d58a47e2d87355dc0378e65376163fcf457
+y cb27e06c5ebf42a61caadd4fb222799772aaef31487bf61ac84c15f58af265d3
+z 0f48b404f989eb25a95140b58f36c4c031d43d55ede1c91cc618226cd8098f04
+
+x 33c2fc57d8ffc29e6d670cfc4e25b695320055cf443ade53f49f6c23c452f644
+y 3814860ccbb4391894c107961170d3af1594988a7972b97d0fb2169631b216fa
+z d5ad764b0d4b8986d9a504663db5e2e51c6cbc44cbc724d6e4ed558d92a0df4a
+
+x d0fd0d5e73be5c534aa37645aecc49b202fadb30733f16d0de719a70bec2c751
+y 910c7b4d317397cff70c91e5bf8ec42ba1700b0866adbbfe99b7fbb2c46c7093
+z 2cf19210424bc5835296e55fee3d85866189d0280d925ad144ba9ebdf955573e
+
+x e0f8130d6b0125e824b254ed57edc59455a8a4704a3f14a4ae8dbf8721595468
+y 4e4f69af6f85742068ad70225e8850c85aef3d3fb3ba3b52c2be979db4eb979d
+z 7fa9aa5dfb7bb0c7bc04e4caf96475ccfab866319784d851ecce27ea6c6dbc4a
+
+x 204d5f69ebab4597d2aa9295ecc2959480a2ab0b225674cc8a147cf7c1e59717
+y 3abdd29c94819ec7507673bd5cc4fb267fcb17c1509abd5e462b46b012f815a8
+z c08f8ccc562aa7cf81341fd88ffe996d01d7934ad1bbb66d44e93547afed816f
+
+x e2d75c74060aee615b6cfc815c8618f826b07c4987e10f20d27ff74eab3ac7d0
+y 7a06b32d284b5faedb91dac8e94cb7f76c678bad81ed78ac4e75eb9edd8d11e9
+z 55d1a946debe8eb37fda21b972396100ba48f19b05f49673830a0cb0cdacb567
+
+x 8d50b0573b0bb945bf128e1a9a37c151e991581673cf6295db5a6223d428ac9d
+y 47ca477794fdf378f3486355b5348960ee957470b8c74d62199ac48b4478c4ca
+z 338668e0a60dc5cccbc92ac5e40238f1fafbe3a5ba071533c2c09d978fb0e752
+
+x b66b49190a99456aaac5c33beaec423a3fa79a84df0f00122aed29151185ceef
+y 13c06f7941743bfa261845d99772fd0d5f1a8258aeda53b161505ed8bdca1bc8
+z a3abd99fc8240a7083ad7e62527a452ce08c182c3135ac60c89ccb3c53bab227
+
+x 44ac89bb8d4de1a8756b00401236ea4e316a2fe637f6e5f052576da70c29c4ea
+y 05dd39ac32768d899b80ed10279aa10d6316d60ab2d061e877dc5f21ce8e1140
+z 52cf4f0f5bd7531fdaea122feb9b4841ce5359db85258408db7a0d863e9ab22a
+
+x ef0f6c7f56ff22260c66d583f79c7f581181d3a0f3167c93786bb6c89de4372c
+y be934afeffaf5e6755a92e6606ffd054627dbe1b18ad6ae543363a01da605512
+z 317c2181564fc4beb6bca61df19dae03af031585db6911ae34357cc7c383e219
+
+x 773e0db8f86c5182b5f51d10376f42cde275dac6a646ab1cab065760e045107e
+y 3f92ddafdfe67d357b4f9b61807bcb8b0f1f6c2dacba27902f48fc15a31db606
+z 38ac2f081986d34c3aa682aeb6f37641d3566e99fa8b838c7bbe5a4a3d285a77
+
+x 34860a848d0afb20e43f4a36b3c8941f5821864216da9cb3ce1a11f056565a3d
+y 9dfed86048acd45ec0009c1ba3b20a1ba645ec141070fd8ae41d25e159bbce9f
+z 84873123455e26c2233fae1a10168a04b2db992d066a9f28eafceb0efd9a8b1d
+
+x 854ba91672ae1b8f6c29395dcfa4f3514ed97dc2c9e1e419f926825619fac55b
+y 7a700653ad355caf17f89045ecfb3ee821194b54048e55d8eed41fea2b0a22ab
+z f8daa2c3c478bfdf5431a817e3a8b4692cc0326ec5538f410a52626cedefa330
+
+x 0c66b3d8c3916940b70d381d232ba8aecfe27e3ae63fa6cbb287216708f224f0
+y 477186656245c4083dff93a95c6e5deb707916e52cd74abbd522743c24c53088
+z c5f42c73614ca5377a0ea473c6bc4ac35e696855b9685b10dd64ad2ae42cf467
+
+###--------------------------------------------------------------------------
+test neg
+
+x 0000000000000000000000000000000000000000000000000000000000000000
+z 0000000000000000000000000000000000000000000000000000000000000000
+
+x 23d767107e23d5ce14189cce939c4b5334d6736da3da40a715236b9d8319efc1
+z b72898ef81dc2a31ebe763316c63b4accb298c925c25bf58eadc94627ce6103e
+
+x 9bb944cfb58b186cc551e0a0eca74528c7618ff47485bf6a723f43d990f69f6e
+z 5246bb304a74e7933aae1f5f1358bad7389e700b8b7a40958dc0bc266f096011
+
+x bff36d2aa923d5a9af5398e2cfcba4acdf3c3181a8ff00b8a1099cd97a4e8542
+z 2e0c92d556dc2a5650ac671d30345b5320c3ce7e5700ff475ef6632685b17a3d
+
+x 1b65a51746eabb7c0d8d9844dda03bde7128407e94661db2d5fd9c0f3790d120
+z d29a5ae8b9154483f27267bb225fc4218ed7bf816b99e24d2a0263f0c86f2e5f
+
+x 88f4cf29a610c4465f63a272fde2f19a4874a70a0829885014379b637ab0e82d
+z 650b30d659ef3bb9a09c5d8d021d0e65b78b58f5f7d677afebc8649c854f1752
+
+x 94ca4d567efcf088e6bf1cb3698f6b8bf2164db4f523e28781aebfcbb501ec63
+z 5935b2a981030f771940e34c967094740de9b24b0adc1d787e5140344afe131c
+
+x 3f8d7ae4f1698921524e49ccb2ce4459e4c048f76f04c5e60179f5417d2d52db
+z 9b72851b0e9676deadb1b6334d31bba61b3fb70890fb3a19fe860abe82d2ad24
+
+x 1eaa0c45af0d8f85d865cc66ff3d0dc3355f1ac36821cdd95a6b9232a27f9044
+z cf55f3ba50f2707a279a339900c2f23ccaa0e53c97de3226a5946dcd5d806f3b
+
+x 33e142c78ee87a7980ade6c796e7ff949cee6d3af0415bf5b6901f84c2db910a
+z ba1ebd38711785867f5219386918006b631192c50fbea40a496fe07b3d246e75
+
+x 24a0c185c47787caf1a666a62002a503f2a3e591e5f2946e148a47b9b114a884
+z b65f3e7a3b8878350e599959dffd5afc0d5c1a6e1a0d6b91eb75b8464eeb577b
+
+x a8bd0c1c3f219a97de87b22e8cb3eb5daea33b5646589b6925ec4ec83ca37455
+z 4542f3e3c0de656821784dd1734c14a2515cc4a9b9a76496da13b137c35c8b2a
+
+x 1a340d2679ca205f6b198cff4bffadcde1afeeed124ef0c574655dbe8732b681
+z c0cbf2d98635dfa094e67300b40052321e501112edb10f3a8b9aa24178cd497e
+
+x da43c139a1f92ba1b5fc996befe5218368eac3c46b42e98a9cca8b8f6f1540f5
+z 00bc3ec65e06d45e4a036694101ade7c97153c3b94bd16756335747090eabf0a
+
+x 81aad864a31e5f4afa32c29eb97f22c103dfe5b1323db05fc9b1545312aa6c0d
+z 6c55279b5ce1a0b505cd3d614680dd3efc201a4ecdc24fa0364eabaced559372
+
+x 28231ad38d214f1421df7005eddb4f4c12e522b10d1cbcd10ee26dfcc222a62c
+z c5dce52c72deb0ebde208ffa1224b0b3ed1add4ef2e3432ef11d92033ddd5953
+
+x c1facefef35c1ed00db767ed0281ebfad1f3c915c6649f5e1c26a6f3f9478b43
+z 2c0531010ca3e12ff2489812fd7e14052e0c36ea399b60a1e3d9590c06b8743c
+
+x c2e4046e7200386ca2afea8ecc9c98c105fbf6e31b598e21e482796a69956040
+z 2b1bfb918dffc7935d5015713363673efa04091ce4a671de1b7d8695966a9f3f
+
+x a42fedea4eac90580a0bbcb0491a7e8cc82de7a99aa74ed35f705c536afa0236
+z 49d01215b1536fa7f5f4434fb6e5817337d218566558b12ca08fa3ac9505fd49
+
+x d1ab8c50d54279ceac870d0ce4a2af56bf8c03e87482dcb7775183a4908ac739
+z 1c5473af2abd86315378f2f31b5d50a94073fc178b7d234888ae7c5b6f753846
+
+x 1ffd85fa5ead53ff509756fc28051ef65eca040303b65f7b5b7e1d1a8508e030
+z ce027a05a152ac00af68a903d7fae109a135fbfcfc49a084a481e2e57af71f4f
+
+###--------------------------------------------------------------------------
+test condneg
+
+x 5330763b29dff20501a1d6c64025c36279083473721f5cacf89168189ff9810d
+m 0x00000000
+z 5330763b29dff20501a1d6c64025c36279083473721f5cacf89168189ff9810d
+
+x 9d9c36e2126d911a503e1cc1a8489ee74949ae2a8408dc7d72ed0d75e4350545
+m 0x00000000
+z 9d9c36e2126d911a503e1cc1a8489ee74949ae2a8408dc7d72ed0d75e4350545
+
+x 47da10abec2cb54c5890e5945999deb1d89ffd268bbbe2eafc86f1acc8bf5f7e
+m 0x00000000
+z 47da10abec2cb54c5890e5945999deb1d89ffd268bbbe2eafc86f1acc8bf5f7e
+
+x 3e6ec07de86be6ffab2dfa1deb9ed67844645be92bdbb22b7ba91379babcdfed
+m 0x00000000
+z 516ec07de86be6ffab2dfa1deb9ed67844645be92bdbb22b7ba91379babcdf6d
+
+x 5f5c0730649586b5c0b60a14d3b669b3649eb6725d71d834e78ff2aa0e5450e5
+m 0xffffffff
+z 7ba3f8cf9b6a794a3f49f5eb2c49964c9b61498da28e27cb18700d55f1abaf1a
+
+x c357befcc6836d89387915e368e5e6162252b433eb58d94eb3cc4b783e98c226
+m 0xffffffff
+z 2aa84103397c9276c786ea1c971a19e9ddad4bcc14a726b14c33b487c1673d59
+
+x 713ad0f656a8fcd75fdee2c4ac248ee7ad09a5f357c565daa94ae46d8590d2c8
+m 0x00000000
+z 843ad0f656a8fcd75fdee2c4ac248ee7ad09a5f357c565daa94ae46d8590d248
+
+x 909d669185e98b4a88a6531b830193b23035d64665929e34e86d53c4a9eef30a
+m 0xffffffff
+z 5d62996e7a1674b57759ace47cfe6c4dcfca29b99a6d61cb1792ac3b56110c75
+
+x 8f23ec139f93258e6d57fa278339f1cb5da193c5d1ad7183fb2b151111262285
+m 0x00000000
+z a223ec139f93258e6d57fa278339f1cb5da193c5d1ad7183fb2b151111262205
+
+x a9a5480c72157f389be80ae7ad63502434c380ccd1cef813dc9bd2e9a85e2f22
+m 0xffffffff
+z 445ab7f38dea80c76417f518529cafdbcb3c7f332e3107ec23642d1657a1d05d
+
+x 316f98b6697e7daa8775d3aa91dee8fbbae4e935a2f62cd2975e2d552f0c9846
+m 0xffffffff
+z bc90674996818255788a2c556e211704451b16ca5d09d32d68a1d2aad0f36739
+
+x 70128d6dd5fb42f287fba3533c71cb5dc2361b6d91c3d9626c58849e27f7d349
+m 0xffffffff
+z 7ded72922a04bd0d78045cacc38e34a23dc9e4926e3c269d93a77b61d8082c36
+
+x 66a6f3dc6274e4122dc401ef23529175d71d96b660a52cdcd64556073b5430b2
+m 0x00000000
+z 79a6f3dc6274e4122dc401ef23529175d71d96b660a52cdcd64556073b543032
+
+x 3909505812b228e6ca5cc6c0b17824ef765923eded6105e6eb0f176781624c5a
+m 0xffffffff
+z b4f6afa7ed4dd71935a3393f4e87db1089a6dc12129efa1914f0e8987e9db325
+
+x b7febd7d63efae3bcc60c1c344f2f6166b272eed785a9e541d3ff4f12e82a5f3
+m 0xffffffff
+z 230142829c1051c4339f3e3cbb0d09e994d8d11287a561abe2c00b0ed17d5a0c
+
+x d1cacc1db40de13351224046975319d7546ae9e88e1909c2a8f46792a140d279
+m 0xffffffff
+z 1c3533e24bf21eccaeddbfb968ace628ab95161771e6f63d570b986d5ebf2d06
+
+x 4c449a50fc1e145be1463e4c171b3c51c9683c41c45005d8aeca607911c9b3be
+m 0xffffffff
+z 8ebb65af03e1eba41eb9c1b3e8e4c3ae3697c3be3baffa2751359f86ee364c41
+
+x c929c50eedbad6ceacdefb00bd58a32820c874c906741e9d93cd0f668819edcc
+m 0x00000000
+z dc29c50eedbad6ceacdefb00bd58a32820c874c906741e9d93cd0f668819ed4c
+
+x 1c57449dcfc7e8f9fab77d226d4b50d7dee06c29d08d3d4f4ae7c8ad238a0a82
+m 0xffffffff
+z bea8bb6230381706054882dd92b4af28211f93d62f72c2b0b5183752dc75f57d
+
+x 396a2ddc48f158e73c95dc289da3f0d3b2128875e20c401cb50fd6cc7a28dd18
+m 0xffffffff
+z b495d223b70ea718c36a23d7625c0f2c4ded778a1df3bfe34af0293385d72267
+
+###--------------------------------------------------------------------------
+test pick2
+
+x e6f52222f35081896f3d9ecc0ffb27fa3e75c8ad1c98e161878d2c3cffd72c78
+y a24cd71f7acb653466b7d67bb41efb5a29503d2627d2ce28fe19680ccd939be5
+i 0x00000000
+z b54cd71f7acb653466b7d67bb41efb5a29503d2627d2ce28fe19680ccd939b65
+
+x 4e51fe2dac96a664d0675962116b7af4e605194a1c9fb774c621a3107994c9ed
+y 508934be10ce5e11e6940d56e84b148e20f48369e748536846763c80bab9af49
+i 0x00000000
+z 508934be10ce5e11e6940d56e84b148e20f48369e748536846763c80bab9af49
+
+x 530175217081c3fb3ecd17702ad334ad48f05affd5ab3754ef10be5b0eb5375d
+y 8aebc7e01e2bb2829f21311462175948d85cd3e65d676eec893e3df13f639d07
+i 0xffffffff
+z 530175217081c3fb3ecd17702ad334ad48f05affd5ab3754ef10be5b0eb5375d
+
+x 0e53c5141d72c8c81d80b1a1283b0267b278f98e28ce08ccac7b010022e5adae
+y 2215cc15e950d6abfffa26113f269628f50f9ac37ad3260ae9189958d75080b6
+i 0xffffffff
+z 2153c5141d72c8c81d80b1a1283b0267b278f98e28ce08ccac7b010022e5ad2e
+
+x 3dc16434679d30686d5023fda4cc574563841caf1d588e965fe1ec1c4ba54398
+y 4ca50330751d33ebba981277926a3fb801d216474cb183f90947680f5ea383a2
+i 0xffffffff
+z 50c16434679d30686d5023fda4cc574563841caf1d588e965fe1ec1c4ba54318
+
+x 09e68cb66b5ae2f3160a71738d1e9a042b9b76335eddc4b9466d0c6b8100eeb6
+y 270eb833ae635bed17df9218a53a91b7afeb74f0df3bfffb8334c04773cf716d
+i 0xffffffff
+z 1ce68cb66b5ae2f3160a71738d1e9a042b9b76335eddc4b9466d0c6b8100ee36
+
+x 831b8a99e3b44bf21cdd4f3c06da7c16a95e98f3dc42cf2ac282edec67d9b2ca
+y 482840e31c7620de6d290d747afc63ca199c60169f8eb62d28ca1142c5336990
+i 0xffffffff
+z 961b8a99e3b44bf21cdd4f3c06da7c16a95e98f3dc42cf2ac282edec67d9b24a
+
+x a022ace6772d82d30832328c7cbfedb622b710d1fe9313a77dc4cc5ca577a7bb
+y 39c86c57bf581c16d8c03b4ef0fe813815b5da1281f03bb3f2cdb0ddf19868d0
+i 0xffffffff
+z b322ace6772d82d30832328c7cbfedb622b710d1fe9313a77dc4cc5ca577a73b
+
+x 719d3f13c38b915873bcb14308bfd9bb6f4a6cfd249a745bceb55787ce480caa
+y c72de6e206ed24555d091763644d4405f2ee5dbd846a036d6a21442a6c40e0c6
+i 0x00000000
+z da2de6e206ed24555d091763644d4405f2ee5dbd846a036d6a21442a6c40e046
+
+x 07cdd3cd677a3c1783bcf7855bf1dbb453809b66c66c7bbbb67690cea33ca581
+y c9d889281ac117390875739e4b62df6dc3cca6c65439c46bb907c81d3a961fa3
+i 0x00000000
+z dcd889281ac117390875739e4b62df6dc3cca6c65439c46bb907c81d3a961f23
+
+x a69a728035cc69d5d3f96dd4a8081864333e53e434820dd569deb9e58393d4b7
+y 3f4ef71dfa1eccd817d3192dbe2e08466e4a66b4d836b0892b3636dc523098ed
+i 0x00000000
+z 524ef71dfa1eccd817d3192dbe2e08466e4a66b4d836b0892b3636dc5230986d
+
+x d249414415ac4960e934d29e08c75ff1b18431a6e18f7404e638293d3d8e81d5
+y 33cd02e07762f74976834d1b6dd3b8eb7e2ad7a5d04ba90bbe747476071f10cb
+i 0x00000000
+z 46cd02e07762f74976834d1b6dd3b8eb7e2ad7a5d04ba90bbe747476071f104b
+
+x efb782aba4dca351a5c9279b370073840b977b2458c6c84c9c9046dc92cc5507
+y 6d9f50eb56b84989aab77c54987f05c715b74185417863f2c275635d2d6f2eeb
+i 0x00000000
+z 809f50eb56b84989aab77c54987f05c715b74185417863f2c275635d2d6f2e6b
+
+x 10c4381ed467e27d756ff7a260a6ffd282ad757b10c9956c518a43117699ee91
+y 9b9a70c67be3296ef9d65fdd8014c4b263c28fd31f3299f4461c688c469ff704
+i 0x00000000
+z 9b9a70c67be3296ef9d65fdd8014c4b263c28fd31f3299f4461c688c469ff704
+
+x 5a30428bee407ee673ec7d2cb4854efd80b9761df5dec906463f888f60be7152
+y fc2e139be53203eb73041e9335253534c420208164682c2e02f31f084f5582f0
+i 0xffffffff
+z 5a30428bee407ee673ec7d2cb4854efd80b9761df5dec906463f888f60be7152
+
+x 43c7cd903c7dd7cdab85c6b5585955163e0da7dd0c5b5882ac620246619af342
+y 0eb52162c69425ad75b778c39746014789f7929119d4e122d4b98bf64784fcde
+i 0xffffffff
+z 43c7cd903c7dd7cdab85c6b5585955163e0da7dd0c5b5882ac620246619af342
+
+x f37f3707e4609d389096c1fea551b572a6b4644fd6af2e9e7a0fa93a91ae38e5
+y d10dd4d911346a5952e3123d4f156a7e40807d142c4afb4bc314ac6f9346dfa8
+i 0xffffffff
+z 06803707e4609d389096c1fea551b572a6b4644fd6af2e9e7a0fa93a91ae3865
+
+x a4f4c203cb892691a6d6e9dff8a10ac1a8d9470b13ba24e1bddac05d6d7f9c0e
+y b88145fabdeaa9fa108bb04a4d283ac034b4c8d8ffe1b2174de9a80254762c54
+i 0xffffffff
+z a4f4c203cb892691a6d6e9dff8a10ac1a8d9470b13ba24e1bddac05d6d7f9c0e
+
+x 649d8ce64f623228553de99b823c5f5c5ef37f00e2ddf658fc9bc2405afde715
+y 0f24ace92223d2db75e2d82e8a5bc8b0e7981478216b999d2bdde9c72732d58f
+i 0xffffffff
+z 649d8ce64f623228553de99b823c5f5c5ef37f00e2ddf658fc9bc2405afde715
+
+x 3f466e24ed4169ca3df624d747f054f97422d5eee3fade2fa3c4eba488694a6c
+y 37e3171c9aa56d07ffcde4f1fd0fdcc41e2086ecf93c9e53f3f6a4c3e4db587c
+i 0xffffffff
+z 3f466e24ed4169ca3df624d747f054f97422d5eee3fade2fa3c4eba488694a6c
+
+###--------------------------------------------------------------------------
+test pickn
+
+v[0] 91aaaaf3ff9e58f299c0f6d0a4a3851d100423e4b7380d5a32a86cde6cb19562
+v[1] e586b4ab140cd20bfc70aa5ae1c389941a8c631ce033f54793d77c91b5e3d50b
+v[2] 911122291921aced748e1346261ce8dc0e50704bf59495c3d7c1a9806ae58b5e
+v[3] dac7c42fc0253029c78310ea1508b2464db2c44689fa7d485fb5863b7c136f15
+i 0
+z 91aaaaf3ff9e58f299c0f6d0a4a3851d100423e4b7380d5a32a86cde6cb19562
+
+v[0] e8864778a3aecd6f35f8afa097072e94c4e50680baf91a6036f4f24fb0dcf111
+v[1] 5dec44933a517f5a8bf6d858920e1200c74e65132baf0d08ca033e36e15a1c46
+v[2] 4fca88e6d122c0a460b5dd502281d80616edd30bede891226b4b3c4b3eb9eea0
+v[3] 5fbf4e034d45326d89ffe92bf4738a7120c63ea42568c25acacf4dd7915b9e8f
+v[4] 343001277d416dd31dc770232fc47c7d02884fef3fc10eaddf6f8b42fbb00b26
+i 1
+z 5dec44933a517f5a8bf6d858920e1200c74e65132baf0d08ca033e36e15a1c46
+
+v[0] f0cfc16fe0cb8910c26f6f46e69954dd34277d171044140c2dc448b6f63e053c
+v[1] d54feccab8d55297eb24f622818aaa2ac5b7fcafee5efe872bb600cbdce85a3a
+v[2] 5f1cb6c6b4e8eedb566150a99a7c92228e7f737efa1810b9d40f9a4ea020e56d
+v[3] c762a32a3f3a6f8cd956412eacdaa75ee56b347b952a7c18dd19c0ee2e50b8fc
+v[4] b6e76d1d2cdf04692036f26515ca6b92d57b1bba625f07553d2d4adf89de9611
+v[5] 874c9e94d425fe9590aa1cde396ec56531342207a0e3b42ef0ae710bc9b68418
+v[6] 872ebc0bbd45d07727887aa8116a5743880093c73b3048c3b46920c04e0f64e2
+v[7] 9cde037629d20a4481ba7050546eca2dfd293b0953aa708764531bd8d0fba387
+v[8] e9f7cb8ed4af14ac61722de66406e97ee9a87d9362dfa87e489a9c98f8b891b6
+v[9] 6c5bb4410d83505ad34d10409d02fc005a47ef802b5d9130f3b5d385ff78957e
+v[10] ff40983b47e7263665a03e4396421fc34209afaf52d7d69012833b4a228e6c40
+v[11] 4588ed141f6401c460ff6ad4888172c9d19f15f214d96bedd59f818d7c03b720
+v[12] 99ede977304bc4e8f5edc44463b48fc13c001f5c584f2b100c791ae472fdddba
+v[13] 8ba76d6aa98a062e1091ca60e05ecf21208657bf287f20c6cacaaeff41a537ff
+v[14] a18760b118187f5b392637dd5c5f97ccce583b5b84b69f8e37d8caf77c616db0
+v[15] 7e921cc5caa3b3884358cb0ffd2d9d160ed54256049fa1540d861dbb6dd1631d
+v[16] aa8102188fbba89c45259c52080b3969c234d070411bc4b91870a8b482eedfbf
+v[17] d98da58b248507edf310beb9fb522dd23d88bc0412ef3b5bd7a13b7a15070647
+v[18] 0626183221836da09c9bb5a1dd07df570883af17a9a8fed1c4bc7e8770e348fe
+v[19] 16b01a5593b3eaf0902d0ade7e00da7b7a57556c2e7169e8b6ba5df5c5fb02a5
+v[20] e40715b07034e109d79a95a8b031eebc6c59dd0bb77de6cb960fe65a6d1be59e
+i 20
+z f70715b07034e109d79a95a8b031eebc6c59dd0bb77de6cb960fe65a6d1be51e
+
+v[0] e30f85631b4ea4aadb9487c76cbec40ab63101a482e5aa2e3ee329fc21071bf4
+v[1] 8bc9fdd41fe1ecf5c2cc2075c72e4ceab370b099ddc672ee16bbd7a7de19dbb4
+v[2] ede086a76fedddb463d9f0fb44b39ac7fb64665061eb96015d4ed39eb33cd772
+v[3] a7cd74dc0c94aa8bfa480a88396b7f293f1ac329e4ce79e04507be4edbf4fef1
+v[4] 45f5c114a46bf0b2c8be1ecb8fc7c81e7fef668a2e4e9769f2f2dfecf405af92
+v[5] 123d101a02348f81088beeb6fafb7f720b49631736829d2f19e95b8d833684a3
+v[6] ba936ae1b5555b05601c2e59bf9585846ac01b5b7f6fe4bbd45e0653e961deaf
+v[7] 51c0c307d99e34a617ead92dd37e1a0f36ebe2e45ef5b3690fd114099d483dc6
+v[8] af94cee7979c057995680c3a5adfe26e7dea759e2640b0b09aff383fa355d289
+v[9] 6ddb6908532c513f463473e449747f88d47766460ad316734c2cca87963b3060
+v[10] 88192953b60710667d47633be71d87214d2dc8be882ceb6928daf311499d2e83
+v[11] 37da1b76c2c16025f0644b6451027c8bc9768379c3aa7ab8410d34d8c8222706
+v[12] 1a46c0531cc13f546e001a67721931f4f6bf8eeeadaaab667ee651db0b272509
+i 7
+z 64c0c307d99e34a617ead92dd37e1a0f36ebe2e45ef5b3690fd114099d483d46
+
+v[0] 9929839bce983fe53c4f8f9d07a462f82e8eebabba2c0daee1378abf585bb53d
+v[1] 4e47d3997d6562c7b0347acc96925bd1907bf3a9c57d51b099c4a574d7bf8fc7
+v[2] a0de02656ba18dd1cfdb2938fbb864f9f59001110391ee1818f5c1dfee64f61a
+v[3] 9c4153154f5b827bb847edfa04ce754e442f2e96ea001fc27f6d94ea8b06fc00
+v[4] 7ba90562980966abd857be3a84c1bffeabbb589415e722e51225f8317e829777
+v[5] ac4657b264ccfad4f5ba3f7a470458101d5c6025c45d00191ddd4bf85ca48705
+v[6] 8b11cfc6ceb02c5d4b3e19c19f1ae745fd0cdfd9da1a80e9df1be8f7bb99ace3
+v[7] 1202bae1f86d05ed8fca09965bb1cfa3fb696a3f2b7089ee10589394639da2bd
+v[8] 143f799fc9ebec77aa444eb5ec95f64029cf61b875a2f94e228323844cb8eff9
+v[9] dcf99568b397db79bd2e8ae49778e1e49865e91525f932a1813d1c395420a43c
+v[10] 84fdfee8137558f0b9f2441c375fce466e3212c0d0de3179919fb130e61b711a
+v[11] 602454ffaf59610f76863a7456146f866539740d6dae63a3628d408e34db8e76
+v[12] 86ae4475d41ea312a97c821ac78b815e459dc6bb4d52c236a39e5e53ff17f5fb
+v[13] 0fd56e878b74a2daebc2acc30c31c279f3dab146d748e7aa9b17eda7ac039c8f
+v[14] e559e8bbd51113f84ebbe35ab16bfd46cf610a5c61307b986111ddbee3037f7a
+v[15] bac90f3afdf4f4828368090958aef5e49aa83d25fc5dc15d9b8a354a30961e75
+v[16] 253eee8f614306e59a31d9fab5423ea269b67babd54c52243b86b8af1372f3ab
+v[17] 69828b787af1831f772a3bb9a410dac8bc47909ac6bddc94a5c600a3167ce780
+v[18] 1903e9ca239847045875b0bd4e1575a724d9f729e3cbfc377de17ad29839a121
+v[19] 57bc65c0fd8495014f31e3be740967f3fd1884bee743b20b947339923530d63d
+v[20] cf7427ebf6088e6f3385275f993b5c06ee14f738b59d49ecc327521ddced2a4a
+v[21] 74c2a4122225e97b646d6a38584626a6ed811506ee7cd00b48ba563b7a776380
+v[22] 604f163d7d7f4987c8aaf2e7a946cec1597ebeb59aaeaad0dbd0737527b9350a
+v[23] 30e7ae69cd5fb42ec00ca840988a59bf5688aa0b810bb2e9ea24fb5b322891a0
+v[24] 68caff542deb61b055bf65127a94d8ab107f5d2496764f97351dbbfbf34928e4
+v[25] c0d307ece7f18150d958bd88bf11912dc818fac7cae06ca9ec3fafd15d452af8
+v[26] 731b9ae286f29660fd0814568351bd6da114f3ee8b87c217cfe531746faa8c90
+i 8
+z 273f799fc9ebec77aa444eb5ec95f64029cf61b875a2f94e228323844cb8ef79
+
+v[0] 85b3448d0292edc0b14cfae9225989a16a61ee8441166d5b97faf876b0ab6c7d
+v[1] 88b0f7c78f8390b6cc1de0afda111326dbb41e7603b82033902eb56ea542c2dc
+v[2] daf45d38b24294648a7b203758ff0654d42507e958bbd98c72229aae0a9e5757
+v[3] 98b44fbbf6e45c81c2473b626307506881a9fa609c546741b3637b731ff62adb
+v[4] c0779c0f0a35658998ee9cb6b0cb6b7e089b7f288ea171c18bd2664ca5c3fc1d
+v[5] 8da42494a2c1e2034d2009fd486cc230085fcc8af171e2bc2cf428bbf9b4bc86
+v[6] 6dfb99cec539941c9e7d26e5640641e4ef2c3f1a732f9c85759858a95c346ea1
+v[7] 471a369f8d1d3341ac707f1c41e5f0655cae51d8a170037ee349b3c14e01be2d
+v[8] c1b75b02941ae0c2e398a2c8871955c8306f6ab88cdc6d751e11b35605d10829
+v[9] ea508e41e33ca0b03b5d93a54ec359e01a5a00a98a80f7e6d998641a6cb7ef58
+v[10] bb009a72b5d5be344a3ba9509b6e8eafbafdab4b0ec9202c8d29983935c6937a
+v[11] fdce2ff0df8548fd7df3b8a087aa30c819af0eff3b8931e5ddedfdb0f4450919
+v[12] eea3990f7f4045a3b6cdae27e4dc8a8062049ac4423ce46108ab464d866b80f3
+v[13] a18000f37c8c4a30195e71864b14f170a3f5c427f4769c736fbdc18b3fe68887
+v[14] ba9aa19e99a69b34f357f92d95a6c409f1bb331d1d27b693164cd0dbb552c771
+v[15] b5863e0215351b2f9b6f661ab94c833016bdef73a34b100b6db79ea8d4b22ec3
+v[16] 983eb31be6cd1cd4cb53e489e4535683e21c00e6c52f685e84bd3cfc98f9ab2b
+v[17] c31c18c6c12feb3be4e51a1671fa6001c1dfadc0ebb35349766d9d07d5a70025
+v[18] 6f81695294071c711947499c2c3d96969a70948c29ea9506ff675d25052f0950
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+v[16] 743cd93d6f6a48161881d2224b7d7c0ce96d56d54adff0b719955cde417b35a6
+v[17] 92b99335dcf6b33de126d05329d8884802cc3afd0f93e9dea7db5f6dbdc6c623
+v[18] 584ccd19fe7395f9f2dc53f2a9da292e0cccfabe82bc46aa64c29581fc570deb
+v[19] f9321c751abb9df278fbc2054e3fa368734cc852589891b49580332a52b6bf72
+v[20] debc2bf3cedb7c897924936aac0b485bc05eb89530c886299e8d1ccad277355a
+v[21] 472d49f8ccc249b8271fd0630ab575721852e98015ea27732915ed06775b444e
+v[22] 7b29b054a2347baeda4dbd1b739072e6d144aae3547adc8287c3af84285057d1
+v[23] d7a79b1f1ca757e17729436fe744ea7d99a64d13bf85737b6a71d41ab13343e4
+v[24] a957b6345193173a231d9db8acb3a6c09bb411d210e0e52c94e75a4d68602aba
+v[25] 6277d818cbecae95f1aea85481ee631ff1e7c77c6693e6349d1804db784238f2
+v[26] 27e1d5a11dd9025508168d9d11cce0b8f0768b6846105161eca53abfa4aeeff6
+v[27] 1823372e2c7cb9fdcdc97ca64ffa06564907b09015472cfa73bf0a45d7c90bec
+v[28] 08cfef24b9eb875598779315de4fcfc918931e05f49b374113c25cb5b23a4944
+v[29] 3a5d9db56bac2f413a3d33b6d7a2f54053aa3a641d6554d6f008779939f2682f
+v[30] 22d0256cb1a53aaefd5d2fde14b63e5adce607ee5a22e8498f29982f88088938
+i 18
+z 6b4ccd19fe7395f9f2dc53f2a9da292e0cccfabe82bc46aa64c29581fc570d6b
+
+v[0] 91a76b64122a404fbf873d65089a7613bd3d93c4227a4b05817223640ec20ee9
+v[1] ab46f7649122de1d73278608e02d44a1367f4f5a7c01d1c17f2a50fb3148dfcf
+i 0
+z a4a76b64122a404fbf873d65089a7613bd3d93c4227a4b05817223640ec20e69
+
+v[0] 1c12d157172079be7ecc31716fac8946f5517a3da6612bf4a0db65707e72764b
+v[1] 9d9ec126bd404e82448a16c187152307ab6319fdd5d4280f070275cedf1cced2
+v[2] 25be86a2abbf7619f7b92855cc50572af4fcf6ee071078d24baa24d623ebe4e5
+v[3] 9b3a13dd1b67a284a9ed869de2663d82035342bc0cad65484da1c7b60b82a55b
+v[4] fb82840bfd348ccaa0d3d362c1123096a5103a09f979e2f4acdf7aa600e55a84
+v[5] c64642a4946ed50924eb1a4c6ab73b53942c5a17cc868f8c6c5ef92ce5986830
+v[6] 8e7aaf58bc15be92a31af4f0b092969a250222e7ccbdb638aa846f8253c33d50
+v[7] 375bb009118659c831591bd6861e9c9eaec85c0fd9a1facd5f2767ff27e3d36f
+v[8] f5b4b72840ef438fb8f7fd1419aa5248dc38126cfc29099cffe68aa94b215b31
+v[9] 3b0cf55a0dc7856788375bfa1390fe4c628c271c99ea76ac78517ad5f36f61ac
+v[10] 82cf74084903490f30152c730970f8b622de5414e1a60e1efafc6aa57ff2fba3
+v[11] 9d476226e3c4f844f392e7efea7726b02bea64c9aa1e78513efb28a000cf9624
+i 11
+z 9d476226e3c4f844f392e7efea7726b02bea64c9aa1e78513efb28a000cf9624
+
+v[0] 4f8b3919461d4408a4d4375688f8985332745cb5253671dd7fea3c58b8e33e5b
+v[1] ecd4f6bf71be54fa88e51fd9d98f60c009fa1b4f15ccacdfa7b26a5ba52b1794
+v[2] b0bc276ac01ed6b25fb569ec8c614f4a9299faadcb93bdee4dc637c888381d29
+v[3] 2fbc1564ecd906f5d56838c9ceb3ba5b5f13925cadd653008f1ee9f54c18ea37
+v[4] 66e9f3ed35f45675f9601181ddcff688229371c6428c1d9dc67699821e3130b6
+v[5] 6b08a213ca51403db7e08bf6945b23ccb62465f582248661b901b6e550345516
+v[6] abdb83672459dad5b11c3cf9e4d21235ff92c01ab00b2d44aa6f10bfe9b274d0
+v[7] f609191b4efb288359af7170acd0904c57d45c7c658c0d670e0fb22f9ebc0044
+v[8] e4056ab4b8afad5e6951c8168477f15ee3e11fe3f236a1d19ea201f78b8898a5
+v[9] f3b253fd18515ee3dcfd4a14409838a3d993a5274bd77a1e5a7088d20ba6c592
+v[10] 710b8819a202ab80bcf308aa94d3305944dc739e33648df045bba215160f8ee9
+v[11] 1b63314e9fbd605ac063546ee4249bf9f37da0b6b78d99848f487c6880f70c3e
+v[12] fb04f3e49a44c4eea104c213446b0e6b81da047a0862604f488e0c6128238d3c
+v[13] 43b1624809a253f46b12d97aa08dc3f16b25613022483b8044cb01b6d23cfb28
+v[14] 0796291d8916b0b70ebdab0f42b8cc55c14734cf7a398d48f94b48d9871ff0c2
+v[15] c55cc772bb71392f13258339eaa1d8b01c402e8f6c9b6061f0e1c564feb98234
+v[16] 882ad3994d999ac7243ebe9955468a52b2242564a295a9740af8980043f9ef0a
+v[17] 201f86fc5826d74580c3bd3fe04cda2a823c2a4d1ace3e862a9bf6873ba25055
+v[18] 5c39347c213f6e1b5ded1de9f92ed21d99721c4e4216d5abe207321caa426971
+v[19] 38ba53a577809f2d2c3cc33016e6141f4a87b6f57b75be70b9cd3d287f07ab00
+v[20] 7b9e12c5293fd99ed3fb50a2eac4587bca4aa8bb97c147626dcb9688593ad2e9
+v[21] 4852c30283c1ffa109aade1353d11e9712d8c4e6d416926f231a2b89b78fbdbd
+v[22] 80d25270ef8002232cd0e35433ecefc135cbcaa06511ba3ac14484b6e41c953a
+v[23] 6159366a1aee4692a9986a12234728c685cf766ad3e2c4cc842f1142c0fb856e
+v[24] 95d34152d18b9942bb13c6bec8e533c259adfd69dbeb06da63c351997463cee9
+v[25] dd5890be52cd0207fecd0f93dbd3a6819aa2c5a592ca0975a419104e7ff4c284
+v[26] d9c3f02b7644b3580d190f03bfc9accc8abf9546463a2171d9cb19b3783e0c92
+v[27] e59449e7a9d07631450d85d108f3cfec2d67d63ad65a7311b310bb10137fcdbc
+i 27
+z f89449e7a9d07631450d85d108f3cfec2d67d63ad65a7311b310bb10137fcd3c
+
+v[0] e5d98efcc2879f32793efa8f96dda9c87b70834fc9d468dc464b0940a7dc160b
+v[1] 04d4bc5cd4690a0c6561feae82c6be57195c7553276f12aa16fb930ac47e315f
+i 0
+z e5d98efcc2879f32793efa8f96dda9c87b70834fc9d468dc464b0940a7dc160b
+
+v[0] bfbed3f0a31b886bd96a817e0b65be1b1e374fddb237514e89fee7ce34a08c45
+v[1] eedd85cd817fc74938e60c366445e6bd5383dedd290db3633d5ed2ff320139a2
+v[2] 006b1e62b3aa1830de71c0ae063fbf090e536304d601e6c851800ff1d501d249
+v[3] a4a63dcc680646b69c8e651dd9c3e043bad07eb9bd6b55bc5bc854d82bbc6b00
+v[4] ffa2e97c95ef5efb87b78e89f35e95f89c1c1b2591673fd2166fcc9765abb4b8
+v[5] 030984d84d3d9667e436996578a3ae58853d44e111990221cd15795167475426
+v[6] da8350e83ac6d67029c24a8d386c6352a27bd22fd6a207474a952742790e4be9
+v[7] 0618b6f82b936b5eca87e9ab8dcd9a2e3744586bae01a75cfabb23b1b64f7aab
+v[8] 5a3e077d0d0d28ba3b6d6fefecc6c2f7ca530fa63bf414976ac8b26ed6596a3b
+v[9] 381e56750672340b18b60612bd462ade52d3b0d5b487f1af8438140740df484a
+v[10] 65275cc865fc4b5d94023fdcb929dd27dcd64870773c79f015d4a5f30751ef2f
+v[11] 724f96fe61888b5a885713d0c52e759726b877031b3f4f80ad24bcf417a3dbba
+v[12] 17f55299b7cd1d851091052401612078978bf2b09fca8c9e2189474e9d24b81f
+v[13] 14b82eebd7325586c1ed8be9353fe5ad9375290a92e76d13947c6405febb2f52
+v[14] eb5a5c7771ccf698a2e803a3a4e6db056ceb0da4d808db5758f2cb28ccc44bee
+v[15] 96db7bfd64b7d41430ca6fd0714487926d02dc71571161f8deea0f6a3b52ba80
+i 6
+z ed8350e83ac6d67029c24a8d386c6352a27bd22fd6a207474a952742790e4b69
+
+###--------------------------------------------------------------------------
+test condswap
+
+x 14e55571df646a69a8280bf8dbf8e9afc15bf5558bb8b8236ebcaa19a96053bd
+y 8bef5021598a8175565e1f2b522ed1c4306fef4e0e973b50d3a03db1fcf11a43
+m 0xffffffff
+xx 8bef5021598a8175565e1f2b522ed1c4306fef4e0e973b50d3a03db1fcf11a43
+yy 27e55571df646a69a8280bf8dbf8e9afc15bf5558bb8b8236ebcaa19a960533d
+
+x 53d8c54864e18f8fc742b2cb996f1d7595122ca9c90de9f49485cf5a5ef05058
+y 9aa95be655b6704a3dd482e8424f82d17443ae26ab41092fad95df9cac678787
+m 0x00000000
+xx 53d8c54864e18f8fc742b2cb996f1d7595122ca9c90de9f49485cf5a5ef05058
+yy ada95be655b6704a3dd482e8424f82d17443ae26ab41092fad95df9cac678707
+
+x 8c7b4ffbf50edf7edcf8d69b67796de38b56a5d4e3a9fb2201354cca0b1b7c57
+y 856e707988c37e59fc6689d024b98bc01b71034484ba194ec7f45106267cb7f6
+m 0xffffffff
+xx 986e707988c37e59fc6689d024b98bc01b71034484ba194ec7f45106267cb776
+yy 8c7b4ffbf50edf7edcf8d69b67796de38b56a5d4e3a9fb2201354cca0b1b7c57
+
+x c8cb24a636f6d8f2c045c8441b21314884a71d55c73d4ef7ad65620ac0d86616
+y 02b47be53df7c8521d57589256e69b8bbeb1e838d84c090287c04a25d5c08e1a
+m 0x00000000
+xx c8cb24a636f6d8f2c045c8441b21314884a71d55c73d4ef7ad65620ac0d86616
+yy 02b47be53df7c8521d57589256e69b8bbeb1e838d84c090287c04a25d5c08e1a
+
+x 7d96f47612fb7135edfa71dd4526d8b4c944d74ddf004e1653d3af52485168b4
+y a4e83162602d20cf71a279c1071038ecf94f38be11ad1191927b3f480d393e1d
+m 0x00000000
+xx 9096f47612fb7135edfa71dd4526d8b4c944d74ddf004e1653d3af5248516834
+yy a4e83162602d20cf71a279c1071038ecf94f38be11ad1191927b3f480d393e1d
+
+x c3a3d4462091b36bd6fd494e70c3166478be0a65bca7f7361246c52dda402981
+y 62d0ae1abbe5cb909328f59e71330269e4f2b1d3c664e7f1f0780e0a4774c262
+m 0xffffffff
+xx 62d0ae1abbe5cb909328f59e71330269e4f2b1d3c664e7f1f0780e0a4774c262
+yy d6a3d4462091b36bd6fd494e70c3166478be0a65bca7f7361246c52dda402901
+
+x 38c9b0d92be50270e29cc3181952e745cbf21c8d145ae0c0a6e59f25394ea59c
+y caf4896a2d3666200741d817ee1dac661652b9a1741ea966d5ed7cbc4c76217a
+m 0x00000000
+xx 4bc9b0d92be50270e29cc3181952e745cbf21c8d145ae0c0a6e59f25394ea51c
+yy caf4896a2d3666200741d817ee1dac661652b9a1741ea966d5ed7cbc4c76217a
+
+x d637a72affa4112bbccd2878208ce34fae442e97175e1b39f43c00b14d312a2b
+y 76209f8b1f152ba7e1e6294f707831021eb2ac03872ed3774ab8fc5e6a0e864f
+m 0x00000000
+xx d637a72affa4112bbccd2878208ce34fae442e97175e1b39f43c00b14d312a2b
+yy 76209f8b1f152ba7e1e6294f707831021eb2ac03872ed3774ab8fc5e6a0e864f
+
+x 12f3bd417fb3860b2a4fd04eb1c51c558a4c5a3dcc1ac457654a45a3cd45b0d4
+y 46f802836c7bde099775f3fb4f5f6345364a7e158bae9e16c4c99aee0cfa5e42
+m 0xffffffff
+xx 46f802836c7bde099775f3fb4f5f6345364a7e158bae9e16c4c99aee0cfa5e42
+yy 25f3bd417fb3860b2a4fd04eb1c51c558a4c5a3dcc1ac457654a45a3cd45b054
+
+x bf1809201f83a34cb07aa2e2372516631ba0513e600956e6702903e9084770c4
+y 414bbc77d13d7b4e706acc07406e8d624f2485463f9948d81b72268c1e086a14
+m 0xffffffff
+xx 414bbc77d13d7b4e706acc07406e8d624f2485463f9948d81b72268c1e086a14
+yy d21809201f83a34cb07aa2e2372516631ba0513e600956e6702903e908477044
+
+x bb8703f2ddaaaaa6ad19219684b1bde576b38bbe9065178b24c1bc55563fe525
+y 1cb3ca7846a3c584b1bc05b25ee91d4779ab9ac64ecef0fcbaea8d311b55d618
+m 0xffffffff
+xx 1cb3ca7846a3c584b1bc05b25ee91d4779ab9ac64ecef0fcbaea8d311b55d618
+yy bb8703f2ddaaaaa6ad19219684b1bde576b38bbe9065178b24c1bc55563fe525
+
+x a07c7110c32e362864a42cd2f371ff420bfd442d291cc15ec079d642b5c85bdf
+y 497fa7867fcd0617c4cd765aa6f46b89390744b5b57d11ab732153e075fcb607
+m 0xffffffff
+xx 497fa7867fcd0617c4cd765aa6f46b89390744b5b57d11ab732153e075fcb607
+yy b37c7110c32e362864a42cd2f371ff420bfd442d291cc15ec079d642b5c85b5f
+
+x 10fddb7f48015b394512257da026938b67f65dd0a84dace51417d68da003a913
+y ebd6706b7cd2ee2d97848ee1adaa990d8ddbfad48e43f51d7ef843fa7597410c
+m 0xffffffff
+xx ebd6706b7cd2ee2d97848ee1adaa990d8ddbfad48e43f51d7ef843fa7597410c
+yy 10fddb7f48015b394512257da026938b67f65dd0a84dace51417d68da003a913
+
+x 1dd835e2173b936a91da37b3aa11e848e4497964a9a78ea929a19105eb981a24
+y 3e6f1ab7d5c460dfb7ad1926c60b64a8dd48ed0115b0655a6d8619666b8c8dde
+m 0xffffffff
+xx 516f1ab7d5c460dfb7ad1926c60b64a8dd48ed0115b0655a6d8619666b8c8d5e
+yy 1dd835e2173b936a91da37b3aa11e848e4497964a9a78ea929a19105eb981a24
+
+x c4541b1380e796a333d88affdccb4d2bc68bc5a1b3890ef2fc1a2c38dbcac725
+y 6f6338ad8dc0562bc02e307743b81013ffff6c135fdf8603f9956b7f94eb55fa
+m 0xffffffff
+xx 826338ad8dc0562bc02e307743b81013ffff6c135fdf8603f9956b7f94eb557a
+yy c4541b1380e796a333d88affdccb4d2bc68bc5a1b3890ef2fc1a2c38dbcac725
+
+x d71f16494f041d1547e5dd9ed539e6b9c1506cebb66f6424e6c7aaf6d0ace080
+y 78c1e6cc0b6f64e161def3b2ede7465f21f6afe61299e9a3c52b1a7a080b9b26
+m 0x00000000
+xx ea1f16494f041d1547e5dd9ed539e6b9c1506cebb66f6424e6c7aaf6d0ace000
+yy 78c1e6cc0b6f64e161def3b2ede7465f21f6afe61299e9a3c52b1a7a080b9b26
+
+x 4d90838ab9cc0a79f4e2aa6a860bf8cfbce5f834aab428d4a06f8ef4a2da582a
+y 53124b302e7675ea5784e2e7d9fdecb38d9c8be158312dd81c51757bafb79b42
+m 0x00000000
+xx 4d90838ab9cc0a79f4e2aa6a860bf8cfbce5f834aab428d4a06f8ef4a2da582a
+yy 53124b302e7675ea5784e2e7d9fdecb38d9c8be158312dd81c51757bafb79b42
+
+x c8e764092ea695b0dd8f0ecbca5a4e02096c821b0f5cd57de8e3e50d8b2a40db
+y db7fb38dfede5259a584dbcc697f259ce380110636e301acb308bf687449110e
+m 0x00000000
+xx dbe764092ea695b0dd8f0ecbca5a4e02096c821b0f5cd57de8e3e50d8b2a405b
+yy db7fb38dfede5259a584dbcc697f259ce380110636e301acb308bf687449110e
+
+x 34cf8e55b3d2494362a87a24907fbdab61cb4f452ef5a889a1aa40a22be6d976
+y 679c6d6f6dca1b71bb098e3854c63ffb8ddb76f1a1cb246ce956fd71d6477c20
+m 0x00000000
+xx 34cf8e55b3d2494362a87a24907fbdab61cb4f452ef5a889a1aa40a22be6d976
+yy 679c6d6f6dca1b71bb098e3854c63ffb8ddb76f1a1cb246ce956fd71d6477c20
+
+x 9638ab322ced065068f98597cc61fc2bd846b5849dc39a881209b8efcbc95eec
+y 32922ff2b62e968417225b765f2787387c8a42fcab1dbec3815298f53813a8cd
+m 0xffffffff
+xx 45922ff2b62e968417225b765f2787387c8a42fcab1dbec3815298f53813a84d
+yy a938ab322ced065068f98597cc61fc2bd846b5849dc39a881209b8efcbc95e6c
+
+###--------------------------------------------------------------------------
+test mulconst
+
+x 8d517a8804d934ae93388e1d59748c3c22866d7be6cec58a357ec43f6dd029db
+a -319312
+z 3f2fea85c9195f2246f4f6fd2e8d5de95c5065edbea45a174bc0d1ef3db4aa54
+
+x 1b5d6a6c9cdd0dabd126e5f5ee2513f3d27c56dd3aad89c882fe9fd2d38a93b9
+a 499342
+z dd310555966ebe7f409dcce2933f91af8e14c8909f78e4f113606789dd7f504b
+
+x 9e03b44e93743e0cf5768f65bd3c0f255e001de330d5e1a863d6e4dbb11748a9
+a -284189
+z 6e8c7f8d0f1476cf2603f5702fe8e8bba5c01e86b6e008ac72987fdd6721183c
+
+x 9cc65e302736aab9bf02dd451c216ac3dd2066af299d7f6bb361eb3b36777f74
+a -15738
+z 8c067e5dccdafaf56301050be17b8895c07e7f13572bbc5ce1af8b5be043d91b
+
+x 7f36ff91ed165c6ee44aca261dc09e3e124c2ed8167064c20d9b84fa226e2555
+a 423857
+z dc7415db1ab5e5a5658d089ced49bf97718bccc55e2f15b83a28157cbe47e559
+
+x e8852c80db69c7e55d476ed00ca7c0735052f7f72f81198a57236feb89a5903c
+a -140934
+z 4923ee40bb01314c2fe9f2f87d0743823311b2d9265219eb7a6de5fdfd09a308
+
+x 505ef65d294b77e260757bc867199c4b0922b5022dfd6a1fe7478ea27ec102c5
+a -307893
+z b14d72c991a0bfc22b1b95934bbe589b6a4a1f9c76a89d7012f8cb03379a8844
+
+x e410c260dc8c1838f3e9658ae586425039b373ee2ab88c750a51853b012af0af
+a 471420
+z 42ae337a920ee1b83768cbf0750f524cf1f9e98b99f195e869785f90a2356756
+
+x e2d181914b54175190462d11402717f42efa37967b2fe0bc4433fd4c862fd646
+a 492178
+z 4c6e1ba6896d2d661fbf99b77f63e3095d3341f04bf258dc3e4f51e39c68f576
+
+x 9cdda0d7da106ef5cfb34774f48308b64953e92869dab0ba804927080509d8a2
+a -312149
+z 4e75e56793563268480efaf6232ad702bc5aef6246bd44e3499ff437810b523b
+
+x 9dac4442858b8dcc324464911e6f23ed046e42612e8105dc3aa2b9eccea15dc8
+a -88818
+z ce52a0897600a05383df0a0b99a451f0d5568146b4323392fc164153715ecb0a
+
+x c9f92ceffa7027ffa71e64b714c36b28a6a18c3608f8170d11d51acbee3c62ba
+a -259755
+z 89582517069925572219b2eec2a25029e8e1c78772ca8c50bf23220d02740763
+
+x 8f8bcf28f4920465680c8e15befba4ebd23c1e27b71c224c98461f69caf76eb1
+a -430350
+z e96b93f0aab6ca70f7d2c1121110efc320aff34e1ec693d7bf17bce1a756d622
+
+x 6f4d413a27388fe84a2585e809927bd470ba1b0dc749ae6e2dfa100617a5a7db
+a 11486
+z 1cf1f5bd0770d949ee36df858e5842805d121722de30d2ef6bc2b82d021fc14b
+
+x e1d05a072d1ab70d895969271f44b7c9d1654171836cf234724d2f90434c04e6
+a 8057
+z e32b3c792cd3b6a770eaa2627ff8de8895873d73d734b961646fbce0643a443d
+
+x d8564ee3ff02c80f0bf3e9cdfce42cd8ac1012ad8ea74f8c0f5754b5775a8de5
+a -304373
+z 884266ea43a6a9b72d113b437dae63c664ef53884c893212fd864412f4e5e457
+
+x bf66769ee0cf873764524e760ee654e8d5090aa774f2e96144d945f8da37af19
+a -159091
+z d7438999b3bdb99a46e2f3dc8492cbaf52b0a19c651cc382c384940861bccb6b
+
+x 72b7d02b1fe23adea87696864c0a9f0466db85e39db397f0eb428a50e277aa2a
+a -521654
+z a611bd153336e178a7f3d912adc2fb39b342132458faeedbdb0a35973efae23e
+
+x ff5c39d4b7fff86810a7a3b14a58bc01e6ecf062116adaa78dac0d1bd3f6039b
+a -140759
+z eb9e32bf7d027cda198048da50aa79a11bc99f3b37a219a2104c78f4affb584f
+
+x a6f1f7f30e3f9e5467f180f92d2c94165fd9427d0c7d383b9077ca9a7e50dac5
+a -317637
+z 56a32847c50bc9609db9796e1650fbe97524aacea746d3cf285f0f2fced01a49
+
+###--------------------------------------------------------------------------
+test mul
+
+## Easy multiplication.
+x 0500000c00003800006000004000000009000006000048000090000040000000
+y 070000180000200000e00000800200000400000c000030000090000080020000
+z de200094610090df0020fe0180270700650d00dc2a00f84100e0340040570000
+
+## Random tests.
+x adcc6f10734dae2273304a6aa493ee8f96e05f2402341c0d997dce58ea57ff6f
+y df3c8d5bb6380fa278d4ff2994c7865bcc146596d3c3126242f0dc3509b57449
+z 5ee2615b75a40367ced4ed4bf1578d13e7afa4d415f38f802b7e7b374365b627
+
+x 054bc4d5e9b78b068fd20645eeb1f03aef2e89a1f56cb50e5f1170a86529526a
+y f976ffa1d1b4a33d0fd866528897cea3eaffdc75e31aa65450a62ff765fe7985
+z 0210280745f6c29a04433f07f880bfd2eddd758d82996e79c65de817c30e7309
+
+x e361c6fedbbe081b7cd683d23a2bf0ac889806be7230b56d9398959713a300ec
+y c8121e53d78c2e9ba2ba7f51b7cb15cec970a63b4a642ac470aa1f2145f07bd0
+z b48bb1c7ddd26cd9e5a2cb73bb3885dbe4a47e03886d4dfd59e5729d544d566a
+
+x 463158a2077f931567d45e19deb4454a2ae77045db70a2c078e160ebdb74fd94
+y 3f311e3f8d225016448fbce3fbfbe84002736e3b0d5a90f57d705ede8706008f
+z 44cd97e25c20ae2fe2ef4f2630981a1fe54c79ebd904bc40e39d9fa615ffa76c
+
+x 1c73fca52556e01204d4b957a01d1049f2247c8666d90c1d3703cff16a38c8bf
+y e9afa0cc85577ec7eb1ac66d87260d5f3659936ff88cde8bd1c3fa1d499e8bcb
+z 0979a8baf734c86a4f57ae400b7790c4985fba3088cb1b265dfc7a66c794121b
+
+x 6e2bab74e427b1a44f0cb181f9dedd6fed43cfd395d3708c4ae8fd2137215eb6
+y ef400834f2dad8763a1a5a58a37d1b36a78873860e4dac808d3166f13724942c
+z 0d481adbce7bd82ebc5a3e5ed7a492e78a032ebf211a5bd2371c528c77954936
+
+x cb3575b41d9521da5c85c6438af14903a8d6d9c3857aa8e101e5295fb277de7b
+y 9f76715d2ae3c8ca182406553d3481fc36d67727ca2d51f5db37940aa3208d8d
+z 0b2fa619265bd424b9e20d38bf4552ad63de8ab552166080d099edea5fbadf7f
+
+x abd66cf3b20dc4c5a866f1a3b965f794a726f96dd00f576d16ead66eea3a1177
+y 97f70fc92e0cda0e010f2a9d7608c33db954af18bc18ad55bf66e7d91ae31abd
+z dcbb2cf34274971ef030827865b093a00761de3da90e46f00e18d0fd934a2b7f
+
+x 3b3c96ff9be8e17e0a0d3979ea5e5623fff5fa18914151abf79fe66639beef06
+y 1d29c361677805f1dd2b839e025e56208a10c0b8d9f2a8c490b0a892c0e27080
+z 0050873016bc67023d0c479fffa56a5a70512f9864d00b0a3e951f1e85c8b412
+
+x b263d4a71b6d963e0a972819e5e5805b9522f142d3c0ff2738c51cce31e9f0d5
+y 64f3fbcff2195c297292df3e1cf900aae457e09864c5a6248ea21ef8efd557d9
+z 7e6f6f511cbf2743c0fc1c6431243908606cb257d20f8a8a0885e6ecd000e811
+
+x 0df0497e1e01dbcc4a48d4865127d9cc31a9a0a56e90cc31619e65c1521b2369
+y 9277f0c6a5bcd7c7ed8dcf7182795f67a12e856b126d09966689834c43aada47
+z 798d270ae34aa2452694b4ff74049a6a5169d71c85bd1a9ac59625e9298cdf1b
+
+x 1dc64bef2189eb5349f5a8983c1854a40141a5390ea4bf8535a15aa71d0289b7
+y fb59dc9b08f9163881b10020ce040da296ed8c1a9a935c27ca0047a4d7f6342b
+z 9fc23104cefd3014a469e6d3a0631338eaf91e24994ecd50bfc0b4547317317e
+
+x 975b108909e87803af98af9425d2a982865b6cc9c144985b32fe5bb842702e24
+y a69e9130dc40be50e827dc50dac05bf900946cf67ec35f1bb1705001314e4fcb
+z 12d042e50d0cff7b43a5ede61ce827a99619bf84995d488fe9eb56a8de769164
+
+x 39c0db5a4b161c368b0f71c7e8ef97dddc444e4a33181e0743519f2a879ae04f
+y d3cc45ff509ed45998bd5f218408ad51f7457b35e8ad69d5431f174047d7c6e5
+z 96b877604f52782ff2a5b1a12d7db642371ca993b648c4971cbf593213503219
+
+x f8c6715e4a327cbbdbb08d74121619abc73dc421d7267029e39b50c1510d2045
+y 63870a83cad4c1c64195ae7b92f3b19c830f35f1a3186815565d846c787c7ffc
+z 286a0b8c6681a7b79a5f85426fb60819b7bd349e93c1e11943c41c8dfd57d00f
+
+x 49c9bcaf5434b8205a348df290a96da27df084f34047efbf91cf544057a50bde
+y 54269f8b23c05b94c9c1cd74eae88d9227af12a6fb337548eb93c2a88a75a8a5
+z 1e3dcab5d7361f00e70198b52e8fb6d1fba74abd79d99480527f6711b21b833b
+
+x c7212b43ff0d10fc52d3a2a7e15bb9cf53856f7ce33b79df89e1d13f95a94511
+y 5213ec20bd054491a5485f665075835da609ad4f3dc005744f061480862ee602
+z e136339fa01067c6c0823a7ebe2f84d917600e244a9883191900bb95a3b59764
+
+x a15d62c6308448f1f70602f43be1825696d228eb170bed55322a21d2b1afa915
+y 58afe65bc8adbe22807026aa1b0d68af330bca268fdc054406aa41c820960e71
+z 996c597e0a024c2ff0ffe289d8c7270e4ea1d38e294d7210eddeb2c0725a1305
+
+x ea233ae033ca93034bc8fd8ea3c0625bbb15b00265264fdd61f62cc808b505fe
+y 09e12ef9b3426991f7119c2e8349278342ed0072317c4ec7ab24561b61396b39
+z 1fd72191fe9f00b0cca6a635d14904bd0c1e0ccd1275e84ad0b7bde134866e2a
+
+x fe1fd3da05524af4ccd538f1d2ede09582101fc2a47c2e63758a546bed6cc5ec
+y 523346406ef3df6ac9a455d0d2e7f732ad01c88245b07a888cc21c40fce11a76
+z de6cac8fdc878d9c4eda6b78f8b629ecf776980e49fed56bab936fc03924f44e
+
+###--------------------------------------------------------------------------
+test sqr
+
+x 4dc87ad85abe8938634492ce2ea10bf48dc4aa2fa37a6a0fde3e5a01e90dde2b
+z 346297c756d77b8ea312ddc455223f4577aea2a2e8d944cb24adb487de143b46
+
+x a33aed91165d7fd13a543760d3915c1b5d411a21895cde81b2f3640b87550cc9
+z f923e49da9d5f45e23a782f911fac1a6c2e67cbbc7b03ee4675a0c5fbec03641
+
+x a1406e453db6c92ef808295d1919c5bb2491c0ce6d5326d276c57e57943e0acc
+z 18425bbd92149991c4545e65495af0e6372289e9a32649c127122243204bdd73
+
+x 70a56b8484234ed002a68c8d535a4e527a61c360f7d4ee5b4970c8ace1e12de0
+z bed1c435139f151d0650577e03c32428f63cdb7bc1920110b5fdbb27f08cb200
+
+x 86c3236a6194f1585b4dbeb09d0247fb7d3ae08063ccf9fc4fde70fc23735710
+z 9b6509acadd5d31c4c843e91cec78be00aec4fdf7d86132965bd6f62f078f711
+
+x 0e5e83c51a8c091673425c38785e0aa1d74c7261a035a891bf734cca8c8a3db3
+z 4efe5029e99438835a8a45d0180b8de357eac82ba9dd8e127baac0d758dfca1d
+
+x 31c39a5afc33f8a8d3c570b9dc5389bea6fdaaeeb44cd7524f6c445b9583a34c
+z 359b7c8791cc87aa8b3c799c9d4d7e1f4062a4f64436d8c01071597e8c262127
+
+x 5a06203c15d6c1db6ea0fcf468a1e3f09d68c4a0f64c3d7e30e70290545e708e
+z 07f8b435ea322bedf613458b1eb420f1d6bc96741d69695899bd40f7eca6f72a
+
+x b1973433646474167b791b326827641260fb33d6a2c96d4e963a6b091f824505
+z 52a62396dbbceead62912f8adfed2707fc25edb51aac19b2a274c246f1209f26
+
+x 96b157d71e107168fac206dd63007f10f4ae1225b0761c470ee18ecdb4fff20b
+z 84ba2a84b156437cdcc39ecc8b1ad01bba934d8dfb7d504b9f2442db0ad01167
+
+x 6167d77675e19785960c28df551b458e41dfd0dfe5e56e785b7367997d5eb0a6
+z 79a558436af4310d3eaee93f9a7cab72bd817fdf59d267e2c530ba8d667a005c
+
+x fb4b2ab08db932ce10dd62639aabbb266f9ce775fb5a5e0875864f18a3ee506c
+z a6013661f2f0ab875739836039bff6bff4c993aefdda43dccecf4c404b9a612a
+
+x ea26bcf0bfc3e15d4df7ddbcac8b5b9e9a7215d74196d77c9e0524e861c6aeb4
+z 113e06861e3d338618695f4713464cea536c8019da77ff0dd9946f3b860df062
+
+x b67b1ffffec757ef147e86cf60898c5dac515f080f43f4e120017caab4eee5ee
+z 7d9748a1ff6ca9cdebeb3dd6668522767afb9ebf1c680fe7fb3f5848f7222036
+
+x c122016f17f12e53f9ac031719fe428c826217b2b757ae44f2f33d1b8b1bb553
+z dc068d032b97c98eea6dd6c8bc42e9a0a6250c81a36a8f64615489e191287c72
+
+x 1266ff0654c08e6183cd6c3cc760cc5c88d1f49b918f2f8f587b3edd4adea513
+z f07f17fadb2e2dbd282d296fe5a15cc5c2baf6b45f5fd5dc4692f252039bc862
+
+x 4c4dd9c6e46fb2c096388583f2a0c969245452b23f16ea43e15064c45357ccef
+z 5127fd4415a84115997b8b3ebe88a590efde9f8b53a43e86b1a4d60782c91025
+
+x 095d149c2616212e5f770f133e719d285a8bc888414271296684e732feb5473f
+z d8038bee551cac14d1c610bbc0960d943b01526072c589bc913ab51fd47bc848
+
+x ad55f9f916d62bb13ceb1461b99e82d76b860c084ca408dd4a18f154b907754a
+z e5c86ee6350c9ab736229f3f53e2ab852641bb8a62fdda609444df377e9ca04a
+
+x 2e4976f45acc671e38add93aa6a89669cdc9874975879b3134dd37c633c9eb14
+z c6513f1a11346d33b05ad65eca13f11125cf70bdcdd6e666a8a7b9c5b6098429
+
+###--------------------------------------------------------------------------
+test inv
+
+x 344ff33a2bc801f861bd13575797da35352c8164808d27f51ea7ca46931b2b1f
+z 07f678dfeef071b038d692bf825cb4e75bc1934bd3a6e3dfea99e78bdaeecf3a
+
+x 670097e2fbbecf6516e949d98f6d722d3f732c33bfb4e62512f9d28d94546b64
+z b2f5cbcd7d8c996ed33a813b1aa39c36f5826b436867bd89b4ce43a156c1e96b
+
+x 234f3bd8760cdc8ae7fac9457da418cd082e42906ffe59a13e52185a7845e61c
+z 7488ff9231e4819684148e16ebc25440732ffe7d211eb3d3263db1af9f1d0513
+
+x 22a39a35b1cabc6dfecd1b898593070f0c81bbd04b4b20f43a9c7c14b5dfe967
+z 892024fdbc8937b9b3aef794f57b8ed8517510b6de3f6088987b1310c1dc7932
+
+x d850c118c69198268826d05650958c6bed55b181090cf1c96493ecc4635a913f
+z 7aeae1b0dc5211f374872e78da8f225325f3f33f9c42bfdeff25d425dff7710f
+
+x 33ccdc0e39f7cd0a61782c87ac089eb7bbcabce4dd222f05088d3d6332efe959
+z 668f87e23239e965c80740d4daa9c913609388f291c11f950684f45e689a061d
+
+x 7c06f93b2f66001c74073b8ba7536049738e89b0a0d859a8a73710de3fadcf79
+z 52df0aa24bb4a7474e6ed9852ba542c1f4c5219372a7b5d60988890e2955491e
+
+x 9a0ce9ff4026bd58abcf8a128dbc55a19c446005834a143634452821d5f9f0ee
+z 79eaa93b6287705c0ba564c31bab1854c7f4354845be065c4bf94d38a7a8b421
+
+x a13a127490bd3443fdba99baf61d113f3aadd6966c9732cd16348f9fbed32e0e
+z 67290b25e6bd7328dd804309a6203c02a75657f593c7e66e48c9192524e5b87b
+
+x 35f7ac3eaa36c4ed338388fe7eda61cf237eff6ddc0847cb0c95255bbaef8ddc
+z 4950601d2cfe75eb9c4524e2f40f404fe82d0014c916dc43d9416cd2e274992d
+
+x 8a058593035986da3a19e63dacaf40fb3db4cf382205fc4e4802e0ff0c61c8d6
+z 6a23b743dc2fa4a4132780cf6edfed4c219760f3b31343b08710ea18d2c0fc43
+
+x a10d03234e700ec92270b6105fdb787d8edd3f960fdd78ea2e169f49dc708d45
+z 101dad1720604d0b093831baaa97fd0701ce773b9c1be1db0403533ad4376c0a
+
+x 52d3b9e030a5ed574f7f9489c47e73f78ef88a39b570045f9ef73c9a3e65f425
+z 83da3e088dbc9a3cbe06496c5a52edc8d7abcbb8a0f839361762137b119d961a
+
+x 9928b5f14ec80a036479d7b08c128e601db880daebef36adde6fbd1f50f82629
+z 8dcaa9a2439b77cbe44928ac2877e09755c505f58df4d0ffb9b23fc256b12779
+
+x 5a956523956f8ace6166ea6cb3c7421f8d1142d26084a81d615f00d578e03448
+z 658a3ee24ec5b5f1d2d12614e535247c9f2f259131b00f654e09b4517c63ea09
+
+x 157492cd38a07802351ca0d1a5615d5c5f254692acce930fb6be351e9a52f088
+z 32fec1eab85ddf8d27a437876e7f5a07f012b02e7971869811c3c31230204164
+
+x 2d07c109c332847567621ef4338e149b99c5bc3bf6e50943695da7fed5d8141e
+z a81472d28a8235bff43ad5cc012d52e95ece3dbc5ba2962dc54cf9e7f81bee04
+
+x 7e172f6c03415e83d4671e0191151d49e5257651ba73848254e68fad0a095c50
+z 1a8efdc57ae9d39ffa64afbc5d2dc1f25a29d365ac3dee0d8529977c14aa4415
+
+x 1934546e37b0bac80319fa7f2f86c18e83de8da830b9d0b5019c26768974eda4
+z ffe55479771f20518d8fc6491055368b5dcce9b4e193d19897f1e116b9cdf946
+
+x 90324ccfe0e34e9b08db1862be3bc17798a8581ee097be76545e3bf9d586a2e6
+z 0f5ccf4920d617c9b4f7fe6e2c9e95e89b5516555d5e3f5f9900485451d7425f
+
+###--------------------------------------------------------------------------
+test quosqrt
+
+x 18798551568191dbfe6bcacf95bf4bf00290de4c773a1d4233d1eae272b3085b
+y 2ee52110807ab6e31e0ed7b4de818d6474b514c63c99206e58a6df38e149123f
+z0 3819accb91d97a3f4dbca732f19723fc772a19b3eb4d307acad706cc7c7e1c1f
+z1 b5e653346e2685c0b24358cd0e68dc0388d5e64c14b2cf853528f9338381e360
+
+x 8671a0ecb7344f2e44fc9066aeb42661e848417e8c51b353680573830857d90f
+y 9c4cfb1aa650924ceaf3e23b260d02b7d8b7dd4445360cad0bd4270428f55292
+z0
+z1
+
+x bb0d27e1743f444e2f612c2ff575c6c6663f01869eaa8666774b8baa59b2a714
+y 2fecb156c393d27d7b9a5e4cc2b57cb5524d5b945e92c5b4bdccdd6d00e684c6
+z0
+z1
+
+x 59af963f7245901807a46a59d4e49bab5b1fdf3001f63ef4e600ef8150d0e13a
+y b5ac3372ca5435577c416ba46a57879b0ca1df29057c540cac4edacc507b5e23
+z0
+z1
+
+x a7b8659775a53e1fa315066be6a37a3f645d782cb69ec6b4f27fcf4daed3d82e
+y 4550c4697a5d29d1a97b50ea65e98ec839567a3fc556ec3790b016c24b867d89
+z0 a190875f536f94ae2af8aae90bf0afabed437b36cf640d85529b150155eed53e
+z1 4c6f78a0ac906b51d5075516f40f505412bc84c9309bf27aad64eafeaa112a41
+
+x 7163512100699c32d5fadbe3583f2f6f314c347f1e66c434b15ac06a5733f3ed
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+###--------------------------------------------------------------------------
+test sub-mulc-add-sub-mul
+
+## A very basic smoke-test.
+u 03
+v 01
+a 5
+w 01
+x 07
+y 02
+z 37
+
+## Stress the bounds.
+u 000000feffff030000f0ffffdfffff7f000000ffffff03000008ffff1f000040
+v 00
+a 0xfffff
+w 000000feffff030000f0ffffdfffff7f000000ffffff03000008ffff1f000040
+x 000000feffff030000f0ffffdfffff7f000000ffffff03000008ffff1f000040
+y 00
+z 00000cf2ffdf4400a09a000079fdffea040098edffa73b024072ffbfe0feff65
+
+## Random tests.
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--- /dev/null
+/* -*-c-*-
+ *
+ * Arithmetic modulo 2^255 - 19
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "f25519.h"
+
+/*----- Basic setup -------------------------------------------------------*/
+
+/* Elements x of GF(2^255 - 19) are represented by ten signed integers x_i: x
+ * = SUM_{0<=i<10} x_i 2^ceil(51i/2), mostly following Bernstein's original
+ * paper.
+ */
+
+typedef int32 piece; typedef int64 dblpiece;
+typedef uint32 upiece; typedef uint64 udblpiece;
+#define P p26
+#define PIECEWD(i) ((i)%2 ? 25 : 26)
+#define NPIECE 10
+
+#define M26 0x03ffffffu
+#define M25 0x01ffffffu
+#define B26 0x04000000u
+#define B25 0x02000000u
+#define B24 0x01000000u
+
+#define PIECES(v) v##0, v##1, v##2, v##3, v##4, v##5, v##6, v##7, v##8, v##9
+#define FETCH(v, w) do { \
+ v##0 = (w)->P[0]; v##1 = (w)->P[1]; \
+ v##2 = (w)->P[2]; v##3 = (w)->P[3]; \
+ v##4 = (w)->P[4]; v##5 = (w)->P[5]; \
+ v##6 = (w)->P[6]; v##7 = (w)->P[7]; \
+ v##8 = (w)->P[8]; v##9 = (w)->P[9]; \
+} while (0)
+#define STASH(w, v) do { \
+ (w)->P[0] = v##0; (w)->P[1] = v##1; \
+ (w)->P[2] = v##2; (w)->P[3] = v##3; \
+ (w)->P[4] = v##4; (w)->P[5] = v##5; \
+ (w)->P[6] = v##6; (w)->P[7] = v##7; \
+ (w)->P[8] = v##8; (w)->P[9] = v##9; \
+} while (0)
+
+/*----- Debugging machinery -----------------------------------------------*/
+
+#if defined(F25519_DEBUG)
+
+#include <stdio.h>
+
+#include "mp.h"
+#include "mptext.h"
+
+static mp *get_2p255m91(void)
+{
+ mpw w19 = 19;
+ mp *p = MP_NEW, m19;
+
+ p = mp_setbit(p, MP_ZERO, 255);
+ mp_build(&m19, &w19, &w19 + 1);
+ p = mp_sub(p, p, &m19);
+ return (p);
+}
+
+DEF_FDUMP(fdump, piece, PIECEWD, NPIECE, 32, get_2p255m91())
+
+#endif
+
+/*----- Loading and storing -----------------------------------------------*/
+
+/* --- @f25519_load@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to store the result
+ * @const octet xv[32]@ = source to read
+ *
+ * Returns: ---
+ *
+ * Use: Reads an element of %$\gf{2^{255} - 19}$% in external
+ * representation from @xv@ and stores it in @z@.
+ *
+ * External representation is little-endian base-256. Some
+ * elements have multiple encodings, which are not produced by
+ * correct software; use of noncanonical encodings is not an
+ * error, and toleration of them is considered a performance
+ * feature.
+ */
+
+void f25519_load(f25519 *z, const octet xv[32])
+{
+
+ uint32 xw0 = LOAD32_L(xv + 0), xw1 = LOAD32_L(xv + 4),
+ xw2 = LOAD32_L(xv + 8), xw3 = LOAD32_L(xv + 12),
+ xw4 = LOAD32_L(xv + 16), xw5 = LOAD32_L(xv + 20),
+ xw6 = LOAD32_L(xv + 24), xw7 = LOAD32_L(xv + 28);
+ piece PIECES(x), b, c;
+
+ /* First, split the 32-bit words into the irregularly-sized pieces we need
+ * for the field representation. These pieces are all positive. We'll do
+ * the sign correction afterwards.
+ *
+ * It may be that the top bit of the input is set. Avoid trouble by
+ * folding that back round into the bottom piece of the representation.
+ *
+ * Here, we briefly have 0 <= x_0 < 2^26 + 19, but will resolve this later.
+ * Otherwise, we have 0 <= x_{2i} < 2^26, and 0 <= x_{2i+1} < 2^25.
+ */
+ x0 = ((xw0 << 0)&0x03ffffff) + 19*((xw7 >> 31)&0x00000001);
+ x1 = ((xw1 << 6)&0x01ffffc0) | ((xw0 >> 26)&0x0000003f);
+ x2 = ((xw2 << 13)&0x03ffe000) | ((xw1 >> 19)&0x00001fff);
+ x3 = ((xw3 << 19)&0x01f80000) | ((xw2 >> 13)&0x0007ffff);
+ x4 = ((xw3 >> 6)&0x03ffffff);
+ x5 = (xw4 << 0)&0x01ffffff;
+ x6 = ((xw5 << 7)&0x03ffff80) | ((xw4 >> 25)&0x0000007f);
+ x7 = ((xw6 << 13)&0x01ffe000) | ((xw5 >> 19)&0x00001fff);
+ x8 = ((xw7 << 20)&0x03f00000) | ((xw6 >> 12)&0x000fffff);
+ x9 = ((xw7 >> 6)&0x01ffffff);
+
+ /* Next, we convert these pieces into a roughly balanced signed
+ * representation. For each piece, check to see if its top bit is set. If
+ * it is, then lend a bit to the next piece over. For x_9, this needs to
+ * be carried around, which is a little fiddly. In particular, we delay
+ * the carry until after all of the pieces have been balanced. If we don't
+ * do this, then we have to do a more expensive test for nonzeroness to
+ * decide whether to lend a bit leftwards rather than just testing a single
+ * bit.
+ *
+ * This fixes up the anomalous size of x_0: the loan of a bit becomes an
+ * actual carry if x_0 >= 2^26. By the end, then, we have:
+ *
+ * { 2^25 if i even
+ * |x_i| <= {
+ * { 2^24 if i odd
+ *
+ * Note that we don't try for a canonical representation here: both upper
+ * and lower bounds are achievable.
+ *
+ * All of the x_i at this point are positive, so we don't need to do
+ * anything wierd when masking them.
+ */
+ b = x9&B24; c = 19&((b >> 19) - (b >> 24)); x9 -= b << 1;
+ b = x8&B25; x9 += b >> 25; x8 -= b << 1;
+ b = x7&B24; x8 += b >> 24; x7 -= b << 1;
+ b = x6&B25; x7 += b >> 25; x6 -= b << 1;
+ b = x5&B24; x6 += b >> 24; x5 -= b << 1;
+ b = x4&B25; x5 += b >> 25; x4 -= b << 1;
+ b = x3&B24; x4 += b >> 24; x3 -= b << 1;
+ b = x2&B25; x3 += b >> 25; x2 -= b << 1;
+ b = x1&B24; x2 += b >> 24; x1 -= b << 1;
+ b = x0&B25; x1 += (b >> 25) + (x0 >> 26); x0 = (x0&M26) - (b << 1);
+ x0 += c;
+
+ /* And with that, we're done. */
+ STASH(z, x);
+}
+
+/* --- @f25519_store@ --- *
+ *
+ * Arguments: @octet zv[32]@ = where to write the result
+ * @const f25519 *x@ = the field element to write
+ *
+ * Returns: ---
+ *
+ * Use: Stores a field element in the given octet vector in external
+ * representation. A canonical encoding is always stored, so,
+ * in particular, the top bit of @xv[31]@ is always left clear.
+ */
+
+void f25519_store(octet zv[32], const f25519 *x)
+{
+
+ piece PIECES(x), PIECES(y), c, d;
+ uint32 zw0, zw1, zw2, zw3, zw4, zw5, zw6, zw7;
+ mask32 m;
+
+ FETCH(x, x);
+
+ /* First, propagate the carries throughout the pieces. By the end of this,
+ * we'll have all of the pieces canonically sized and positive, and maybe
+ * there'll be (signed) carry out. The carry c is in { -1, 0, +1 }, and
+ * the remaining value will be in the half-open interval [0, 2^255). The
+ * whole represented value is then x + 2^255 c.
+ *
+ * It's worth paying careful attention to the bounds. We assume that we
+ * start out with |x_i| <= 2^30. We start by cutting off and reducing the
+ * carry c_9 from the topmost piece, x_9. This leaves 0 <= x_9 < 2^25; and
+ * we'll have |c_9| <= 2^5. We multiply this by 19 and we'll add it onto
+ * x_0 and propagate the carries: but what bounds can we calculate on x
+ * before this?
+ *
+ * Let o_i = floor(51 i/2). We have X_i = SUM_{0<=j<i} x_j 2^{o_i}, so
+ * x = X_10. We see, inductively, that |X_i| < 2^{31+o_{i-1}}: X_0 = 0;
+ * |x_i| <= 2^30; and |X_{i+1}| = |X_i + x_i 2^{o_i}| <= |X_i| + 2^{30+o_i}
+ * < 2^{31+o_i}. Then x = X_9 + 2^230 x_9, and we have better bounds for
+ * x_9, so
+ *
+ * -2^235 < x + 19 c_9 < 2^255 + 2^235
+ *
+ * Here, the x_i are signed, so we must be cautious about bithacking them.
+ */
+ c = ASR(piece, x9, 25); x9 = (upiece)x9&M25;
+ x0 += 19*c; c = ASR(piece, x0, 26); x0 = (upiece)x0&M26;
+ x1 += c; c = ASR(piece, x1, 25); x1 = (upiece)x1&M25;
+ x2 += c; c = ASR(piece, x2, 26); x2 = (upiece)x2&M26;
+ x3 += c; c = ASR(piece, x3, 25); x3 = (upiece)x3&M25;
+ x4 += c; c = ASR(piece, x4, 26); x4 = (upiece)x4&M26;
+ x5 += c; c = ASR(piece, x5, 25); x5 = (upiece)x5&M25;
+ x6 += c; c = ASR(piece, x6, 26); x6 = (upiece)x6&M26;
+ x7 += c; c = ASR(piece, x7, 25); x7 = (upiece)x7&M25;
+ x8 += c; c = ASR(piece, x8, 26); x8 = (upiece)x8&M26;
+ x9 += c; c = ASR(piece, x9, 25); x9 = (upiece)x9&M25;
+
+ /* Now we have a slightly fiddly job to do. If c = +1, or if c = 0 and
+ * x >= 2^255 - 19, then we should subtract 2^255 - 19 from the whole
+ * value; if c = -1 then we should add 2^255 - 19; and otherwise we should
+ * do nothing.
+ *
+ * But conditional behaviour is bad, m'kay. So here's what we do instead.
+ *
+ * The first job is to sort out what we wanted to do. If c = -1 then we
+ * want to (a) invert the constant addend and (b) feed in a carry-in;
+ * otherwise, we don't.
+ */
+ m = SIGN(c);
+ d = m&1;
+
+ /* Now do the addition/subtraction. Remember that all of the x_i are
+ * nonnegative, so shifting and masking are safe and easy.
+ */
+ d += x0 + (19 ^ (M26&m)); y0 = d&M26; d >>= 26;
+ d += x1 + (M25&m); y1 = d&M25; d >>= 25;
+ d += x2 + (M26&m); y2 = d&M26; d >>= 26;
+ d += x3 + (M25&m); y3 = d&M25; d >>= 25;
+ d += x4 + (M26&m); y4 = d&M26; d >>= 26;
+ d += x5 + (M25&m); y5 = d&M25; d >>= 25;
+ d += x6 + (M26&m); y6 = d&M26; d >>= 26;
+ d += x7 + (M25&m); y7 = d&M25; d >>= 25;
+ d += x8 + (M26&m); y8 = d&M26; d >>= 26;
+ d += x9 + (M25&m); y9 = d&M25; d >>= 25;
+
+ /* The final carry-out is in d; since we only did addition, and the x_i are
+ * nonnegative, then d is in { 0, 1 }. We want to keep y, rather than x,
+ * if (a) c /= 0 (in which case we know that the old value was
+ * unsatisfactory), or (b) if d = 1 (in which case, if c = 0, we know that
+ * the subtraction didn't cause a borrow, so we must be in the case where
+ * 2^255 - 19 <= x < 2^255).
+ */
+ m = NONZEROP(c) | ~NONZEROP(d - 1);
+ x0 = (y0&m) | (x0&~m); x1 = (y1&m) | (x1&~m);
+ x2 = (y2&m) | (x2&~m); x3 = (y3&m) | (x3&~m);
+ x4 = (y4&m) | (x4&~m); x5 = (y5&m) | (x5&~m);
+ x6 = (y6&m) | (x6&~m); x7 = (y7&m) | (x7&~m);
+ x8 = (y8&m) | (x8&~m); x9 = (y9&m) | (x9&~m);
+
+ /* Extract 32-bit words from the value. */
+ zw0 = ((x0 >> 0)&0x03ffffff) | (((uint32)x1 << 26)&0xfc000000);
+ zw1 = ((x1 >> 6)&0x0007ffff) | (((uint32)x2 << 19)&0xfff80000);
+ zw2 = ((x2 >> 13)&0x00001fff) | (((uint32)x3 << 13)&0xffffe000);
+ zw3 = ((x3 >> 19)&0x0000003f) | (((uint32)x4 << 6)&0xffffffc0);
+ zw4 = ((x5 >> 0)&0x01ffffff) | (((uint32)x6 << 25)&0xfe000000);
+ zw5 = ((x6 >> 7)&0x0007ffff) | (((uint32)x7 << 19)&0xfff80000);
+ zw6 = ((x7 >> 13)&0x00000fff) | (((uint32)x8 << 12)&0xfffff000);
+ zw7 = ((x8 >> 20)&0x0000003f) | (((uint32)x9 << 6)&0x7fffffc0);
+
+ /* Store the result as an octet string. */
+ STORE32_L(zv + 0, zw0); STORE32_L(zv + 4, zw1);
+ STORE32_L(zv + 8, zw2); STORE32_L(zv + 12, zw3);
+ STORE32_L(zv + 16, zw4); STORE32_L(zv + 20, zw5);
+ STORE32_L(zv + 24, zw6); STORE32_L(zv + 28, zw7);
+}
+
+/* --- @f25519_set@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to write the result
+ * @int a@ = a small-ish constant
+ *
+ * Returns: ---
+ *
+ * Use: Sets @z@ to equal @a@.
+ */
+
+void f25519_set(f25519 *x, int a)
+{
+ unsigned i;
+
+ x->P[0] = a;
+ for (i = 1; i < NPIECE; i++) x->P[i] = 0;
+}
+
+/*----- Basic arithmetic --------------------------------------------------*/
+
+/* --- @f25519_add@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the sum %$x + y$%.
+ */
+
+void f25519_add(f25519 *z, const f25519 *x, const f25519 *y)
+{
+ z->P[0] = x->P[0] + y->P[0]; z->P[1] = x->P[1] + y->P[1];
+ z->P[2] = x->P[2] + y->P[2]; z->P[3] = x->P[3] + y->P[3];
+ z->P[4] = x->P[4] + y->P[4]; z->P[5] = x->P[5] + y->P[5];
+ z->P[6] = x->P[6] + y->P[6]; z->P[7] = x->P[7] + y->P[7];
+ z->P[8] = x->P[8] + y->P[8]; z->P[9] = x->P[9] + y->P[9];
+}
+
+/* --- @f25519_sub@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the difference %$x - y$%.
+ */
+
+void f25519_sub(f25519 *z, const f25519 *x, const f25519 *y)
+{
+ z->P[0] = x->P[0] - y->P[0]; z->P[1] = x->P[1] - y->P[1];
+ z->P[2] = x->P[2] - y->P[2]; z->P[3] = x->P[3] - y->P[3];
+ z->P[4] = x->P[4] - y->P[4]; z->P[5] = x->P[5] - y->P[5];
+ z->P[6] = x->P[6] - y->P[6]; z->P[7] = x->P[7] - y->P[7];
+ z->P[8] = x->P[8] - y->P[8]; z->P[9] = x->P[9] - y->P[9];
+}
+
+/* --- @f25519_neg@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
+ * @const f25519 *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Set @z = -x@.
+ */
+
+void f25519_neg(f25519 *z, const f25519 *x)
+{
+ z->P[0] = -x->P[0]; z->P[1] = -x->P[1];
+ z->P[2] = -x->P[2]; z->P[3] = -x->P[3];
+ z->P[4] = -x->P[4]; z->P[5] = -x->P[5];
+ z->P[6] = -x->P[6]; z->P[7] = -x->P[7];
+ z->P[8] = -x->P[8]; z->P[9] = -x->P[9];
+}
+
+/*----- Constant-time utilities -------------------------------------------*/
+
+/* --- @f25519_pick2@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, set @z = y@; if @m@ is all-bits-set, then set
+ * @z = x@. If @m@ has some other value, then scramble @z@ in
+ * an unhelpful way.
+ */
+
+void f25519_pick2(f25519 *z, const f25519 *x, const f25519 *y, uint32 m)
+{
+ mask32 mm = FIX_MASK32(m);
+
+ z->P[0] = PICK2(x->P[0], y->P[0], mm);
+ z->P[1] = PICK2(x->P[1], y->P[1], mm);
+ z->P[2] = PICK2(x->P[2], y->P[2], mm);
+ z->P[3] = PICK2(x->P[3], y->P[3], mm);
+ z->P[4] = PICK2(x->P[4], y->P[4], mm);
+ z->P[5] = PICK2(x->P[5], y->P[5], mm);
+ z->P[6] = PICK2(x->P[6], y->P[6], mm);
+ z->P[7] = PICK2(x->P[7], y->P[7], mm);
+ z->P[8] = PICK2(x->P[8], y->P[8], mm);
+ z->P[9] = PICK2(x->P[9], y->P[9], mm);
+}
+
+/* --- @f25519_pickn@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result
+ * @const f25519 *v@ = a table of entries
+ * @size_t n@ = the number of entries in @v@
+ * @size_t i@ = an index
+ *
+ * Returns: ---
+ *
+ * Use: If @0 <= i < n < 32@ then set @z = v[i]@. If @n >= 32@ then
+ * do something unhelpful; otherwise, if @i >= n@ then set @z@
+ * to zero.
+ */
+
+void f25519_pickn(f25519 *z, const f25519 *v, size_t n, size_t i)
+{
+ uint32 b = (uint32)1 << (31 - i);
+ mask32 m;
+
+ z->P[0] = z->P[1] = z->P[2] = z->P[3] = z->P[4] =
+ z->P[5] = z->P[6] = z->P[7] = z->P[8] = z->P[9] = 0;
+ while (n--) {
+ m = SIGN(b);
+ CONDPICK(z->P[0], v->P[0], m);
+ CONDPICK(z->P[1], v->P[1], m);
+ CONDPICK(z->P[2], v->P[2], m);
+ CONDPICK(z->P[3], v->P[3], m);
+ CONDPICK(z->P[4], v->P[4], m);
+ CONDPICK(z->P[5], v->P[5], m);
+ CONDPICK(z->P[6], v->P[6], m);
+ CONDPICK(z->P[7], v->P[7], m);
+ CONDPICK(z->P[8], v->P[8], m);
+ CONDPICK(z->P[9], v->P[9], m);
+ v++; b <<= 1;
+ }
+}
+
+/* --- @f25519_condswap@ --- *
+ *
+ * Arguments: @f25519 *x, *y@ = two operands
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then
+ * exchange @x@ and @y@. If @m@ has some other value, then
+ * scramble @x@ and @y@ in an unhelpful way.
+ */
+
+void f25519_condswap(f25519 *x, f25519 *y, uint32 m)
+{
+ mask32 mm = FIX_MASK32(m);
+
+ CONDSWAP(x->P[0], y->P[0], mm);
+ CONDSWAP(x->P[1], y->P[1], mm);
+ CONDSWAP(x->P[2], y->P[2], mm);
+ CONDSWAP(x->P[3], y->P[3], mm);
+ CONDSWAP(x->P[4], y->P[4], mm);
+ CONDSWAP(x->P[5], y->P[5], mm);
+ CONDSWAP(x->P[6], y->P[6], mm);
+ CONDSWAP(x->P[7], y->P[7], mm);
+ CONDSWAP(x->P[8], y->P[8], mm);
+ CONDSWAP(x->P[9], y->P[9], mm);
+}
+
+/* --- @f25519_condneg@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
+ * @const f25519 *x@ = an operand
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, set @z = x@; if @m@ is all-bits-set, then set
+ * @z = -x@. If @m@ has some other value then scramble @z@ in
+ * an unhelpful way.
+ */
+
+void f25519_condneg(f25519 *z, const f25519 *x, uint32 m)
+{
+ mask32 m_xor = FIX_MASK32(m);
+ piece m_add = m&1;
+# define CONDNEG(x) (((x) ^ m_xor) + m_add)
+
+ z->P[0] = CONDNEG(x->P[0]);
+ z->P[1] = CONDNEG(x->P[1]);
+ z->P[2] = CONDNEG(x->P[2]);
+ z->P[3] = CONDNEG(x->P[3]);
+ z->P[4] = CONDNEG(x->P[4]);
+ z->P[5] = CONDNEG(x->P[5]);
+ z->P[6] = CONDNEG(x->P[6]);
+ z->P[7] = CONDNEG(x->P[7]);
+ z->P[8] = CONDNEG(x->P[8]);
+ z->P[9] = CONDNEG(x->P[9]);
+
+#undef CONDNEG
+}
+
+/*----- Multiplication ----------------------------------------------------*/
+
+/* Let B = 2^63 - 1 be the largest value such that +B and -B can be
+ * represented in a double-precision piece. On entry, it must be the case
+ * that |X_i| <= M <= B - 2^25 for some M. If this is the case, then, on
+ * exit, we will have |Z_i| <= 2^25 + 19 M/2^25.
+ */
+#define CARRYSTEP(z, x, m, b, f, xx, n) do { \
+ (z) = (dblpiece)((udblpiece)(x)&(m)) - (b) + \
+ (f)*ASR(dblpiece, (xx), (n)); \
+} while (0)
+#define CARRY_REDUCE(z, x) do { \
+ dblpiece PIECES(_t); \
+ \
+ /* Bias the input pieces. This keeps the carries and so on centred \
+ * around zero rather than biased positive. \
+ */ \
+ _t0 = (x##0) + B25; _t1 = (x##1) + B24; \
+ _t2 = (x##2) + B25; _t3 = (x##3) + B24; \
+ _t4 = (x##4) + B25; _t5 = (x##5) + B24; \
+ _t6 = (x##6) + B25; _t7 = (x##7) + B24; \
+ _t8 = (x##8) + B25; _t9 = (x##9) + B24; \
+ \
+ /* Calculate the reduced pieces. Careful with the bithacking. */ \
+ CARRYSTEP(z##0, _t0, M26, B25, 19, _t9, 25); \
+ CARRYSTEP(z##1, _t1, M25, B24, 1, _t0, 26); \
+ CARRYSTEP(z##2, _t2, M26, B25, 1, _t1, 25); \
+ CARRYSTEP(z##3, _t3, M25, B24, 1, _t2, 26); \
+ CARRYSTEP(z##4, _t4, M26, B25, 1, _t3, 25); \
+ CARRYSTEP(z##5, _t5, M25, B24, 1, _t4, 26); \
+ CARRYSTEP(z##6, _t6, M26, B25, 1, _t5, 25); \
+ CARRYSTEP(z##7, _t7, M25, B24, 1, _t6, 26); \
+ CARRYSTEP(z##8, _t8, M26, B25, 1, _t7, 25); \
+ CARRYSTEP(z##9, _t9, M25, B24, 1, _t8, 26); \
+} while (0)
+
+/* --- @f25519_mulconst@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
+ * @const f25519 *x@ = an operand
+ * @long a@ = a small-ish constant; %$|a| < 2^{20}$%.
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the product %$a x$%.
+ */
+
+void f25519_mulconst(f25519 *z, const f25519 *x, long a)
+{
+
+ piece PIECES(x);
+ dblpiece PIECES(z), aa = a;
+
+ FETCH(x, x);
+
+ /* Suppose that |x_i| <= 2^27, and |a| <= 2^23. Then we'll have
+ * |z_i| <= 2^50.
+ */
+ z0 = aa*x0; z1 = aa*x1; z2 = aa*x2; z3 = aa*x3; z4 = aa*x4;
+ z5 = aa*x5; z6 = aa*x6; z7 = aa*x7; z8 = aa*x8; z9 = aa*x9;
+
+ /* Following `CARRY_REDUCE', we'll have |z_i| <= 2^26. */
+ CARRY_REDUCE(z, z);
+ STASH(z, z);
+}
+
+/* --- @f25519_mul@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the product %$x y$%.
+ */
+
+void f25519_mul(f25519 *z, const f25519 *x, const f25519 *y)
+{
+
+ piece PIECES(x), PIECES(y);
+ dblpiece PIECES(z);
+ unsigned i;
+
+ FETCH(x, x); FETCH(y, y);
+
+ /* Suppose that |x_i|, |y_i| <= 2^27. Then we'll have
+ *
+ * |z_0| <= 267*2^54
+ * |z_1| <= 154*2^54
+ * |z_2| <= 213*2^54
+ * |z_3| <= 118*2^54
+ * |z_4| <= 159*2^54
+ * |z_5| <= 82*2^54
+ * |z_6| <= 105*2^54
+ * |z_7| <= 46*2^54
+ * |z_8| <= 51*2^54
+ * |z_9| <= 10*2^54
+ *
+ * all of which are less than 2^63 - 2^25.
+ */
+
+#define M(a, b) ((dblpiece)(a)*(b))
+ z0 = M(x0, y0) +
+ 19*(M(x2, y8) + M(x4, y6) + M(x6, y4) + M(x8, y2)) +
+ 38*(M(x1, y9) + M(x3, y7) + M(x5, y5) + M(x7, y3) + M(x9, y1));
+ z1 = M(x0, y1) + M(x1, y0) +
+ 19*(M(x2, y9) + M(x3, y8) + M(x4, y7) + M(x5, y6) +
+ M(x6, y5) + M(x7, y4) + M(x8, y3) + M(x9, y2));
+ z2 = M(x0, y2) + M(x2, y0) +
+ 2* M(x1, y1) +
+ 19*(M(x4, y8) + M(x6, y6) + M(x8, y4)) +
+ 38*(M(x3, y9) + M(x5, y7) + M(x7, y5) + M(x9, y3));
+ z3 = M(x0, y3) + M(x1, y2) + M(x2, y1) + M(x3, y0) +
+ 19*(M(x4, y9) + M(x5, y8) + M(x6, y7) +
+ M(x7, y6) + M(x8, y5) + M(x9, y4));
+ z4 = M(x0, y4) + M(x2, y2) + M(x4, y0) +
+ 2*(M(x1, y3) + M(x3, y1)) +
+ 19*(M(x6, y8) + M(x8, y6)) +
+ 38*(M(x5, y9) + M(x7, y7) + M(x9, y5));
+ z5 = M(x0, y5) + M(x1, y4) + M(x2, y3) +
+ M(x3, y2) + M(x4, y1) + M(x5, y0) +
+ 19*(M(x6, y9) + M(x7, y8) + M(x8, y7) + M(x9, y6));
+ z6 = M(x0, y6) + M(x2, y4) + M(x4, y2) + M(x6, y0) +
+ 2*(M(x1, y5) + M(x3, y3) + M(x5, y1)) +
+ 19* M(x8, y8) +
+ 38*(M(x7, y9) + M(x9, y7));
+ z7 = M(x0, y7) + M(x1, y6) + M(x2, y5) + M(x3, y4) +
+ M(x4, y3) + M(x5, y2) + M(x6, y1) + M(x7, y0) +
+ 19*(M(x8, y9) + M(x9, y8));
+ z8 = M(x0, y8) + M(x2, y6) + M(x4, y4) + M(x6, y2) + M(x8, y0) +
+ 2*(M(x1, y7) + M(x3, y5) + M(x5, y3) + M(x7, y1)) +
+ 38* M(x9, y9);
+ z9 = M(x0, y9) + M(x1, y8) + M(x2, y7) + M(x3, y6) + M(x4, y5) +
+ M(x5, y4) + M(x6, y3) + M(x7, y2) + M(x8, y1) + M(x9, y0);
+#undef M
+
+ /* From above, we have |z_i| <= 2^63 - 2^25. A pass of `CARRY_REDUCE' will
+ * leave |z_i| <= 2^38 + 2^25; and a second pass will leave |z_i| <= 2^25 +
+ * 2^13, which is comfortable for an addition prior to the next
+ * multiplication.
+ */
+ for (i = 0; i < 2; i++) CARRY_REDUCE(z, z);
+ STASH(z, z);
+}
+
+/* --- @f25519_sqr@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the square %$x^2$%.
+ */
+
+void f25519_sqr(f25519 *z, const f25519 *x)
+{
+
+ piece PIECES(x);
+ dblpiece PIECES(z);
+ unsigned i;
+
+ FETCH(x, x);
+
+ /* See `f25519_mul' for bounds. */
+
+#define M(a, b) ((dblpiece)(a)*(b))
+ z0 = M(x0, x0) +
+ 38*(M(x2, x8) + M(x4, x6) + M(x5, x5)) +
+ 76*(M(x1, x9) + M(x3, x7));
+ z1 = 2* M(x0, x1) +
+ 38*(M(x2, x9) + M(x3, x8) + M(x4, x7) + M(x5, x6));
+ z2 = 2*(M(x0, x2) + M(x1, x1)) +
+ 19* M(x6, x6) +
+ 38* M(x4, x8) +
+ 76*(M(x3, x9) + M(x5, x7));
+ z3 = 2*(M(x0, x3) + M(x1, x2)) +
+ 38*(M(x4, x9) + M(x5, x8) + M(x6, x7));
+ z4 = M(x2, x2) +
+ 2* M(x0, x4) +
+ 4* M(x1, x3) +
+ 38*(M(x6, x8) + M(x7, x7)) +
+ 76* M(x5, x9);
+ z5 = 2*(M(x0, x5) + M(x1, x4) + M(x2, x3)) +
+ 38*(M(x6, x9) + M(x7, x8));
+ z6 = 2*(M(x0, x6) + M(x2, x4) + M(x3, x3)) +
+ 4* M(x1, x5) +
+ 19* M(x8, x8) +
+ 76* M(x7, x9);
+ z7 = 2*(M(x0, x7) + M(x1, x6) + M(x2, x5) + M(x3, x4)) +
+ 38* M(x8, x9);
+ z8 = M(x4, x4) +
+ 2*(M(x0, x8) + M(x2, x6)) +
+ 4*(M(x1, x7) + M(x3, x5)) +
+ 38* M(x9, x9);
+ z9 = 2*(M(x0, x9) + M(x1, x8) + M(x2, x7) + M(x3, x6) + M(x4, x5));
+#undef M
+
+ /* See `f25519_mul' for details. */
+ for (i = 0; i < 2; i++) CARRY_REDUCE(z, z);
+ STASH(z, z);
+}
+
+/*----- More complicated things -------------------------------------------*/
+
+/* --- @f25519_inv@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
+ * @const f25519 *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If
+ * %$x = 0$% then @z@ is set to zero. This is considered a
+ * feature.
+ */
+
+void f25519_inv(f25519 *z, const f25519 *x)
+{
+ f25519 t, u, t2, t11, t2p10m1, t2p50m1;
+ unsigned i;
+
+#define SQRN(z, x, n) do { \
+ f25519_sqr((z), (x)); \
+ for (i = 1; i < (n); i++) f25519_sqr((z), (z)); \
+} while (0)
+
+ /* Calculate x^-1 = x^(p - 2) = x^(2^255 - 21), which also handles x = 0 as
+ * intended. The addition chain here is from Bernstein's implementation; I
+ * couldn't find a better one.
+ */ /* step | value */
+ f25519_sqr(&t2, x); /* 1 | 2 */
+ SQRN(&u, &t2, 2); /* 3 | 8 */
+ f25519_mul(&t, &u, x); /* 4 | 9 */
+ f25519_mul(&t11, &t, &t2); /* 5 | 11 = 2^5 - 21 */
+ f25519_sqr(&u, &t11); /* 6 | 22 */
+ f25519_mul(&t, &t, &u); /* 7 | 31 = 2^5 - 1 */
+ SQRN(&u, &t, 5); /* 12 | 2^10 - 2^5 */
+ f25519_mul(&t2p10m1, &t, &u); /* 13 | 2^10 - 1 */
+ SQRN(&u, &t2p10m1, 10); /* 23 | 2^20 - 2^10 */
+ f25519_mul(&t, &t2p10m1, &u); /* 24 | 2^20 - 1 */
+ SQRN(&u, &t, 20); /* 44 | 2^40 - 2^20 */
+ f25519_mul(&t, &t, &u); /* 45 | 2^40 - 1 */
+ SQRN(&u, &t, 10); /* 55 | 2^50 - 2^10 */
+ f25519_mul(&t2p50m1, &t2p10m1, &u); /* 56 | 2^50 - 1 */
+ SQRN(&u, &t2p50m1, 50); /* 106 | 2^100 - 2^50 */
+ f25519_mul(&t, &t2p50m1, &u); /* 107 | 2^100 - 1 */
+ SQRN(&u, &t, 100); /* 207 | 2^200 - 2^100 */
+ f25519_mul(&t, &t, &u); /* 208 | 2^200 - 1 */
+ SQRN(&u, &t, 50); /* 258 | 2^250 - 2^50 */
+ f25519_mul(&t, &t2p50m1, &u); /* 259 | 2^250 - 1 */
+ SQRN(&u, &t, 5); /* 264 | 2^255 - 2^5 */
+ f25519_mul(z, &u, &t11); /* 265 | 2^255 - 21 */
+
+#undef SQRN
+}
+
+/* --- @f25519_quosqrt@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ *
+ * Returns: Zero if successful, @-1@ if %$x/y$% is not a square.
+ *
+ * Use: Stores in @z@ the one of the square roots %$\pm\sqrt{x/y}$%.
+ * If %$x = y = 0% then the result is zero; if %$y = 0$% but %$x
+ * \ne 0$% then the operation fails. If you wanted a specific
+ * square root then you'll have to pick it yourself.
+ */
+
+static const piece sqrtm1_pieces[NPIECE] = {
+ -32595792, -7943725, 9377950, 3500415, 12389472,
+ -272473, -25146209, -2005654, 326686, 11406482
+};
+#define SQRTM1 ((const f25519 *)sqrtm1_pieces)
+
+int f25519_quosqrt(f25519 *z, const f25519 *x, const f25519 *y)
+{
+ f25519 t, u, w, beta, xy3, t2p50m1;
+ octet xb[32], b0[32], b1[32];
+ int32 rc = -1;
+ mask32 m;
+ unsigned i;
+
+#define SQRN(z, x, n) do { \
+ f25519_sqr((z), (x)); \
+ for (i = 1; i < (n); i++) f25519_sqr((z), (z)); \
+} while (0)
+
+ /* This is a bit tricky; the algorithm is from Bernstein, Duif, Lange,
+ * Schwabe, and Yang, `High-speed high-security signatures', 2011-09-26,
+ * https://ed25519.cr.yp.to/ed25519-20110926.pdf.
+ *
+ * First of all, a complicated exponentation. The addition chain here is
+ * mine. We start with some preliminary values.
+ */ /* step | value */
+ SQRN(&u, y, 1); /* 1 | 0, 2 */
+ f25519_mul(&t, &u, y); /* 2 | 0, 3 */
+ f25519_mul(&xy3, &t, x); /* 3 | 1, 3 */
+ SQRN(&u, &u, 1); /* 4 | 0, 4 */
+ f25519_mul(&w, &u, &xy3); /* 5 | 1, 7 */
+
+ /* And now we calculate w^((p - 5)/8) = w^(252 - 3). */
+ SQRN(&u, &w, 1); /* 6 | 2 */
+ f25519_mul(&t, &w, &u); /* 7 | 3 */
+ SQRN(&u, &t, 1); /* 8 | 6 */
+ f25519_mul(&t, &u, &w); /* 9 | 7 */
+ SQRN(&u, &t, 3); /* 12 | 56 */
+ f25519_mul(&t, &t, &u); /* 13 | 63 = 2^6 - 1 */
+ SQRN(&u, &t, 6); /* 19 | 2^12 - 2^6 */
+ f25519_mul(&t, &t, &u); /* 20 | 2^12 - 1 */
+ SQRN(&u, &t, 12); /* 32 | 2^24 - 2^12 */
+ f25519_mul(&t, &t, &u); /* 33 | 2^24 - 1 */
+ SQRN(&u, &t, 1); /* 34 | 2^25 - 2 */
+ f25519_mul(&t, &u, &w); /* 35 | 2^25 - 1 */
+ SQRN(&u, &t, 25); /* 60 | 2^50 - 2^25 */
+ f25519_mul(&t2p50m1, &t, &u); /* 61 | 2^50 - 1 */
+ SQRN(&u, &t2p50m1, 50); /* 111 | 2^100 - 2^50 */
+ f25519_mul(&t, &t2p50m1, &u); /* 112 | 2^100 - 1 */
+ SQRN(&u, &t, 100); /* 212 | 2^200 - 2^100 */
+ f25519_mul(&t, &t, &u); /* 213 | 2^200 - 1 */
+ SQRN(&u, &t, 50); /* 263 | 2^250 - 2^50 */
+ f25519_mul(&t, &t2p50m1, &u); /* 264 | 2^250 - 1 */
+ SQRN(&u, &t, 2); /* 266 | 2^252 - 4 */
+ f25519_mul(&t, &u, &w); /* 267 | 2^252 - 3 */
+
+ /* And finally... */
+ f25519_mul(&beta, &t, &xy3); /* 268 | ... */
+
+ /* Now we have beta = (x y^3) (x y^7)^((p - 5)/8) = (x/y)^((p + 3)/8), and
+ * we're ready to finish the computation. Suppose that alpha^2 = u/w.
+ * Then beta^4 = (x/y)^((p + 3)/2) = alpha^(p + 3) = alpha^4 = (x/y)^2, so
+ * we have beta^2 = ±x/y. If y beta^2 = x then beta is the one we wanted;
+ * if -y beta^2 = x, then we want beta sqrt(-1), which we already know. Of
+ * course, it might not match either, in which case we fail.
+ *
+ * The easiest way to compare is to encode. This isn't as wasteful as it
+ * sounds: the hard part is normalizing the representations, which we have
+ * to do anyway.
+ */
+ f25519_sqr(&t, &beta);
+ f25519_mul(&t, &t, y);
+ f25519_neg(&u, &t);
+ f25519_store(xb, x);
+ f25519_store(b0, &t);
+ f25519_store(b1, &u);
+ f25519_mul(&u, &beta, SQRTM1);
+
+ m = -consttime_memeq(b0, xb, 32);
+ rc = PICK2(0, rc, m);
+ f25519_pick2(z, &beta, &u, m);
+ m = -consttime_memeq(b1, xb, 32);
+ rc = PICK2(0, rc, m);
+
+ /* And we're done. */
+ return (rc);
+}
+
+/*----- That's all, folks -------------------------------------------------*/
--- /dev/null
+/* -*-c-*-
+ *
+ * Arithmetic modulo 2^255 - 19
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+#ifndef CATACOMB_F25519_H
+#define CATACOMB_F25519_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "fake-mLib-bits.h"
+
+#ifndef CATACOMB_QFARITH_H
+# include "qfarith.h"
+#endif
+
+/*----- Data structures ---------------------------------------------------*/
+
+typedef union {
+ int32 p26[10];
+} f25519;
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @f25519_set@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to write the result
+ * @int a@ = a small-ish constant
+ *
+ * Returns: ---
+ *
+ * Use: Sets @z@ to equal @a@.
+ */
+
+extern void f25519_set(f25519 */*x*/, int /*a*/);
+
+/* --- @f25519_load@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to store the result
+ * @const octet xv[32]@ = source to read
+ *
+ * Returns: ---
+ *
+ * Use: Reads an element of %$\gf{2^{255} - 19}$% in external
+ * representation from @xv@ and stores it in @z@.
+ *
+ * External representation is little-endian base-256. Elements
+ * have multiple encodings, which are not produced by correct
+ * software; use of noncanonical encodings is not an error, and
+ * toleration of them is considered a performance feature.
+ *
+ * Some specifications, e.g., RFC7748, require the topmost bit
+ * (i.e., bit 7 of @wv[31]@) to be ignored. Callers
+ * implementing such specifications should clear the bit
+ * explicitly. (It's much easier for a caller who wants the bit
+ * to be ignored to clear it than for a caller who wants the bit
+ * to be significant to apply the necessary change by hand.)
+ */
+
+extern void f25519_load(f25519 */*z*/, const octet /*xv*/[32]);
+
+/* --- @f25519_store@ --- *
+ *
+ * Arguments: @octet zv[32]@ = where to write the result
+ * @const f25519 *x@ = the field element to write
+ *
+ * Returns: ---
+ *
+ * Use: Stores a field element in the given octet vector in external
+ * representation. A canonical encoding is always stored, so,
+ * in particular, the top bit of @xv[31]@ is always left clear.
+ */
+
+extern void f25519_store(octet /*zv*/[32], const f25519 */*x*/);
+
+/* --- @f25519_pick2@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, set @z = y@; if @m@ is all-bits-set, then set
+ * @z = x@. If @m@ has some other value, then scramble @z@ in
+ * an unhelpful way.
+ */
+
+extern void f25519_pick2(f25519 */*z*/, const f25519 */*x*/,
+ const f25519 */*y*/, uint32 /*m*/);
+
+/* --- @f25519_pickn@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result
+ * @const f25519 *v@ = a table of entries
+ * @size_t n@ = the number of entries in @v@
+ * @size_t i@ = an index
+ *
+ * Returns: ---
+ *
+ * Use: If @0 <= i < n < 32@ then set @z = v[i]@. If @n >= 32@ then
+ * do something unhelpful; otherwise, if @i >= n@ then set @z@
+ * to zero.
+ */
+
+extern void f25519_pickn(f25519 */*z*/, const f25519 */*v*/, size_t /*n*/,
+ size_t /*i*/);
+
+/* --- @f25519_condswap@ --- *
+ *
+ * Arguments: @f25519 *x, *y@ = two operands
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then
+ * exchange @x@ and @y@. If @m@ has some other value, then
+ * scramble @x@ and @y@ in an unhelpful way.
+ */
+
+extern void f25519_condswap(f25519 */*x*/, f25519 */*y*/, uint32 /*m*/);
+
+/* --- @f25519_add@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the sum %$x + y$%.
+ */
+
+extern void f25519_add(f25519 */*z*/,
+ const f25519 */*x*/, const f25519 */*y*/);
+
+/* --- @f25519_sub@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the difference %$x - y$%.
+ */
+
+extern void f25519_sub(f25519 */*z*/,
+ const f25519 */*x*/, const f25519 */*y*/);
+
+/* --- @f25519_neg@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
+ * @const f25519 *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Set @z = -x@.
+ */
+
+extern void f25519_neg(f25519 */*z*/, const f25519 */*x*/);
+
+/* --- @f25519_condneg@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
+ * @const f25519 *x@ = an operand
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, set @z = x@; if @m@ is all-bits-set, then set
+ * @z = -x@. If @m@ has some other value then scramble @z@ in
+ * an unhelpful way.
+ */
+
+extern void f25519_condneg(f25519 */*z*/, const f25519 */*x*/, uint32 /*m*/);
+
+/* --- @f25519_mulconst@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
+ * @const f25519 *x@ = an operand
+ * @long a@ = a small-ish constant; %$|a| < 2^{20}$%.
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the product %$a x$%.
+ */
+
+extern void f25519_mulconst(f25519 */*z*/, const f25519 */*x*/, long /*a*/);
+
+/* --- @f25519_mul@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the product %$x y$%.
+ */
+
+extern void f25519_mul(f25519 */*z*/,
+ const f25519 */*x*/, const f25519 */*y*/);
+
+/* --- @f25519_sqr@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the square %$x^2$%.
+ */
+
+extern void f25519_sqr(f25519 */*z*/, const f25519 */*x*/);
+
+/* --- @f25519_inv@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
+ * @const f25519 *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If
+ * %$x = 0$% then @z@ is set to zero. This is considered a
+ * feature.
+ */
+
+extern void f25519_inv(f25519 */*z*/, const f25519 */*x*/);
+
+/* --- @f25519_quosqrt@ --- *
+ *
+ * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
+ * @const f25519 *x, *y@ = two operands
+ *
+ * Returns: Zero if successful, @-1@ if %$x/y$% is not a square.
+ *
+ * Use: Stores in @z@ the one of the square roots %$\pm\sqrt{x/y}$%.
+ * If %$x = y = 0% then the result is zero; if %$y = 0$% but %$x
+ * \ne 0$% then the operation fails. If you wanted a specific
+ * square root then you'll have to pick it yourself.
+ */
+
+extern int f25519_quosqrt(f25519 */*z*/,
+ const f25519 */*x*/, const f25519 */*y*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
--- /dev/null
+### Test cases for arithmetic mod 2^448 - 2^224 - 1. -*-conf-*-
+### Extracted from Catacomb.
+
+###--------------------------------------------------------------------------
+test add
+
+## Some easy ones.
+x ffffffffffffff01000030000000ffffff2f00000002000030000000ffffff5f000000fbfffffffffffffcffff4f000000ffffffefffffff
+y 00
+z ffffffffffffff01000030000000ffffff2f00000002000030000000ffffff5f000000fbfffffffffffffcffff4f000000ffffffefffffff
+
+x fefffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff
+y 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+z fefffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff
+
+x fefffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff
+y 01
+z 00
+
+## Random tests.
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+###--------------------------------------------------------------------------
+test sub
+
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+z 6e1136912135ab628146ae4b7567e6e5b79e1829bfc3d638a39499b0545adb0660c4bbeffe2c8abb7ed2e79df8e2e809d043941fcf4614a7
+
+x 25ce194230be078d7f35b85d68706d768fec7994654fcd3f63f3d32eaf59f17bc87a617d41f76b7d0c78b63377a203e43194f0b056d26b0b
+y 76266bea72a15cdc355867a490e775c909b7b6cfc833107e7c6b7dbaed2c8491c6d000b2d7d2beb72d72937285aa1bceff18aa35d0c52158
+z aea7ae57bd1cabb049dd50b9d788f7ac8535c3c49c1bbdc1e6875674c02c6dea01aa60cb6924adc5de0523c1f1f7e715327b467b860c4ab3
+
+x c010bfa3d130f868f2b975318139c2a847c69014b76164192b437fd7e26b892a5a2425670fe3e8fd9efdfa250f57579d1af2d24f8eb6ce92
+y bfe65616e278b6ce46b295600131bf5ea092451a87f6bc3adf1c86f2fe717351b073062ced1394a14051bb33f3874cca569aae8ba97605f9
+z 002a688defb7419aab07e0d07f08034aa7334bfa2f6ba7de4b26f9e4e2f915d9a9b01e3b22cf545c5eac3ff21bcf0ad3c35724c4e43fc999
+
+x b2f21992b1f2155b7afc3a1d731b52c03cf14208e634b7da123888d652afcd919e9f5f0bea8b9986c71a7ba08fefe58ee0402d9a23b95f2c
+y ae241fa6292c63f3c09301255a866825b39c9645512ea123486f9a873cacab567cd169c463fb1cf0417633a7055d831d23fd1d58dd42e726
+z 04cefaeb87c6b267b96839f81895e99a8954acc2940616b7cac8ed4e1603223b22cef54686907c9685a447f989926271bd430f4246767805
+
+x b714b60b2614ab6ce63bf8eae621357f2e921f79de94982fcd5f524015db3faa52b15ff042733958fa202786f61bfed0b9fb5d5873619aec
+y 0c99e1da4c747ad1a625321cf9359b1d823544d1eacfddc38e4bfd729ed2f9fb37760242340f7986843fb8fa0435bcb5cffdf11453caebcf
+z ab7bd430d99f309b3f16c6ceedeb9961ac5cdba7f3c4ba6b3e1455cd760846ae1a3b5dae0e64c0d175e16e8bf1e6411beafd6b432097ae1c
+
+x c5425daf8f7089def2ff910e256d9496fc109d2698cf15dec1ce3f8116231969c5ed327626362b0658c60e74023a3cae5ef128fb5d27cad7
+y bc4e49fbf095f73894c4d623a210475cb7ba78ebbcbee8ab55a851162f789fb21e72de95afe4ddd45b90289f94f6d02b5f5a4b90c603ea31
+z 09f413b49eda91a55e3bbbea825c4d3a4556243bdb102d326c26ee6ae7aa79b6a67b54e076514d31fc35e6d46d436b82ff96dd6a9723e0a5
+
+x 9aa20b4259efd3a701a63347181fa63f56f42a97ef836bf3aab88d30bbf28a91bbf713a0170024e6057e2281ac113f9b58cb13d63e850ea7
+y 09e7104367d8c0441d811ecc619af04def9236752c2d47bc508b0de3c3b29c74533d8eb9fee13279aed8d58247e4010206c697d9b72bab43
+z 91bbfafef1161363e424157bb684b5f16661f421c35624375a2d804df73fee1c68ba85e6181ef16c57a54cfe642d3d9952057cfc86596363
+
+x e8ead9316aeb8f56d43418cd3bb1a71234c9e20b4a6dc1604ffdfdbcaacebe73b71d18c2c167544304d895d67e2daa2538a4ad0708cd9acf
+y ff3603f0960bb7a92f2b7fbfe242b467164e0ca72e89bcab6c467b5391166d05c601b38de40643f04d5b50ff8ec62b18c69e9df74f01babe
+z e9b3d641d3dfd8aca409990d596ef3aa1d7bd6641be404b5e2b6826919b8516ef11b6534dd601153b67c45d7ef667e0d72051010b8cbe010
+
+x f37b41d9950036d560f02b8befd6f5c73096b8995850b9fc563291fba59fd994916744fbd4c1dd5d17a9e5ecd4ec4a658dfdae1ba7024bc6
+y eeda58ba400f16a946381fb11f0ac0db895957236bcc629ce9d1ea425eef8412ea73af488b97f1afa950736f26c3cace887417b699cc3410
+z 05a1e81e55f11f2c1ab80cdacfcc35eca63c6176ed8356606d60a6b847b05482a7f394b2492aecad6d58727dae298096048997650d3616b6
+
+x 2bdb71a053047c4173718ce104e5b8671fbd61c59bfe8b20b890ceda15a69d24eec3775f4ce8a9c16d36e50626bc334e0fc1be492d800c06
+y b1ccd0dac33ac46b2709f9626ed70136f98dfbc705ad93ea8f1b325d644daf2c0180cb83bfdbb7398d3f58c0f6600056a174850b9db91ed4
+z 790ea1c58fc9b7d54b68937e960db731262f66fd9551f83528759c7db058eef7ec43acdb8c0cf287e0f68c462f5b33f86d4c393e90c6ed31
+
+x 8f3fd6346c7f2dacf0d7cdb88a5bca3b222a895a07b169d0bcd0af0a9aa634876ae1a939262dd75bd12b5a97127155a015e00acac7d5cbc8
+y 0e9c03c5a06accdddd0d8613e41a00f2b586e297e366987e02e7536e0ca1b4c2c75fed619655acddffe8585c7a828432d90575731a4c8519
+z 81a3d26fcb1461ce12ca47a5a640ca496ca3a6c2234ad151bae95b9c8d0580c4a281bcd78fd72a7ed142013b98eed06d3cda9556ad8946af
+
+###--------------------------------------------------------------------------
+test condswap
+
+x db0be3ccfda1e2f8492bffb5d3344f1856ff1896b6a067d2fa064423ac5b05b669db1c9b51899c44a7f470be4173856d9aa3d1cd10cb8c9b
+y 3005560f89232a97cebf6808e7493dd0f17e572556b53723b57faee51d8a0a45c7fb51aeb916f59c74ea6041494483b2fdce72189d1bd031
+m 0xffffffff
+xx 3005560f89232a97cebf6808e7493dd0f17e572556b53723b57faee51d8a0a45c7fb51aeb916f59c74ea6041494483b2fdce72189d1bd031
+yy db0be3ccfda1e2f8492bffb5d3344f1856ff1896b6a067d2fa064423ac5b05b669db1c9b51899c44a7f470be4173856d9aa3d1cd10cb8c9b
+
+x ea009751f6a7045ec7d6d46b16cbe663f5a78fca3835626c79864bec4030443bb9349654d52b2edab92b8f4aa876a97e868aa6267a54e6b1
+y 8c6f864ef7f664f4985ed8c1ea0c63bd7ab355b5321c2712791b610a2dadddc90a65ca8d5c25ff199b011193796b08f96420934615103b7b
+m 0x00000000
+xx ea009751f6a7045ec7d6d46b16cbe663f5a78fca3835626c79864bec4030443bb9349654d52b2edab92b8f4aa876a97e868aa6267a54e6b1
+yy 8c6f864ef7f664f4985ed8c1ea0c63bd7ab355b5321c2712791b610a2dadddc90a65ca8d5c25ff199b011193796b08f96420934615103b7b
+
+x dc3aa7d363058993cbdc54e95f3c972a2cea17cdf9370fccdfedfa1ba939ca35f762c5c6283f84348282fd56d83539804427eabe3bd6170d
+y 8c47a0990eccf7300986232dbc8ee26e8996c3bb4b73663ec5525312bea8975221c9f49039840c181d042654a8c1806bb86702ac7d0b80f4
+m 0x00000000
+xx dc3aa7d363058993cbdc54e95f3c972a2cea17cdf9370fccdfedfa1ba939ca35f762c5c6283f84348282fd56d83539804427eabe3bd6170d
+yy 8c47a0990eccf7300986232dbc8ee26e8996c3bb4b73663ec5525312bea8975221c9f49039840c181d042654a8c1806bb86702ac7d0b80f4
+
+x 69b45538513af2148e0a2903539bc5e20fca4da447278bf5967091d2e781121080c14a41989f9ee5218c444d3a42989ba890c7be7faae5d3
+y 935eadbde0c571c29deb4d8404dd39a8cca177ced36c359abfa7a6cafe6075422e1d79cba8d81cdbdfa4a5144faf37b19ca22b2b40fe1a0b
+m 0x00000000
+xx 69b45538513af2148e0a2903539bc5e20fca4da447278bf5967091d2e781121080c14a41989f9ee5218c444d3a42989ba890c7be7faae5d3
+yy 935eadbde0c571c29deb4d8404dd39a8cca177ced36c359abfa7a6cafe6075422e1d79cba8d81cdbdfa4a5144faf37b19ca22b2b40fe1a0b
+
+x de30072f175127ad4200a08099f4d0df0edfa40eb02e21a03c5628dcb2f70da8bce9ebbb1ebed2aca391e73a4114c06bcdbf762bf28777cf
+y 5eaf3aecf1f7d1fd3b43be8fa450163c79f162b0c6eaa4b1ad39baaf3a4c36564e001c935fdce38e90789151beff0f3cc4fdfc2d86dcb587
+m 0x00000000
+xx de30072f175127ad4200a08099f4d0df0edfa40eb02e21a03c5628dcb2f70da8bce9ebbb1ebed2aca391e73a4114c06bcdbf762bf28777cf
+yy 5eaf3aecf1f7d1fd3b43be8fa450163c79f162b0c6eaa4b1ad39baaf3a4c36564e001c935fdce38e90789151beff0f3cc4fdfc2d86dcb587
+
+x 1bb20a5a05b190737ad6b2bc5bc2b9259fa7e36eac8f3032a7c56ed59c1510baaea32bba898b329b0c64fadbe454095b9f82b366bfae3d8b
+y cf0a87c8befed020caf82f37b4c5f17d2aa9ff8ab75baa156cfe2716ac1eaabf9bc760c2ddcd66a9d02a8384ad1db9e8f857b151d126e0ef
+m 0x00000000
+xx 1bb20a5a05b190737ad6b2bc5bc2b9259fa7e36eac8f3032a7c56ed59c1510baaea32bba898b329b0c64fadbe454095b9f82b366bfae3d8b
+yy cf0a87c8befed020caf82f37b4c5f17d2aa9ff8ab75baa156cfe2716ac1eaabf9bc760c2ddcd66a9d02a8384ad1db9e8f857b151d126e0ef
+
+x c186531a219344dc485cd5dad6500616ac8e0653693168573cb9be590b02dfb1ddc5d87d27f2d9fa46ffeda955a6285b7ef2b9bf84825d06
+y 91f3be7eb2e0be38d92974d81be5126ef40d358f242d23aa4863fb16ba3e8844e02edc87c0206e211587886ed532da0ab148cfcf64e9b58d
+m 0x00000000
+xx c186531a219344dc485cd5dad6500616ac8e0653693168573cb9be590b02dfb1ddc5d87d27f2d9fa46ffeda955a6285b7ef2b9bf84825d06
+yy 91f3be7eb2e0be38d92974d81be5126ef40d358f242d23aa4863fb16ba3e8844e02edc87c0206e211587886ed532da0ab148cfcf64e9b58d
+
+x 9f2476d6db424d19ee0cba4ed091da5b44ca63caf2f711eaeb7edcc75f49e0d0c367c1f2817b6bb39460f897432901064cabed7f6a03b1f0
+y 66e7dcd34d76a19e3285685112b7619f9a3557764a918922faf1370bb97c2b2fa845dd34662cfe7299ab702c68fd43b5f6f15a0af6625f2e
+m 0xffffffff
+xx 66e7dcd34d76a19e3285685112b7619f9a3557764a918922faf1370bb97c2b2fa845dd34662cfe7299ab702c68fd43b5f6f15a0af6625f2e
+yy 9f2476d6db424d19ee0cba4ed091da5b44ca63caf2f711eaeb7edcc75f49e0d0c367c1f2817b6bb39460f897432901064cabed7f6a03b1f0
+
+x f124ac31d304a29cdd94bdc0611c61064a7c5f09cf6847bccd52fc7a7b77ede73b42b1ef75f000de4361028e0fb63896f4ef5ad3bc1b9c90
+y 6629084a230c793086e469b9a01e052ad7a5680d6955667e0dfb19a250f447d9e238695400dc4ecaeefcebed44d374e57ec4e414f5629e63
+m 0x00000000
+xx f124ac31d304a29cdd94bdc0611c61064a7c5f09cf6847bccd52fc7a7b77ede73b42b1ef75f000de4361028e0fb63896f4ef5ad3bc1b9c90
+yy 6629084a230c793086e469b9a01e052ad7a5680d6955667e0dfb19a250f447d9e238695400dc4ecaeefcebed44d374e57ec4e414f5629e63
+
+x b64f2952510827bef3d32ef6347251274c7241d9913268a7a6a5c360a4b29e7ed04d09a9ee5aa83235eaf8c0582b076b21d78b7062952773
+y 77897028a9a81fd54362a6085aa2c2fd6fdd44589f447c7310b9b3b5a29b54ed15c57e2c9fbff16f20129a4dbd43640a0d1037e277ca5c93
+m 0xffffffff
+xx 77897028a9a81fd54362a6085aa2c2fd6fdd44589f447c7310b9b3b5a29b54ed15c57e2c9fbff16f20129a4dbd43640a0d1037e277ca5c93
+yy b64f2952510827bef3d32ef6347251274c7241d9913268a7a6a5c360a4b29e7ed04d09a9ee5aa83235eaf8c0582b076b21d78b7062952773
+
+x 4d75efd204a66aed323456e6f55cb891ee7a31d739ae89726e0ea84532f9c740d1b647b117094fb85da2c62da04f3b9cb13db6b840046b7c
+y 0afd07bb073a150e7b82711e1f42f7b0789af8192ea6b4e1b24a3d48de7f8b802875aca5a02a9d24deca0b58c895992a449d01026495b96c
+m 0x00000000
+xx 4d75efd204a66aed323456e6f55cb891ee7a31d739ae89726e0ea84532f9c740d1b647b117094fb85da2c62da04f3b9cb13db6b840046b7c
+yy 0afd07bb073a150e7b82711e1f42f7b0789af8192ea6b4e1b24a3d48de7f8b802875aca5a02a9d24deca0b58c895992a449d01026495b96c
+
+x 1ff4eb5f0280744f0c909cede8be29cccb8ae43e4626018a9a1d352a97d987678863ba34bdeb183bb5e9347e96760665f5881570778a2e19
+y 49cd390a9edc7fad6c84c2e44ce09e490161094d2dc6cad30759fbef10aa30e5aa6474bc46571188418f3e4a2b19ecfc379a1f94e3a44e48
+m 0x00000000
+xx 1ff4eb5f0280744f0c909cede8be29cccb8ae43e4626018a9a1d352a97d987678863ba34bdeb183bb5e9347e96760665f5881570778a2e19
+yy 49cd390a9edc7fad6c84c2e44ce09e490161094d2dc6cad30759fbef10aa30e5aa6474bc46571188418f3e4a2b19ecfc379a1f94e3a44e48
+
+x e96c0316baf01c25ef8a41c02e99aa84c82f8eecd3249be268834afb5f7e95f0ad10bfad4160bb335c30ffd6a1090c91c57eb6ac7a7a5e66
+y 115e6f115bc4e19af60710f3dd821fb58cb680a32d6973eae9ea3e48f1928dc1d9f684a8c8de80affc59bc0fb342bb040f89d2d46b8ff8fc
+m 0x00000000
+xx e96c0316baf01c25ef8a41c02e99aa84c82f8eecd3249be268834afb5f7e95f0ad10bfad4160bb335c30ffd6a1090c91c57eb6ac7a7a5e66
+yy 115e6f115bc4e19af60710f3dd821fb58cb680a32d6973eae9ea3e48f1928dc1d9f684a8c8de80affc59bc0fb342bb040f89d2d46b8ff8fc
+
+x 71bd8f5036da4c33f6940348ea448c2f9bccb152dab40b410bd695923a9e255b33aaf361055be4bb9a570e201dce784cc1ccb0f89faca85f
+y 971b2f6569ddd9099a87ec4086d8218abcfbe81579f25f03634e471170a5088f48a6cfd09ed9e389ca37b780165c00b206304229135b6044
+m 0xffffffff
+xx 971b2f6569ddd9099a87ec4086d8218abcfbe81579f25f03634e471170a5088f48a6cfd09ed9e389ca37b780165c00b206304229135b6044
+yy 71bd8f5036da4c33f6940348ea448c2f9bccb152dab40b410bd695923a9e255b33aaf361055be4bb9a570e201dce784cc1ccb0f89faca85f
+
+x 0f1165e19968f3e6159e9f7f843c1b849e5c3917af4e2798869112c6efca9993ed339c8495eec8c54b286820bf7befdc8ae344e4d309c077
+y 7ce5a2ae66b9bddd30c98d9aa9fcdd6ef90d244d10115d15cf5d81e9e389f6852b153a42c642447043fcfd278166b92c624508973449b0e8
+m 0xffffffff
+xx 7ce5a2ae66b9bddd30c98d9aa9fcdd6ef90d244d10115d15cf5d81e9e389f6852b153a42c642447043fcfd278166b92c624508973449b0e8
+yy 0f1165e19968f3e6159e9f7f843c1b849e5c3917af4e2798869112c6efca9993ed339c8495eec8c54b286820bf7befdc8ae344e4d309c077
+
+x 6dd07b4891d8f45ad1ee64da38383ec50d6f29634767607eca19a547cadc3c157ebe7d86a28d4d2fa2d40f2c5402d8b338cfd8d30aeadb6a
+y 63da9a5a0cd51e58168ddb305c0e70a2f898279dae6394e1b3e1ef3a0763847d5d2f15be493114360204d037d7d3c3a9e746d27dcb544ded
+m 0xffffffff
+xx 63da9a5a0cd51e58168ddb305c0e70a2f898279dae6394e1b3e1ef3a0763847d5d2f15be493114360204d037d7d3c3a9e746d27dcb544ded
+yy 6dd07b4891d8f45ad1ee64da38383ec50d6f29634767607eca19a547cadc3c157ebe7d86a28d4d2fa2d40f2c5402d8b338cfd8d30aeadb6a
+
+x d91228b648f75350d775432af35be9aa283e9729fcd3b689f0c7ee02ea67efd33493980ae5eec92ad6ab42ccd253a7aab5a62c26be275278
+y 07c5d1b4f9b8db88cd4187b1ae5e175bf703af12b26d066c1d55dd367569d3e23e3d0470f3c47e6761746ce7de39cf563500d026a6791980
+m 0xffffffff
+xx 07c5d1b4f9b8db88cd4187b1ae5e175bf703af12b26d066c1d55dd367569d3e23e3d0470f3c47e6761746ce7de39cf563500d026a6791980
+yy d91228b648f75350d775432af35be9aa283e9729fcd3b689f0c7ee02ea67efd33493980ae5eec92ad6ab42ccd253a7aab5a62c26be275278
+
+x f9e764e20657319802b53ee29df43b0d83d994d9049b9820fc0c31b631265c49f6613923a042eadce5902fb81753784ff5a9c0de2c4f6b12
+y 6ab2f8279e82aa65e8326e5c60bfa067e4967b3ea67d0369853282e5429736529a43eeee3fdf24ebbe5ca85b59647994fc99c90da83c6229
+m 0xffffffff
+xx 6ab2f8279e82aa65e8326e5c60bfa067e4967b3ea67d0369853282e5429736529a43eeee3fdf24ebbe5ca85b59647994fc99c90da83c6229
+yy f9e764e20657319802b53ee29df43b0d83d994d9049b9820fc0c31b631265c49f6613923a042eadce5902fb81753784ff5a9c0de2c4f6b12
+
+x 772289865ac905fac203e4654b258890ddb91cac71c6d2af3826e3acfebfa222c937b40069ce3a757e2ffd960b5821ed1ad54e4ad2e3c6fd
+y 58dbf838ab81a754533c7f80fea48cbc981f724e4c150ddbb0afb5c711a8e21079446f77c427f7eb1892c096fa3eae5e2b070413611cd184
+m 0xffffffff
+xx 58dbf838ab81a754533c7f80fea48cbc981f724e4c150ddbb0afb5c711a8e21079446f77c427f7eb1892c096fa3eae5e2b070413611cd184
+yy 772289865ac905fac203e4654b258890ddb91cac71c6d2af3826e3acfebfa222c937b40069ce3a757e2ffd960b5821ed1ad54e4ad2e3c6fd
+
+x 0bd6656d68c41bfc5389db274367f69191754919435ba58d2256017b5bc595d102c6f4f745b3ceb0c32bd0a6cdadded3a3dc925ef2b5c73c
+y 1d903009c74d3d135a192bd42466cd28303f482626a7d10832f1f6eae72c3b051b0373e62300a71226011475034f0bfc6c9a65601bb83993
+m 0xffffffff
+xx 1d903009c74d3d135a192bd42466cd28303f482626a7d10832f1f6eae72c3b051b0373e62300a71226011475034f0bfc6c9a65601bb83993
+yy 0bd6656d68c41bfc5389db274367f69191754919435ba58d2256017b5bc595d102c6f4f745b3ceb0c32bd0a6cdadded3a3dc925ef2b5c73c
+
+###--------------------------------------------------------------------------
+test mulconst
+
+x cb908747a1af81f52715ef8440aed06aaacbcd7903c99cdecef5ec54e7845bedaad6475028b0cbdb0d53b6eeb71843f900fefd398a083d5a
+a -417895
+z e95e64fd1b2e2e79d1bfef5c96942eaf7ca5d40b1af774ed9c4ea2351c8ae81013f896bafd1f0b0e3a3c2ca3347c6cf88f988877af5e009b
+
+x 46b23d83c0848e79af947191cb76b087483beec6224af749e59c0c5ae27ff8abada31da895f8132aae0457f5ddc30d18a8d52046fbe6ef55
+a 384370
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+
+x 53e19751de62909506bebf74411d359014ec4b6afbb8ce14eeed8a3938013f0fee6897e3cc3adcbc90d7df321c4caa1941d0e5909551335d
+a -49682
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+
+x 7ff3b9b3d8ee248a48d0c8d308d8c3658374acc92303143061a46656ae2b35094ed7b5b27d23366c0e42ee0a9471a4355d81cda0e4390348
+a 131908
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+
+x f532f4f5ab5447b083ee4225246aaa4448696e4fc8bcf5b0ec1b52df88354e5327d7a3cf6e15db9945205968c275755ea3906a27437d29ed
+a 383911
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+
+x ef0e2a829097e50575eae6b1ad3fa10b8e417b0363654e0cb07a563a905c02e367c6f1ad7be1469b9f5295e3db0726853adffb820715f7d1
+a -226220
+z a7c5387af1b9f61f09d628feac1a050173021386775c9f534557b8841b812155325e3632eee7a2302ef8af0b4746575d6c2bcf3b29f674b0
+
+x 3b4655b1c22542ca413f76bc24751a01cdab6b385b50301d67fd62ba31ad132150e38e12a849405112c4742e93b92849bd8b872c29edb2f9
+a -89924
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+
+x 48bdc2073bff25ae9bf7fcc368d65602a71e48c343bc7181c361331f108867d56c588f698aa5b91222f5dbbc859bce656f2607b053222fc7
+a 66432
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+
+x 98a26f23f83673a480076b2fc7ccfef07fbbe70c4160d5af638c345f7d17b00931efff543fd47b7b8b362a70657a458566ada4aefd1c5eaf
+a 492192
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+
+x 6ebf7c4e06837120cc852a077945656046e64c2d88ce440bdfc8d38736a4d510a722bc8b0d225f11df0e704e4b04c48bf481da68fd1e150e
+a -7098
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+
+x 94e49f2bb473a7273abed94363c4dc3d13db159e3c3698a62ce5f321252aa03c7f63dd6eff9529c985f43abc7283d11140cb44ff6fd0f3d3
+a -392951
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+
+x cd262298ce3b73294bfb523c30206fc3771144890a0ebcef19e02e5085973a6aeefabdf8cb7186d57be38ee84b114b9a7a22556c0cf88df1
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+
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+
+x d8ab6b8f3523e98f49140e051c0b744bb0068d20f499c0763aa28ec1d1dd7e86356f357149c317376be96cd520b3ae04a2c4d468d74745e8
+a -360296
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+
+x 6036fbfb9fcc223a1776ec67c9424788aabe553a7d6a0472159edc747ebaf97e99f7263ece635ef0b702a3610aef32e17f59fae503e18d74
+a -5433
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+
+x a3433dfc89ec4d6d858bb5b018e2d474b7de7604ed4491957fe16453d3793740ef88136814f59b19ed3610252e74cbc3a36571d02e57913b
+a 237641
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+
+x c17ecc6099e9630a4ec20f4199abe1c10d414f6d734014ada1e6f097090a2bb4e638fb52d9bf56080d77c2b535f52cb091cbaad3c65072e8
+a 517226
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+
+x 134263fd765e5f1da64900df5643c5241d4fa8a9e96ee59f01667b64f9122e85e995b90d4bf5d5fe9f68825dfa6edd19d8ce009270ae2984
+a 390674
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+
+x 54326fffef9f0fe1207a07c8ac063d64b3fe81528e005f857319a74da2c3423a552b05f8c465908b028a2dcf15cb7158c99a1d2bdfd890da
+a -255467
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+
+x 5c30f73ec3addb2d27e0e79579063f2d30fa9fb47c2b6a3a32553120a047cad83abc901e5a5b4a65f8e51144f7eb0abec9a4d105236b2618
+a -466309
+z 5ec894f6abe2d88971da11b982c3322d1f533a326057816f6273585bfa186a7f569ddf93c27e8e74719ddb515689d5935c56e6b86936f22b
+
+###--------------------------------------------------------------------------
+test mul
+
+## Easy tests.
+x 03
+y 02
+z 06
+
+x f7ffffdfffffff00000050000000000000a0ffffff03000090fffffffbffffafffffff00000020000000fdffff9ffffffff9ffff7fffffff
+y ffffffffffffff01000030000000ffffff2f00000002000030000000ffffff5f000000fbfffffffffffffcffff4f000000ffffffefffffff
+z bfffff6f02000083ffff5f010000a1ffff9ffcffffc0ffff6ffdffffc4ffffff02000082ffff8f03000089ffff6ffaffff7cffffff000000
+
+x f8ff7ffeff5f00001000000800000300000100a0ffffafffff130000fbffff0100000000e0ffffebffffffff7ffffffffeff1f0000080000
+y f7ff7f0200e0ffffefffff070000faff7ffefffffefffffffff7ffff040080ffff1fffff8ffffff7ffff0500800200000000f0fffffbffff
+z 0a0100240020f5ff7ffdff4fffff4100003a00201400400300a8feff030180e6fffff9ff8f02003001002c0000f0ff9f0600d0f8ff670200
+
+## Random tests.
+x 94aa99eaba90c5eb2efd7101c8efeffc1e44c8fcd84ccb8ef27b9792ae12534c0a250e5400407177bd655e51c343f776a3fd26474da4dc74
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+
+x a434abefb0de3c7f5e33f9230ead871bb3f06888c0d568b9a74fa32b676dc600fed2d54a042e1b97340852c4d6ef796a18561884d760d4ad
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+
+x fe9911abbe57f1ddd61acd062d59637b129a1571af65fb70169db0d8b12b498a66d1eefcf9c8cbea01179f113afef0ae192550828885689c
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+
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+
+x 9014dd22854f1f21fa1475d74eba669101c871c2a21ffd5d10f0792e3cc5d34f15b4735759575dda169e2dd868a5ae64dbeaa2a654cfde5c
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+
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+
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+
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+
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+
+x 1fbba059c333843e3cf0cff19bec99bd0cfc89c3b390200165680b742fe540b32042959022e7393c9e13ef7fa3f1dd5ac46595803210c536
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+
+x 26f5bc0c2c49899690fa423478ab1cf7000be27609bf683896a6ce3f619510b061ca04debb6c64540e724d113cd4b8ff3485337851367700
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+
+x 6c044d6556abb8efdf5b180695293464a8bc4b9cab201822053c7295973ea0a8866425629cfff1d372a48f51dbc6a7f828691194c32c2c5c
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+z a599fabf997468487b9376500b58a51e0e00c86d9eac6f50157aa1017d99ac8b95e7842b36071a192784ef72433c06a1dd042990b71ffe8f
+
+x 50378c6ac56816962d428ea523a0cf87121fb3c53b37bac6d3a05fcbdfb8a5fb20aa014f1e1b01a3963534d403baeb7c436f72cf3cc5db58
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+z 00127644003ed4b518f04abbd058a46015fb328883b92070bc5cf0fd98d7307dfabbc65f3e8551c622792efabe55f03953e498e360410790
+
+x 5db2f6db35af2e1c84ab6832b967bf987cd03adea7113fb8806ce8fb3ffa426dc10997e13afcd39cf5cd65f65f8a09e650fad8e5f6ef2648
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+
+x d5baefaae7fc9000e0d55f287f740dfb1899ba6e9e36338959a16ac5e5f45442a37086b5519a0b439f38b129328aebf468dec4b59c89a249
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+
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+
+x f4048d4a1602eeec43cdf20c3ac9f7b359935bae3648070276faf07a5c58fdf79771ba6c077ddeae47617971e2145f4960587637e7028822
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+
+x 9023c019bf7ef6df45e0e44111903c622220bd3dde046679540302451d001e47a153b0ac7dcfb9831e2d262d8e27002197d9640900e4c1cc
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+z bf2c241efc180988232b83cda91e12dd0aec0d22ab68353c9841c4ea0547fd1b377fbca125f8cf92c426f8eb859f85a3853516ec104d9b6e
+
+x bbdecfafa9284e3067081b7d1bd7ce0e488829859628a8f6a38bc1a3ca6ec3130dbc1345b69abb7224b047fd3f2dadcf9cc11a8ec46a6436
+y 49a956ee69cdfecf29440d60fde9db1edd94619af97f625d45dc83c64994fe6c1ac858150cb526ca3c58a9fdc09d409ee3ed0b0cbcdb711c
+z 7abfd47fdfcceb278c917afd059e335110bec63fea48dedf7f8275da8922201ea06be39e3d1bccea2d38f5eb7d7aa5ef4e6fe6792a9f0ce0
+
+x a9483d4f0c94eac273adc392c3f425be610206683cbb6806dca47be3b54ad142fa2c54a7a473675556bcc8cfd50649af3c58d7a91e84b428
+y b986365aa08f088fe04aaaf2e00468af3fb41cda961b56ece5bedfd83cf9a0fb959ae70c23d9b27cd1eaf8b611d9e578aa0b9d899b81d5f1
+z 4af529627637ad3f3f1269319f4fd426d31e276287ee525d0c64974e55fca1cd58694eadf47e44dc3e843e01c36b22f9717067a907840ca1
+
+###--------------------------------------------------------------------------
+test sqr
+
+## Easy tests.
+x 03
+z 09
+
+x f7ffffdfffffff00000050000000000000a0ffffff03000090fffffffbffffafffffff00000020000000fdffff9ffffffff9ffff7fffffff
+z 8c000040010000f3ffffff040000f4000040120000ff0000800a000099000060060000030000000a0000e7010000180000290200800b0000
+
+## Random tests.
+x 776cf7ee39df23538f76e6be87ecbb1ed78477b858e3520f24b2b36f09a7dd61daf7bd5990af13c11b1419d8215eb69c30efc3917097797b
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+###--------------------------------------------------------------------------
+test inv
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+
+###--------------------------------------------------------------------------
+test sub-mulc-add-sub-mul
+
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--- /dev/null
+/* -*-c-*-
+ *
+ * Arithmetic in the Goldilocks field GF(2^448 - 2^224 - 1)
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "fgoldi.h"
+
+/*----- Basic setup -------------------------------------------------------*
+ *
+ * Let φ = 2^224; then p = φ^2 - φ - 1, and, in GF(p), we have φ^2 = φ + 1
+ * (hence the name).
+ */
+
+/* We represent an element of GF(p) as 16 28-bit signed integer pieces x_i:
+ * x = SUM_{0<=i<16} x_i 2^(28i).
+ */
+
+typedef int32 piece; typedef int64 dblpiece;
+typedef uint32 upiece; typedef uint64 udblpiece;
+#define PIECEWD(i) 28
+#define NPIECE 16
+#define P p28
+
+#define B28 0x10000000u
+#define B27 0x08000000u
+#define M28 0x0fffffffu
+#define M27 0x07ffffffu
+#define M32 0xffffffffu
+
+/*----- Debugging machinery -----------------------------------------------*/
+
+#if defined(FGOLDI_DEBUG)
+
+#include <stdio.h>
+
+#include "mp.h"
+#include "mptext.h"
+
+static mp *get_pgoldi(void)
+{
+ mp *p = MP_NEW, *t = MP_NEW;
+
+ p = mp_setbit(p, MP_ZERO, 448);
+ t = mp_setbit(t, MP_ZERO, 224);
+ p = mp_sub(p, p, t);
+ p = mp_sub(p, p, MP_ONE);
+ mp_drop(t);
+ return (p);
+}
+
+DEF_FDUMP(fdump, piece, PIECEWD, NPIECE, 56, get_pgoldi())
+
+#endif
+
+/*----- Loading and storing -----------------------------------------------*/
+
+/* --- @fgoldi_load@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to store the result
+ * @const octet xv[56]@ = source to read
+ *
+ * Returns: ---
+ *
+ * Use: Reads an element of %$\gf{2^{448} - 2^{224} - 19}$% in
+ * external representation from @xv@ and stores it in @z@.
+ *
+ * External representation is little-endian base-256. Some
+ * elements have multiple encodings, which are not produced by
+ * correct software; use of noncanonical encodings is not an
+ * error, and toleration of them is considered a performance
+ * feature.
+ */
+
+void fgoldi_load(fgoldi *z, const octet xv[56])
+{
+
+ unsigned i;
+ uint32 xw[14];
+ piece b, c;
+
+ /* First, read the input value as words. */
+ for (i = 0; i < 14; i++) xw[i] = LOAD32_L(xv + 4*i);
+
+ /* Extract unsigned 28-bit pieces from the words. */
+ z->P[ 0] = (xw[ 0] >> 0)&M28;
+ z->P[ 7] = (xw[ 6] >> 4)&M28;
+ z->P[ 8] = (xw[ 7] >> 0)&M28;
+ z->P[15] = (xw[13] >> 4)&M28;
+ for (i = 1; i < 7; i++) {
+ z->P[i + 0] = ((xw[i + 0] << (4*i)) | (xw[i - 1] >> (32 - 4*i)))&M28;
+ z->P[i + 8] = ((xw[i + 7] << (4*i)) | (xw[i + 6] >> (32 - 4*i)))&M28;
+ }
+
+ /* Convert the nonnegative pieces into a balanced signed representation, so
+ * each piece ends up in the interval |z_i| <= 2^27. For each piece, if
+ * its top bit is set, lend a bit leftwards; in the case of z_15, reduce
+ * this bit by adding it onto z_0 and z_8, since this is the φ^2 bit, and
+ * φ^2 = φ + 1. We delay this carry until after all of the pieces have
+ * been balanced. If we don't do this, then we have to do a more expensive
+ * test for nonzeroness to decide whether to lend a bit leftwards rather
+ * than just testing a single bit.
+ *
+ * Note that we don't try for a canonical representation here: both upper
+ * and lower bounds are achievable.
+ */
+ b = z->P[15]&B27; z->P[15] -= b << 1; c = b >> 27;
+ for (i = NPIECE - 1; i--; )
+ { b = z->P[i]&B27; z->P[i] -= b << 1; z->P[i + 1] += b >> 27; }
+ z->P[0] += c; z->P[8] += c;
+}
+
+/* --- @fgoldi_store@ --- *
+ *
+ * Arguments: @octet zv[56]@ = where to write the result
+ * @const fgoldi *x@ = the field element to write
+ *
+ * Returns: ---
+ *
+ * Use: Stores a field element in the given octet vector in external
+ * representation. A canonical encoding is always stored.
+ */
+
+void fgoldi_store(octet zv[56], const fgoldi *x)
+{
+
+ piece y[NPIECE], yy[NPIECE], c, d;
+ uint32 u, v;
+ mask32 m;
+ unsigned i;
+
+ for (i = 0; i < NPIECE; i++) y[i] = x->P[i];
+
+ /* First, propagate the carries. By the end of this, we'll have all of the
+ * the pieces canonically sized and positive, and maybe there'll be
+ * (signed) carry out. The carry c is in { -1, 0, +1 }, and the remaining
+ * value will be in the half-open interval [0, φ^2). The whole represented
+ * value is then y + φ^2 c.
+ *
+ * Assume that we start out with |y_i| <= 2^30. We start off by cutting
+ * off and reducing the carry c_15 from the topmost piece, y_15. This
+ * leaves 0 <= y_15 < 2^28; and we'll have |c_15| <= 4. We'll add this
+ * onto y_0 and y_8, and propagate the carries. It's very clear that we'll
+ * end up with |y + (φ + 1) c_15 - φ^2/2| << φ^2.
+ *
+ * Here, the y_i are signed, so we must be cautious about bithacking them.
+ */
+ c = ASR(piece, y[15], 28); y[15] = (upiece)y[15]&M28; y[8] += c;
+ for (i = 0; i < NPIECE; i++)
+ { y[i] += c; c = ASR(piece, y[i], 28); y[i] = (upiece)y[i]&M28; }
+
+ /* Now we have a slightly fiddly job to do. If c = +1, or if c = 0 and
+ * y >= p, then we should subtract p from the whole value; if c = -1 then
+ * we should add p; and otherwise we should do nothing.
+ *
+ * But conditional behaviour is bad, m'kay. So here's what we do instead.
+ *
+ * The first job is to sort out what we wanted to do. If c = -1 then we
+ * want to (a) invert the constant addend and (b) feed in a carry-in;
+ * otherwise, we don't.
+ */
+ m = SIGN(c)&M28;
+ d = m&1;
+
+ /* Now do the addition/subtraction. Remember that all of the y_i are
+ * nonnegative, so shifting and masking are safe and easy.
+ */
+ d += y[0] + (1 ^ m); yy[0] = d&M28; d >>= 28;
+ for (i = 1; i < 8; i++)
+ { d += y[i] + m; yy[i] = d&M28; d >>= 28; }
+ d += y[8] + (1 ^ m); yy[8] = d&M28; d >>= 28;
+ for (i = 9; i < 16; i++)
+ { d += y[i] + m; yy[i] = d&M28; d >>= 28; }
+
+ /* The final carry-out is in d; since we only did addition, and the y_i are
+ * nonnegative, then d is in { 0, 1 }. We want to keep y', rather than y,
+ * if (a) c /= 0 (in which case we know that the old value was
+ * unsatisfactory), or (b) if d = 1 (in which case, if c = 0, we know that
+ * the subtraction didn't cause a borrow, so we must be in the case where
+ * p <= y < φ^2.
+ */
+ m = NONZEROP(c) | ~NONZEROP(d - 1);
+ for (i = 0; i < NPIECE; i++) y[i] = (yy[i]&m) | (y[i]&~m);
+
+ /* Extract 32-bit words from the value. */
+ for (i = 0; i < 7; i++) {
+ u = ((y[i + 0] >> (4*i)) | ((uint32)y[i + 1] << (28 - 4*i)))&M32;
+ v = ((y[i + 8] >> (4*i)) | ((uint32)y[i + 9] << (28 - 4*i)))&M32;
+ STORE32_L(zv + 4*i, u);
+ STORE32_L(zv + 4*i + 28, v);
+ }
+}
+
+/* --- @fgoldi_set@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to write the result
+ * @int a@ = a small-ish constant
+ *
+ * Returns: ---
+ *
+ * Use: Sets @z@ to equal @a@.
+ */
+
+void fgoldi_set(fgoldi *x, int a)
+{
+ unsigned i;
+
+ x->P[0] = a;
+ for (i = 1; i < NPIECE; i++) x->P[i] = 0;
+}
+
+/*----- Basic arithmetic --------------------------------------------------*/
+
+/* --- @fgoldi_add@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the sum %$x + y$%.
+ */
+
+void fgoldi_add(fgoldi *z, const fgoldi *x, const fgoldi *y)
+{
+ unsigned i;
+ for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] + y->P[i];
+}
+
+/* --- @fgoldi_sub@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the difference %$x - y$%.
+ */
+
+void fgoldi_sub(fgoldi *z, const fgoldi *x, const fgoldi *y)
+{
+ unsigned i;
+ for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] - y->P[i];
+}
+
+/*----- Constant-time utilities -------------------------------------------*/
+
+/* --- @fgoldi_condswap@ --- *
+ *
+ * Arguments: @fgoldi *x, *y@ = two operands
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then
+ * exchange @x@ and @y@. If @m@ has some other value, then
+ * scramble @x@ and @y@ in an unhelpful way.
+ */
+
+void fgoldi_condswap(fgoldi *x, fgoldi *y, uint32 m)
+{
+ unsigned i;
+ mask32 mm = FIX_MASK32(m);
+
+ for (i = 0; i < NPIECE; i++) CONDSWAP(x->P[i], y->P[i], mm);
+}
+
+/*----- Multiplication ----------------------------------------------------*/
+
+/* Let B = 2^63 - 1 be the largest value such that +B and -B can be
+ * represented in a double-precision piece. On entry, it must be the case
+ * that |X_i| <= M <= B - 2^27 for some M. If this is the case, then, on
+ * exit, we will have |Z_i| <= 2^27 + M/2^27.
+ */
+#define CARRY_REDUCE(z, x) do { \
+ dblpiece _t[NPIECE], _c; \
+ unsigned _i; \
+ \
+ /* Bias the input pieces. This keeps the carries and so on centred \
+ * around zero rather than biased positive. \
+ */ \
+ for (_i = 0; _i < NPIECE; _i++) _t[_i] = (x)[_i] + B27; \
+ \
+ /* Calculate the reduced pieces. Careful with the bithacking. */ \
+ _c = ASR(dblpiece, _t[15], 28); \
+ (z)[0] = (dblpiece)((udblpiece)_t[0]&M28) - B27 + _c; \
+ for (_i = 1; _i < NPIECE; _i++) { \
+ (z)[_i] = (dblpiece)((udblpiece)_t[_i]&M28) - B27 + \
+ ASR(dblpiece, _t[_i - 1], 28); \
+ } \
+ (z)[8] += _c; \
+} while (0)
+
+/* --- @fgoldi_mulconst@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
+ * @const fgoldi *x@ = an operand
+ * @long a@ = a small-ish constant; %$|a| < 2^{20}$%.
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the product %$a x$%.
+ */
+
+void fgoldi_mulconst(fgoldi *z, const fgoldi *x, long a)
+{
+ unsigned i;
+ dblpiece zz[NPIECE], aa = a;
+
+ for (i = 0; i < NPIECE; i++) zz[i] = aa*x->P[i];
+ CARRY_REDUCE(z->P, zz);
+}
+
+/* --- @fgoldi_mul@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the product %$x y$%.
+ */
+
+void fgoldi_mul(fgoldi *z, const fgoldi *x, const fgoldi *y)
+{
+ dblpiece zz[NPIECE], u[NPIECE];
+ piece ab[NPIECE/2], cd[NPIECE/2];
+ const piece
+ *a = x->P + NPIECE/2, *b = x->P,
+ *c = y->P + NPIECE/2, *d = y->P;
+ unsigned i, j;
+
+# define M(x,i, y,j) ((dblpiece)(x)[i]*(y)[j])
+
+ /* Behold the magic.
+ *
+ * Write x = a φ + b, and y = c φ + d. Then x y = a c φ^2 +
+ * (a d + b c) φ + b d. Karatsuba and Ofman observed that a d + b c =
+ * (a + b) (c + d) - a c - b d, saving a multiplication, and Hamburg chose
+ * the prime p so that φ^2 = φ + 1. So
+ *
+ * x y = ((a + b) (c + d) - b d) φ + a c + b d
+ */
+
+ for (i = 0; i < NPIECE; i++) zz[i] = 0;
+
+ /* Our first job will be to calculate (1 - φ) b d, and write the result
+ * into z. As we do this, an interesting thing will happen. Write
+ * b d = u φ + v; then (1 - φ) b d = u φ + v - u φ^2 - v φ = (1 - φ) v - u.
+ * So, what we do is to write the product end-swapped and negated, and then
+ * we'll subtract the (negated, remember) high half from the low half.
+ */
+ for (i = 0; i < NPIECE/2; i++) {
+ for (j = 0; j < NPIECE/2 - i; j++)
+ zz[i + j + NPIECE/2] -= M(b,i, d,j);
+ for (; j < NPIECE/2; j++)
+ zz[i + j - NPIECE/2] -= M(b,i, d,j);
+ }
+ for (i = 0; i < NPIECE/2; i++)
+ zz[i] -= zz[i + NPIECE/2];
+
+ /* Next, we add on a c. There are no surprises here. */
+ for (i = 0; i < NPIECE/2; i++)
+ for (j = 0; j < NPIECE/2; j++)
+ zz[i + j] += M(a,i, c,j);
+
+ /* Now, calculate a + b and c + d. */
+ for (i = 0; i < NPIECE/2; i++)
+ { ab[i] = a[i] + b[i]; cd[i] = c[i] + d[i]; }
+
+ /* Finally (for the multiplication) we must add on (a + b) (c + d) φ.
+ * Write (a + b) (c + d) as u φ + v; then we actually want u φ^2 + v φ =
+ * v φ + (1 + φ) u. We'll store u in a temporary place and add it on
+ * twice.
+ */
+ for (i = 0; i < NPIECE; i++) u[i] = 0;
+ for (i = 0; i < NPIECE/2; i++) {
+ for (j = 0; j < NPIECE/2 - i; j++)
+ zz[i + j + NPIECE/2] += M(ab,i, cd,j);
+ for (; j < NPIECE/2; j++)
+ u[i + j - NPIECE/2] += M(ab,i, cd,j);
+ }
+ for (i = 0; i < NPIECE/2; i++)
+ { zz[i] += u[i]; zz[i + NPIECE/2] += u[i]; }
+
+#undef M
+
+ /* That wraps it up for the multiplication. Let's figure out some bounds.
+ * Fortunately, Karatsuba is a polynomial identity, so all of the pieces
+ * end up the way they'd be if we'd done the thing the easy way, which
+ * simplifies the analysis. Suppose we started with |x_i|, |y_i| <= 9/5
+ * 2^28. The overheads in the result are given by the coefficients of
+ *
+ * ((u^16 - 1)/(u - 1))^2 mod u^16 - u^8 - 1
+ *
+ * the greatest of which is 38. So |z_i| <= 38*81/25*2^56 < 2^63.
+ *
+ * Anyway, a round of `CARRY_REDUCE' will leave us with |z_i| < 2^27 +
+ * 2^36; and a second round will leave us with |z_i| < 2^27 + 512.
+ */
+ for (i = 0; i < 2; i++) CARRY_REDUCE(zz, zz);
+ for (i = 0; i < NPIECE; i++) z->P[i] = zz[i];
+}
+
+/* --- @fgoldi_sqr@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the square %$x^2$%.
+ */
+
+void fgoldi_sqr(fgoldi *z, const fgoldi *x)
+{
+
+ dblpiece zz[NPIECE], u[NPIECE];
+ piece ab[NPIECE];
+ const piece *a = x->P + NPIECE/2, *b = x->P;
+ unsigned i, j;
+
+# define M(x,i, y,j) ((dblpiece)(x)[i]*(y)[j])
+
+ /* The magic is basically the same as `fgoldi_mul' above. We write
+ * x = a φ + b and use Karatsuba and the special prime shape. This time,
+ * we have
+ *
+ * x^2 = ((a + b)^2 - b^2) φ + a^2 + b^2
+ */
+
+ for (i = 0; i < NPIECE; i++) zz[i] = 0;
+
+ /* Our first job will be to calculate (1 - φ) b^2, and write the result
+ * into z. Again, this interacts pleasantly with the prime shape.
+ */
+ for (i = 0; i < NPIECE/4; i++) {
+ zz[2*i + NPIECE/2] -= M(b,i, b,i);
+ for (j = i + 1; j < NPIECE/2 - i; j++)
+ zz[i + j + NPIECE/2] -= 2*M(b,i, b,j);
+ for (; j < NPIECE/2; j++)
+ zz[i + j - NPIECE/2] -= 2*M(b,i, b,j);
+ }
+ for (; i < NPIECE/2; i++) {
+ zz[2*i - NPIECE/2] -= M(b,i, b,i);
+ for (j = i + 1; j < NPIECE/2; j++)
+ zz[i + j - NPIECE/2] -= 2*M(b,i, b,j);
+ }
+ for (i = 0; i < NPIECE/2; i++)
+ zz[i] -= zz[i + NPIECE/2];
+
+ /* Next, we add on a^2. There are no surprises here. */
+ for (i = 0; i < NPIECE/2; i++) {
+ zz[2*i] += M(a,i, a,i);
+ for (j = i + 1; j < NPIECE/2; j++)
+ zz[i + j] += 2*M(a,i, a,j);
+ }
+
+ /* Now, calculate a + b. */
+ for (i = 0; i < NPIECE/2; i++)
+ ab[i] = a[i] + b[i];
+
+ /* Finally (for the multiplication) we must add on (a + b)^2 φ.
+ * Write (a + b)^2 as u φ + v; then we actually want (u + v) φ + u. We'll
+ * store u in a temporary place and add it on twice.
+ */
+ for (i = 0; i < NPIECE; i++) u[i] = 0;
+ for (i = 0; i < NPIECE/4; i++) {
+ zz[2*i + NPIECE/2] += M(ab,i, ab,i);
+ for (j = i + 1; j < NPIECE/2 - i; j++)
+ zz[i + j + NPIECE/2] += 2*M(ab,i, ab,j);
+ for (; j < NPIECE/2; j++)
+ u[i + j - NPIECE/2] += 2*M(ab,i, ab,j);
+ }
+ for (; i < NPIECE/2; i++) {
+ u[2*i - NPIECE/2] += M(ab,i, ab,i);
+ for (j = i + 1; j < NPIECE/2; j++)
+ u[i + j - NPIECE/2] += 2*M(ab,i, ab,j);
+ }
+ for (i = 0; i < NPIECE/2; i++)
+ { zz[i] += u[i]; zz[i + NPIECE/2] += u[i]; }
+
+#undef M
+
+ /* Finally, carrying. */
+ for (i = 0; i < 2; i++) CARRY_REDUCE(zz, zz);
+ for (i = 0; i < NPIECE; i++) z->P[i] = zz[i];
+}
+
+/*----- More advanced operations ------------------------------------------*/
+
+/* --- @fgoldi_inv@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
+ * @const fgoldi *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If
+ * %$x = 0$% then @z@ is set to zero. This is considered a
+ * feature.
+ */
+
+void fgoldi_inv(fgoldi *z, const fgoldi *x)
+{
+ fgoldi t, u;
+ unsigned i;
+
+#define SQRN(z, x, n) do { \
+ fgoldi_sqr((z), (x)); \
+ for (i = 1; i < (n); i++) fgoldi_sqr((z), (z)); \
+} while (0)
+
+ /* Calculate x^-1 = x^(p - 2) = x^(2^448 - 2^224 - 3), which also handles
+ * x = 0 as intended. The addition chain is home-made.
+ */ /* step | value */
+ fgoldi_sqr(&u, x); /* 1 | 2 */
+ fgoldi_mul(&t, &u, x); /* 2 | 3 */
+ SQRN(&u, &t, 2); /* 4 | 12 */
+ fgoldi_mul(&t, &u, &t); /* 5 | 15 */
+ SQRN(&u, &t, 4); /* 9 | 240 */
+ fgoldi_mul(&u, &u, &t); /* 10 | 255 = 2^8 - 1 */
+ SQRN(&u, &u, 4); /* 14 | 2^12 - 16 */
+ fgoldi_mul(&t, &u, &t); /* 15 | 2^12 - 1 */
+ SQRN(&u, &t, 12); /* 27 | 2^24 - 2^12 */
+ fgoldi_mul(&u, &u, &t); /* 28 | 2^24 - 1 */
+ SQRN(&u, &u, 12); /* 40 | 2^36 - 2^12 */
+ fgoldi_mul(&t, &u, &t); /* 41 | 2^36 - 1 */
+ fgoldi_sqr(&t, &t); /* 42 | 2^37 - 2 */
+ fgoldi_mul(&t, &t, x); /* 43 | 2^37 - 1 */
+ SQRN(&u, &t, 37); /* 80 | 2^74 - 2^37 */
+ fgoldi_mul(&u, &u, &t); /* 81 | 2^74 - 1 */
+ SQRN(&u, &u, 37); /* 118 | 2^111 - 2^37 */
+ fgoldi_mul(&t, &u, &t); /* 119 | 2^111 - 1 */
+ SQRN(&u, &t, 111); /* 230 | 2^222 - 2^111 */
+ fgoldi_mul(&t, &u, &t); /* 231 | 2^222 - 1 */
+ fgoldi_sqr(&u, &t); /* 232 | 2^223 - 2 */
+ fgoldi_mul(&u, &u, x); /* 233 | 2^223 - 1 */
+ SQRN(&u, &u, 223); /* 456 | 2^446 - 2^223 */
+ fgoldi_mul(&t, &u, &t); /* 457 | 2^446 - 2^222 - 1 */
+ SQRN(&t, &t, 2); /* 459 | 2^448 - 2^224 - 4 */
+ fgoldi_mul(z, &t, x); /* 460 | 2^448 - 2^224 - 3 */
+
+#undef SQRN
+}
+
+/*----- That's all, folks -------------------------------------------------*/
--- /dev/null
+/* -*-c-*-
+ *
+ * Arithmetic in the Goldilocks field GF(2^448 - 2^224 - 1)
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+#ifndef CATACOMB_FGOLDI_H
+#define CATACOMB_FGOLDI_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "fake-mLib-bits.h"
+
+#ifndef CATACOMB_QFARITH_H
+# include "qfarith.h"
+#endif
+
+/*----- Data structures ---------------------------------------------------*/
+
+typedef union {
+ int32 p28[16];
+} fgoldi;
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @fgoldi_load@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to store the result
+ * @const octet xv[56]@ = source to read
+ *
+ * Returns: ---
+ *
+ * Use: Reads an element of %$\gf{2^{448} - 2^{224} - 19}$% in
+ * external representation from @xv@ and stores it in @z@.
+ *
+ * External representation is little-endian base-256. Some
+ * elements have multiple encodings, which are not produced by
+ * correct software; use of noncanonical encodings is not an
+ * error, and toleration of them is considered a performance
+ * feature.
+ */
+
+extern void fgoldi_load(fgoldi */*z*/, const octet /*xv*/[56]);
+
+/* --- @fgoldi_store@ --- *
+ *
+ * Arguments: @octet zv[56]@ = where to write the result
+ * @const fgoldi *x@ = the field element to write
+ *
+ * Returns: ---
+ *
+ * Use: Stores a field element in the given octet vector in external
+ * representation. A canonical encoding is always stored.
+ */
+
+extern void fgoldi_store(octet /*zv*/[56], const fgoldi */*x*/);
+
+/* --- @fgoldi_set@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to write the result
+ * @int a@ = a small-ish constant
+ *
+ * Returns: ---
+ *
+ * Use: Sets @z@ to equal @a@.
+ */
+
+extern void fgoldi_set(fgoldi */*x*/, int /*a*/);
+
+/* --- @fgoldi_add@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the sum %$x + y$%.
+ */
+
+extern void fgoldi_add(fgoldi */*z*/,
+ const fgoldi */*x*/, const fgoldi */*y*/);
+
+/* --- @fgoldi_sub@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the difference %$x - y$%.
+ */
+
+extern void fgoldi_sub(fgoldi */*z*/,
+ const fgoldi */*x*/, const fgoldi */*y*/);
+
+/* --- @fgoldi_condswap@ --- *
+ *
+ * Arguments: @fgoldi *x, *y@ = two operands
+ * @uint32 m@ = a mask
+ *
+ * Returns: ---
+ *
+ * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then
+ * exchange @x@ and @y@. If @m@ has some other value, then
+ * scramble @x@ and @y@ in an unhelpful way.
+ */
+
+extern void fgoldi_condswap(fgoldi */*x*/, fgoldi */*y*/, uint32 /*m*/);
+
+/* --- @fgoldi_mulconst@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
+ * @const fgoldi *x@ = an operand
+ * @long a@ = a small-ish constant; %$|a| < 2^{20}$%.
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the product %$a x$%.
+ */
+
+extern void fgoldi_mulconst(fgoldi */*z*/, const fgoldi */*x*/, long /*a*/);
+
+/* --- @fgoldi_mul@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x, *y@ = two operands
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the product %$x y$%.
+ */
+
+extern void fgoldi_mul(fgoldi */*z*/,
+ const fgoldi */*x*/, const fgoldi */*y*/);
+
+/* --- @fgoldi_sqr@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Set @z@ to the square %$x^2$%.
+ */
+
+extern void fgoldi_sqr(fgoldi */*z*/, const fgoldi */*x*/);
+
+/* --- @fgoldi_inv@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
+ * @const fgoldi *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If
+ * %$x = 0$% then @z@ is set to zero. This is considered a
+ * feature.
+ */
+
+extern void fgoldi_inv(fgoldi */*z*/, const fgoldi */*x*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
--- /dev/null
+/* -*-c-*-
+ *
+ * Definitions for Montgomery's ladder
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+#ifndef CATACOMB_MONTLADDER_H
+#define CATACOMB_MONTLADDER_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Notes on the Montgomery ladder ------------------------------------*
+ *
+ * The algorithm here is Montgomery's famous binary ladder for calculating
+ * x-coordinates of scalar products on a particular shape of elliptic curve,
+ * as elucidated by Daniel Bernstein.
+ *
+ * Let Q = (x_1, y_1) be the base point, for some unknown y_1 (which will
+ * turn out to be unimportant). Define x_n, z_n by x(n Q) = (x_n : z_n).
+ * Given x_n, z_n, x_{n+1}, z_{n+1}, Montgomery's differential addition
+ * formulae calculate x_{2i}, z_{2i}, x_{2i+1}, z_{2i+1}. Furthermore,
+ * calculating x_{2i}, z_{2i} requires only x_n, z_n, and the calculation of
+ * x_{2i+1}, z_{2i+1} is symmetrical.
+ */
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* F designates a field, both naming the type of its elements and acting as a
+ * prefix for the standard field operations `F_add', `F_sub', `F_mul',
+ * `F_sqr', and `F_inv' (the last of which should return zero its own
+ * inverse); and the constant-time utility `F_condswap'.
+ *
+ * The macro calculates the x-coordinate of the product k Q, where Q is a
+ * point on the elliptic curve B y^2 = x^3 + A x^2 + x or its quadratic
+ * twist, for some irrelevant B. The x-coordinate of Q is given as X1 (a
+ * pointer to a field element). The scalar k is given as a vector of NK
+ * unsigned integers KW, each containing NBITS significant bits, with the
+ * least-significant element first. The result is written to the field
+ * element pointed to by Z.
+ *
+ * The curve coefficient A is given indirectly, as the name of a macro MULA0
+ * such that
+ *
+ * MULA0(z, x)
+ *
+ * will store in z the value (A - 2)/4 x.
+ */
+#define MONT_LADDER(f, mula0, kw, nk, nbits, z, x1) do { \
+ f _x, _z, _u, _w; \
+ f _t0, _t1, _t2, _t3, _t4; \
+ uint32 _m = 0, _mm = 0, _k; \
+ unsigned _i, _j; \
+ \
+ /* Initialize the main variables. We'll have, (x, z) and (u, w) \
+ * holding (x_n, z_n) and (x_{n+1}, z_{n+1}) in some order, but \
+ * there's some weirdness: if m = 0 then (x, z) = (x_n, z_n) and \
+ * (u, v) = (x_{n+1}, z_{n+1}); if m /= 0, then the pairs are \
+ * swapped over. \
+ * \
+ * Initially, we have (x_0, z_0) = (1, 0), representing the identity \
+ * at projective-infinity, which works fine; and we have z_1 = 1. \
+ */ \
+ _u = *(x1); f##_set(&_w, 1); f##_set(&_x, 1); f##_set(&_z, 0); \
+ \
+ /* The main ladder loop. Work through each bit of the clamped key. */ \
+ for (_i = (nk); _i--; ) { \
+ _k = (kw)[_i]; \
+ for (_j = 0; _j < (nbits); _j++) { \
+ /* We're at bit i of the scalar key (represented by 32 (7 - i) + \
+ * (31 - j) in our loop variables -- don't worry about that). \
+ * Let k = 2^i k_i + k'_i, with 0 <= k'_i < 2^i. In particular, \
+ * then, k_0 = k. Write Q(i) = (x_i, z_i). \
+ * \
+ * We currently have, in (x, z) and (u, w), Q(k_i) and Q(k_i + \
+ * 1), in some order. The ladder step will double the point in \
+ * (x, z), and leave the sum of (x : z) and (u : w) in (u, w). \
+ */ \
+ \
+ _mm = -((_k >> ((nbits) - 1))&1u); _k <<= 1; \
+ f##_condswap(&_x, &_u, _m ^ _mm); \
+ f##_condswap(&_z, &_w, _m ^ _mm); \
+ _m = _mm; \
+ \
+ f##_add(&_t0, &_x, &_z); /* x + z */ \
+ f##_sub(&_t1, &_x, &_z); /* x - z */ \
+ f##_add(&_t2, &_u, &_w); /* u + w */ \
+ f##_sub(&_t3, &_u, &_w); /* u - w */ \
+ f##_mul(&_t2, &_t2, &_t1); /* (x - z) (u + w) */ \
+ f##_mul(&_t3, &_t3, &_t0); /* (x + z) (u - w) */ \
+ f##_sqr(&_t0, &_t0); /* (x + z)^2 */ \
+ f##_sqr(&_t1, &_t1); /* (x - z)^2 */ \
+ f##_mul(&_x, &_t0, &_t1); /* (x + z)^2 (x - z)^2 */ \
+ f##_sub(&_t1, &_t0, &_t1); /* (x + z)^2 - (x - z)^2 */ \
+ mula0(&_t4, &_t1); /* A_0 ((x + z)^2 - (x - z)^2) */ \
+ f##_add(&_t0, &_t0, &_t4); /* A_0 ... + (x + z)^2 */ \
+ f##_mul(&_z, &_t0, &_t1); /* (...^2 - ...^2) (A_0 ... + ...) */ \
+ f##_add(&_t0, &_t2, &_t3); /* (x - z) (u + w) + (x + z) (u - w) */ \
+ f##_sub(&_t1, &_t2, &_t3); /* (x - z) (u + w) - (x + z) (u - w) */ \
+ f##_sqr(&_u, &_t0); /* (... + ...)^2 */ \
+ f##_sqr(&_t1, &_t1); /* (... - ...)^2 */ \
+ f##_mul(&_w, &_t1, (x1)); /* x_1 (... - ...)^2 */ \
+ } \
+ } \
+ \
+ /* Almost done. Undo the swap, if any. */ \
+ f##_condswap(&_x, &_u, _m); \
+ f##_condswap(&_z, &_w, _m); \
+ \
+ /* And convert to affine. */ \
+ f##_inv(&_t0, &_z); \
+ f##_mul((z), &_x, &_t0); \
+} while (0)
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
--- /dev/null
+/* -*-c-*-
+ *
+ * Utilities for quick field arithmetic
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+#ifndef CATACOMB_QFARITH_H
+#define CATACOMB_QFARITH_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#include <limits.h>
+
+#include "fake-mLib-bits.h"
+/*----- Signed integer types ----------------------------------------------*/
+
+typedef int32_t int32;
+typedef int64_t int64;
+#define HAVE_INT64 1
+
+/*----- General bit-hacking utilities -------------------------------------*/
+
+/* Individual bits, and masks for low bits. */
+#define BIT(n) (1ul << (n))
+#define MASK(n) (BIT(n) - 1)
+
+/* Arithmetic right shift. If X is a value of type TY, and N is a
+ * nonnegative integer, then return the value of X shifted right by N bits;
+ * alternatively, this is floor(X/2^N).
+ *
+ * GCC manages to compile this into a simple shift operation if one is
+ * available, but it's correct for all C targets.
+ */
+#define ASR(ty, x, n) (((x) - (ty)((u##ty)(x)&MASK(n)))/(ty)BIT(n))
+
+/*----- Constant-time utilities -------------------------------------------*/
+
+/* The following have better implementations on a two's complement target. */
+
+/* If we have two's complement arithmetic then masks are signed; this
+ * avoids a switch to unsigned representation, with the consequent problem
+ * of overflow when we convert back.
+ */
+typedef int32 mask32;
+
+/* Convert an unsigned mask M into a `mask32'. This is a hairy-looking
+ * no-op on many targets, but, given that we have two's complement
+ * integers, it is free of arithmetic overflow.
+ */
+#define FIX_MASK32(m) \
+ ((mask32)((m)&0x7fffffffu) + (-(mask32)0x7fffffff - 1)*(((m) >> 31)&1u))
+
+/* If Z is zero and M has its low 32 bits set, then copy (at least) the low
+ * 32 bits of X to Z; if M is zero, do nothing. Otherwise, scramble Z
+ * unhelpfully.
+ */
+#define CONDPICK(z, x, m) do { (z) |= (x)&(m); } while (0)
+
+/* If M has its low 32 bits set, then return (at least) the low 32 bits of
+ * X in Z; if M is zero, then return (at least) the low 32 bits of Y in Z.
+ * Otherwise, return an unhelful result.
+ */
+#define PICK2(x, y, m) (((x)&(m)) | ((y)&~(m)))
+
+/* If M has its low 32 bits set then swap (at least) the low 32 bits of X
+ * and Y; if M is zero, then do nothing. Otherwise, scramble X and Y
+ * unhelpfully.
+ */
+#define CONDSWAP(x, y, m) \
+ do { mask32 t_ = ((x) ^ (y))&(m); (x) ^= t_; (y) ^= t_; } while (0)
+
+/* Return zero if bit 31 of X is clear, or a mask with (at least) the low 32
+ * bits set if bit 31 of X is set.
+ */
+#define SIGN(x) (-(mask32)(((uint32)(x) >> 31)&1))
+
+/* Return zero if X is zero, or a mask with (at least) the low 32 bits set if
+ * X is nonzero.
+ */
+#define NONZEROP(x) SIGN((U32(x) >> 1) - U32(x))
+
+/*----- Debugging utilities -----------------------------------------------*/
+
+/* Define a debugging function DUMPFN, which will dump an integer represented
+ * modulo M. The integer is represented as a vector of NPIECE pieces of type
+ * PIECETY. The pieces are assembled at possibly irregular offsets: piece i
+ * logically has width PIECEWD(i), but may overhang the next piece. The
+ * pieces may be signed. GETMOD is an expression which calculates and
+ * returns the value of M, as an `mp *'.
+ *
+ * The generated function writes the value of such an integer X to the stream
+ * FP, labelled with the string WHAT.
+ *
+ * The definition assumes that <stdio.h>, <catacomb/mp.h>, and
+ * <catacomb/mptext.h> have been included.
+ */
+#define DEF_FDUMP(dumpfn, piecety, piecewd, npiece, noctet, getmod) \
+ static void dumpfn(FILE *fp, const char *what, const piecety *x) \
+ { \
+ mpw w; \
+ mp m, *y = MP_ZERO, *t = MP_NEW, *p; \
+ octet b[noctet]; \
+ unsigned i, o; \
+ \
+ p = getmod; \
+ mp_build(&m, &w, &w + 1); \
+ for (i = o = 0; i < npiece; i++) { \
+ if (x[i] >= 0) { w = x[i]; m.f &= ~MP_NEG; } \
+ else { w = -x[i]; m.f |= MP_NEG; } \
+ t = mp_lsl(t, &m, o); \
+ y = mp_add(y, y, t); \
+ o += piecewd(i); \
+ } \
+ \
+ fprintf(fp, "%s = <", what); \
+ for (i = 0; i < npiece; i++) { \
+ if (i) fputs(", ", fp); \
+ fprintf(fp, "%ld", (long)x[i]); \
+ } \
+ fputs(">\n\t= ", fp); \
+ mp_writefile(y, fp, 10); \
+ fputs("\n\t== ", fp); \
+ mp_div(0, &y, y, p); \
+ mp_writefile(y, fp, 10); \
+ fputs("\n\t= 0x", fp); \
+ mp_writefile(y, fp, 16); \
+ fputs(" (mod 2^255 - 19)\n\t= [", fp); \
+ mp_storel(y, b, sizeof(b)); \
+ for (i = 0; i < 32; i++) { \
+ if (i && !(i%4)) fputc(':', fp); \
+ fprintf(fp, "%02x", b[i]); \
+ } \
+ fputs("]\n", fp); \
+ mp_drop(y); mp_drop(p); mp_drop(t); \
+ }
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
--- /dev/null
+### Tests for X25519. -*-conf-*-
+### Extracted from Catacomb.
+
+###--------------------------------------------------------------------------
+test x25519
+
+## These are from Daniel J. Bernstein, `Cryptography in NaCl', 2009-03-10,
+## https://cr.yp.to/highspeed/naclcrypto-20090310.pdf
+## Make Alice's public key.
+x 77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a
+Y 0900000000000000000000000000000000000000000000000000000000000000
+Z 8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a
+
+## Make Bob's public key.
+x 5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb
+Y 0900000000000000000000000000000000000000000000000000000000000000
+Z de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f
+
+## Make the shared secret using Alice's private key.
+x 77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a
+Y de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f
+Z 4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742
+
+## Make the (same) shared secret using Bob's private key.
+x 5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb
+Y 8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a
+Z 4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742
+
+## These tests are from RFC7748. I've clamped the public values because
+## RFC7748 wants the top bits ignored.
+x a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4
+Y e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c
+Z c3da55379de9c6908e94ea4df28d084f32eccf03491c71f754b4075577a28552
+
+x 4b66e9d4d1b4673c5ad22691957d6af5c11b6421e0ea01d42ca4169e7918ba0d
+Y e5210f12786811d3f4b7959d0538ae2c31dbe7106fc03c3efc4cd549c715a413
+Z 95cbde9476e8907d7aade45cb4b873f88b595a68799fa152e6f8f7647aac7957
+
+###--------------------------------------------------------------------------
+test x25519-mct
+
+## These tests are from RFC7748.
+x 0900000000000000000000000000000000000000000000000000000000000000
+Y 0900000000000000000000000000000000000000000000000000000000000000
+n 1
+Z 422c8e7a6227d7bca1350b3e2bb7279f7897b87bb6854b783c60e80311ae3079
+
+x 0900000000000000000000000000000000000000000000000000000000000000
+Y 0900000000000000000000000000000000000000000000000000000000000000
+n 1000
+Z 684cf59ba83309552800ef566f2f4d3c1c3887c49360e3875f2eb94d99532c51
+
+## This one takes aaaaages.
+## 0900000000000000000000000000000000000000000000000000000000000000
+## 0900000000000000000000000000000000000000000000000000000000000000
+## 1000000 7c3911e0ab2586fd864497297e575e6f3bc601c0883c30df5f4dd2d24f665424;
--- /dev/null
+/* -*-c-*-
+ *
+ * The X25519 key-agreement algorithm
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "fake-mLib-bits.h"
+
+#include "montladder.h"
+#include "f25519.h"
+#include "x25519.h"
+
+/*----- Important constants -----------------------------------------------*/
+
+const octet x25519_base[32] = { 9, 0, /* ... */ };
+
+#define A0 121665
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @x25519@ --- *
+ *
+ * Arguments: @octet zz[X25519_OUTSZ]@ = where to put the result
+ * @const octet k[X25519_KEYSZ]@ = pointer to private key
+ * @const octet qx[X25519_PUBSZ]@ = pointer to public value
+ *
+ * Returns: ---
+ *
+ * Use: Calculates X25519 of @k@ and @qx@.
+ *
+ * Note that there is disagreement over whether the most
+ * significant bit of @qx@ (i.e., the value @qx[31]&0x80@)
+ * should be ignored or counted towards the represented value.
+ * Historically implementations respected the bit; later
+ * convention seems to be to ignore it. This implementation
+ * honours the bit: a caller who wants to ignore the bit can
+ * easily clear it, while caller who wants to respect it has a
+ * difficult job if this function ignores it.
+ */
+
+void x25519(octet zz[X25519_OUTSZ],
+ const octet k[X25519_KEYSZ],
+ const octet qx[X25519_PUBSZ])
+{
+ uint32 kw[8];
+ f25519 x1;
+
+ /* Load and clamp the key. The low bits are cleared to kill the small
+ * subgroups on the curve and its twist, and a high bit is set to guard
+ * against careless implementations, though this isn't one of those.
+ */
+ kw[0] = LOAD32_L(k + 0); kw[1] = LOAD32_L(k + 4);
+ kw[2] = LOAD32_L(k + 8); kw[3] = LOAD32_L(k + 12);
+ kw[4] = LOAD32_L(k + 16); kw[5] = LOAD32_L(k + 20);
+ kw[6] = LOAD32_L(k + 24); kw[7] = LOAD32_L(k + 28);
+ kw[0] &= 0xfffffff8; kw[7] = (kw[7]&0x3fffffff) | 0x40000000;
+
+ /* And run the ladder. */
+ f25519_load(&x1, qx);
+#define MULA0(z, x) do { f25519_mulconst((z), (x), A0); } while (0)
+ MONT_LADDER(f25519, MULA0, kw, 8, 32, &x1, &x1);
+#undef MULA0
+ f25519_store(zz, &x1);
+}
+
+/*----- That's all, folks -------------------------------------------------*/
--- /dev/null
+/* -*-c-*-
+ *
+ * The X25519 key-agreement algorithm
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+#ifndef CATACOMB_X25519_H
+#define CATACOMB_X25519_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Notes on the X25519 key-agreement algorithm -----------------------*
+ *
+ * This is X25519, as described in Daniel J. Bernstein, `Curve25519: new
+ * Diffie--Hellman speed records', PKC 2006,
+ * https://cr.yp.to/ecdh/curve25519-20060209.pdf
+ *
+ * Since then, the name `Curve25519' has shifted somewhat, to refer to the
+ * specific elliptic curve used, and the x-coordinate Diffie--Hellman
+ * operation is now named `X25519'.
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "fake-mLib-bits.h"
+
+/*----- Important constants -----------------------------------------------*/
+
+#define X25519_KEYSZ 32u
+#define X25519_PUBSZ 32u
+#define X25519_OUTSZ 32u
+
+extern const octet x25519_base[32];
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @x25519@ --- *
+ *
+ * Arguments: @octet zz[X25519_OUTSZ]@ = where to put the result
+ * @const octet k[X25519_KEYSZ]@ = pointer to private key
+ * @const octet qx[X25519_PUBSZ]@ = pointer to public value
+ *
+ * Returns: ---
+ *
+ * Use: Calculates X25519 of @k@ and @qx@.
+ *
+ * Note that there is disagreement over whether the most
+ * significant bit of @qx@ (i.e., the value @qx[31]&0x80@)
+ * should be ignored or counted towards the represented value.
+ * Historically implementations respected the bit; later
+ * convention seems to be to ignore it. This implementation
+ * honours the bit: a caller who wants to ignore the bit can
+ * easily clear it, while caller who wants to respect it has a
+ * difficult job if this function ignores it.
+ */
+
+extern void x25519(octet /*zz*/[X25519_OUTSZ],
+ const octet /*k*/[X25519_KEYSZ],
+ const octet /*qx*/[X25519_PUBSZ]);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
--- /dev/null
+### Tests for X448. -*-conf-*-
+### Extracted from Catacomb.
+
+###--------------------------------------------------------------------------
+test x448
+
+## These are taken from RFC7748.
+x 3d262fddf9ec8e88495266fea19a34d28882acef045104d0d1aae121700a779c984c24f8cdd78fbff44943eba368f54b29259a4f1c600ad3
+Y 06fce640fa3487bfda5f6cf2d5263f8aad88334cbd07437f020f08f9814dc031ddbdc38c19c6da2583fa5429db94ada18aa7a7fb4ef8a086
+Z ce3e4ff95a60dc6697da1db1d85e6afbdf79b50a2412d7546d5f239fe14fbaadeb445fc66a01b0779d98223961111e21766282f73dd96b6f
+
+x 203d494428b8399352665ddca42f9de8fef600908e0d461cb021f8c538345dd77c3e4806e25f46d3315c44e0a5b4371282dd2c8d5be3095f
+Y 0fbcc2f993cd56d3305b0b7d9e55d4c1a8fb5dbb52f8e9a1e9b6201b165d015894e56c4d3570bee52fe205e28a78b91cdfbde71ce8d157db
+Z 884a02576239ff7a2f2f63b2db6a9ff37047ac13568e1e30fe63c4a7ad1b3ee3a5700df34321d62077e63633c575c1c954514e99da7c179d
+
+x 9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b
+Y 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+Z 9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0
+
+x 1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d
+Y 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+Z 3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b43027d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609
+
+x 9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b
+Y 3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b43027d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609
+Z 07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d
+
+x 1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d
+Y 9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0
+Z 07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d
+
+###--------------------------------------------------------------------------
+test x448-mct
+
+## These are taken from RFC7748.
+x 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+Y 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+n 1
+Z 3f482c8a9f19b01e6c46ee9711d9dc14fd4bf67af30765c2ae2b846a4d23a8cd0db897086239492caf350b51f833868b9bc2b3bca9cf4113
+
+x 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+Y 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+n 1000
+Z aa3b4749d55b9daf1e5b00288826c467274ce3ebbdd5c17b975e09d4af6c67cf10d087202db88286e2b79fceea3ec353ef54faa26e219f38
+
+## This one takes aaaaages.
+## 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+## 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+## 1000000 077f453681caca3693198420bbe515cae0002472519b3e67661a7e89cab94695c8f4bcd66e61b9b9c946da8d524de3d69bd9d9d66b997e37;
--- /dev/null
+/* -*-c-*-
+ *
+ * The X448 key-agreement algorithm
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "fake-mLib-bits.h"
+
+#include "montladder.h"
+#include "fgoldi.h"
+#include "x448.h"
+
+/*----- Important constants -----------------------------------------------*/
+
+const octet x448_base[56] = { 5, 0, /* ... */ };
+
+#define A0 39081
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @x448@ --- *
+ *
+ * Arguments: @octet zz[X448_OUTSZ]@ = where to put the result
+ * @const octet k[X448_KEYSZ]@ = pointer to private key
+ * @const octet qx[X448_PUBSZ]@ = pointer to public value
+ *
+ * Returns: ---
+ *
+ * Use: Calculates X448 of @k@ and @qx@.
+ */
+
+void x448(octet zz[X448_OUTSZ],
+ const octet k[X448_KEYSZ],
+ const octet qx[X448_PUBSZ])
+{
+ uint32 kw[14];
+ fgoldi x1;
+ unsigned i;
+
+ /* Load and clamp the key. The low bits are cleared to kill the small
+ * subgroups on the curve and its twist, and a high bit is set to guard
+ * against careless implementations, though this isn't one of those.
+ */
+ for (i = 0; i < 14; i++) kw[i] = LOAD32_L(k + 4*i);
+ kw[0] &= 0xfffffffc; kw[13] |= 0x80000000;
+
+ /* And run the ladder. */
+ fgoldi_load(&x1, qx);
+#define MULA0(z, x) do { fgoldi_mulconst((z), (x), A0); } while (0)
+ MONT_LADDER(fgoldi, MULA0, kw, 14, 32, &x1, &x1);
+#undef MULA0
+ fgoldi_store(zz, &x1);
+}
+
+/*----- That's all, folks -------------------------------------------------*/
--- /dev/null
+/* -*-c-*-
+ *
+ * The X448 key-agreement algorithm
+ *
+ * (c) 2017 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+#ifndef CATACOMB_X448_H
+#define CATACOMB_X448_H
+
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+/*----- Notes on the X448 key-agreement algorithm -------------------------*
+ *
+ * This is X448, as described in RFC7748, based on the elliptic curve defined
+ * in Mike Hamburg, `Ed448-Goldilocks, a new elliptic curve', EUROCRYPT 2016,
+ * https://eprint.iacr.org/2015/625/.
+ *
+ * The RFC-specified operation is simpler than the Diffie--Hellman function
+ * described in Hamburg's paper, since it doesn't involve the `Decaf'
+ * cofactor elimination procedure. Indeed, it looks very much like X25519
+ * with Hamburg's curve slotted in in place of Bernstein's.
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "fake-mLib-bits.h"
+
+/*----- Important constants -----------------------------------------------*/
+
+#define X448_KEYSZ 56
+#define X448_PUBSZ 56
+#define X448_OUTSZ 56
+
+extern const octet x448_base[56];
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @x448@ --- *
+ *
+ * Arguments: @octet zz[X448_OUTSZ]@ = where to put the result
+ * @const octet k[X448_KEYSZ]@ = pointer to private key
+ * @const octet qx[X448_PUBSZ]@ = pointer to public value
+ *
+ * Returns: ---
+ *
+ * Use: Calculates X448 of @k@ and @qx@.
+ */
+
+extern void x448(octet /*zz*/[X448_OUTSZ],
+ const octet /*k*/[X448_KEYSZ],
+ const octet /*qx*/[X448_PUBSZ]);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
~mdw / secnet / commitdiff