libcrypto/bn/bn_gcd.c

/*	$OpenBSD: bn_gcd.c,v 1.3 2023/04/07 17:09:54 tb Exp $ */

/*
 * Copyright (c) 2023 Theo Buehler <tb@openbsd.org>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

#include <err.h>
#include <stdio.h>
#include <string.h>

#include <openssl/bn.h>
#include <openssl/err.h>

int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int BN_gcd_ct(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);

static const struct gcd_test_fn {
	const char *name;
	int (*fn)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
	int fails_on_zero;
} gcd_fn[] = {
	{
		.name = "BN_gcd",
		.fn = BN_gcd,
	},
	{
		.name = "BN_gcd_ct",
		.fn = BN_gcd_ct,
		.fails_on_zero = 1,
	},
};

#define N_GCD_FN (sizeof(gcd_fn) / sizeof(gcd_fn[0]))

static const struct gcd_test {
	const char *a;
	const char *b;
	const char *r;
} bn_gcd_tests[] = {
	{
		.a = "0",
		.b = "0",
		.r = "0",
	},
	{
		.a = "1",
		.b = "1",
		.r = "1",
	},
	{
		.a = "1",
		.b = "0",
		.r = "1",
	},
	{
		.a = "0",
		.b = "1",
		.r = "1",
	},
	{
		.a = "57",
		.b = "0",
		.r = "57",
	},
	{
		.a = "0",
		.b = "57",
		.r = "57",
	},

	/*
	 * The following test cases were randomly generated.
	 */

	{
		.a = "255",
		.b = "278d3",
		.r = "3",
	},
	{
		.a = "6a54d",
		.b = "619",
		.r = "7",
	},
	{
		.a = "e9",
		.b = "e695",
		.r = "1",
	},
	{
		.a = "3f3a9",
		.b = "41f",
		.r = "5",
	},
	{
		.a = "643",
		.b = "5bff1",
		.r = "7",
	},
	{
		.a = "2bb",
		.b = "29be3",
		.r = "3",
	},
	{
		.a = "49e",
		.b = "5770e",
		.r = "6",
	},
	{
		.a = "f1d5",
		.b = "fb",
		.r = "1",
	},
	{
		.a = "250eb50",
		.b = "206b0",
		.r = "2b0",
	},
	{
		.a = "57ad2",
		.b = "64927d6",
		.r = "6a6",
	},
	{
		.a = "430bc",
		.b = "48757a4",
		.r = "564",
	},
	{
		.a = "7593a8c",
		.b = "7161c",
		.r = "7ec",
	},
	{
		.a = "5771161",
		.b = "53d9b",
		.r = "5e9",
	},
	{
		.a = "4132d82",
		.b = "37b1e",
		.r = "49e",
	},
	{
		.a = "72492b0",
		.b = "65f90",
		.r = "730",
	},
	{
		.a = "14bab",
		.b = "163605b",
		.r = "1af",
	},
	{
		.a = "602d952bd",
		.b = "5a08833",
		.r = "62ebb",
	},
	{
		.a = "698bf2b",
		.b = "65849195f",
		.r = "701db",
	},
	{
		.a = "37d4a5f",
		.b = "402dcce6f",
		.r = "488d3",
	},
	{
		.a = "614e922",
		.b = "6644a8e72",
		.r = "6cc7a",
	},
	{
		.a = "1eea0a75c",
		.b = "1ea5c64",
		.r = "21ac4",
	},
	{
		.a = "6136d54",
		.b = "6acfd5d8c",
		.r = "7e544",
	},
	{
		.a = "2bba7aaf2",
		.b = "33894f6",
		.r = "34902",
	},
	{
		.a = "467c1e94",
		.b = "3c036c",
		.r = "4d34",
	},
	{
		.a = "19c3fcfc5",
		.b = "15f969b26a7",
		.r = "1b9928b",
	},
	{
		.a = "145666d9a",
		.b = "13bbb7f3bb6",
		.r = "159a73a",
	},
	{
		.a = "1b0c38f9e",
		.b = "18765759b3e",
		.r = "1f0ce22",
	},
	{
		.a = "784064e87",
		.b = "667b4b1bc85",
		.r = "7fbc6f7",
	},
	{
		.a = "498054afdd3",
		.b = "44d269073",
		.r = "596efd7",
	},
	{
		.a = "198ba337af6",
		.b = "1f5755eca",
		.r = "214ab6a",
	},
	{
		.a = "5effbed2b",
		.b = "6a7cdb539bd",
		.r = "7b7352f",
	},
	{
		.a = "14388cf1265",
		.b = "153338971",
		.r = "174af49",
	},
	{
		.a = "2d4aff46122f30851a52b",
		.b = "2edb8fdd14ab1b645",
		.r = "332805d24fd69",
	},
	{
		.a = "43733ea897495e14339f9",
		.b = "3e843370070058d8d",
		.r = "49977f36263b5",
	},
	{
		.a = "58aafd7662b8de019",
		.b = "5538bdda74849754e4949",
		.r = "5daa7b4439b0f",
	},
	{
		.a = "474100872e962de8b0596",
		.b = "45223dbbeaaba9e92",
		.r = "580218df81b62",
	},
	{
		.a = "307c55bb52be32b4d",
		.b = "2cc525ce8e2d2bc67aa6d",
		.r = "30c17810923d9",
	},
	{
		.a = "4a2a6504adf43e733",
		.b = "497c44b84fb6f8774f787",
		.r = "5ea902856aae1",
	},
	{
		.a = "5b8e523f7c7b60972",
		.b = "4aebe8c99000a8bd30652",
		.r = "63b8fd8af9062",
	},
	{
		.a = "53a047f3c3f81986811d7",
		.b = "53b004a9fa740fcbb",
		.r = "64d12a952833b",
	},
	{
		.a = "6f177c61fa6afe2d209",
		.b = "670a0a35553c35d52fb18f5",
		.r = "74c624a8a32333b",
	},
	{
		.a = "5343fd2374414df3034",
		.b = "507c3e327a45f92c78eeb84",
		.r = "5974af2eca1fe94",
	},
	{
		.a = "4a07f6267329d80c7d4bdfa",
		.b = "56a012dd8379b7a0e16",
		.r = "59052131189608e",
	},
	{
		.a = "63bba164fd337e80d0c",
		.b = "615a76fb66b1094efbcba2c",
		.r = "735585f95d70274",
	},
	{
		.a = "2453ea8b7fca0284b883078",
		.b = "234099d522bcad7e248",
		.r = "2d69bd4f4b8d088",
	},
	{
		.a = "61b5dc7806b84d2b08c",
		.b = "58b8dde9e5f8ecfde43cd74",
		.r = "75ff164a01eaa7c",
	},
	{
		.a = "3816984948c1e79f882",
		.b = "3b5b01106809f6bb2e2e016",
		.r = "48170e737316bca",
	},
	{
		.a = "41b4deb320e45f566b",
		.b = "4874dbcc44f53775a6a1d7",
		.r = "4977a5459131df",
	},
	{
		.a = "364580a30652080c07c9dc48",
		.b = "2e1c73c5131cbbf50628",
		.r = "36825feeccb49b58",
	},
	{
		.a = "695d74ad760a5795570a3",
		.b = "62bc190742c20aa29644c84eb",
		.r = "6abcf0da95d5be6f7",
	},
	{
		.a = "74db3db1ab6c202baff804bcd",
		.b = "6380a7b03658ba56b34a3",
		.r = "756f230199f1529ab",
	},
	{
		.a = "4b26c75874a09700b9d512ed8",
		.b = "4ca3361909906b0cf7618",
		.r = "53055ca37fd154698",
	},
	{
		.a = "1f81faea97f44cd5c6adb457d",
		.b = "22c452983db5a6ce9736f",
		.r = "241a04dc3e4719c37",
	},
	{
		.a = "95e5584090df556539aa9fd9",
		.b = "b02f19eec1f1f2d44c59",
		.r = "c5c889564b7e8bab",
	},
	{
		.a = "4a908939e089498a7feab",
		.b = "60045b573dccb74a9e2e379d5",
		.r = "6116326ef394c59e7",
	},
	{
		.a = "39443c6a7d6bd95529a12",
		.b = "409e977e693f5bd1b17b0433a",
		.r = "49802f618e94d218a",
	},
	{
		.a = "3e6fc6cf9eaba3e94f24f03",
		.b = "345aa9ded17c65a6c85dd7e6d61",
		.r = "3ea3e52d4d5d024c389",
	},
	{
		.a = "64f62375ce39484ec7e85f4e3d",
		.b = "69459ea484d6480a376e91",
		.r = "748b7824736c5c39e5",
	},
	{
		.a = "4186cead307cad31530dd205a39",
		.b = "4f5ee69f4afbb46507ccc8b",
		.r = "533aef3d540410a6b2b",
	},
	{
		.a = "536b816e2daa705e44bae82",
		.b = "4e8a14632ccec82f41941b1fd7e",
		.r = "5bf87a677ef2ec1bd76",
	},
	{
		.a = "6518022e9b5920c69de925",
		.b = "6d90bcb3174b93f44a2854f601",
		.r = "7cc47ec91e90d61599",
	},
	{
		.a = "2f443ac559d746b4b8f87c802af",
		.b = "2ef35b22f59380207cd3a09",
		.r = "33f82dc6aa168711c2f",
	},
	{
		.a = "17418a08c177e039b1e5000",
		.b = "183bf7b0342fe483457340ab000",
		.r = "1da412c88f3a0c3f000",
	},
	{
		.a = "77685efaa0d4e6a25268eaa07",
		.b = "65b89e487f7a272f6187b",
		.r = "80861458bce7097f7",
	},
	{
		.a = "1488a0aab5415ee1ce826ecb38f7b33",
		.b = "131c43cca73843a27b9feac46cd03d5de7a2f",
		.r = "17b3a3001f3660377791cd8cf",
	},
	{
		.a = "5349d29af82e6b8fae6c25859fadec6207032",
		.b = "64d277bfb253b9a22f3c0187445253a",
		.r = "6573b739e39b0650a9c2c2f02",
	},
	{
		.a = "21df6046ab805b9f71a304d34236fe8",
		.b = "1fe085864e8e75ea073efebfe6fbab133e4e8",
		.r = "23e3d1525042d237154d245f8",
	},
	{
		.a = "56454c66089738f7074ce55236dce53b22a11",
		.b = "5d5308342f5a0c2277762ba37273f07",
		.r = "71fb0beacaae6adab73b8cfbb",
	},
	{
		.a = "25e20fcd81385c099f1db654feba9b1",
		.b = "2134ea8527e2ad47f460d70b918ba69fd4c6b",
		.r = "268d03475633df8adccd7eda9",
	},
	{
		.a = "6713eb612dab2940e2741150dfa203f632d5f",
		.b = "611184b794056ec03b0aeb7c1646be9",
		.r = "752472cea4fe17a0cc5881d23",
	},
	{
		.a = "39a3fe02e4f8cb7cfc972275862512c6e863c",
		.b = "356731db8ae0f405b01423d24a00df4",
		.r = "4230cc0ff4cb762463e8f45a4",
	},
	{
		.a = "48c66d2a5a9f354fbe6a24379b3c868",
		.b = "3d52dfc550d9288335bc4ca727d0008e225d8",
		.r = "4e38e92332937fe6d87b9e888",
	},
	{
		.a = "30de4f96ec186d1f64298c5ae4510f448",
		.b = "30cbcdb08d24818e2845286f4b70760116f96e8",
		.r = "32f5f8996bc47879755ea626348",
	},
	{
		.a = "4e3cbdc0d866680fd0cf79732b914033c",
		.b = "4c0fc242dbe2f4ba5592ffc621eca68499e807c",
		.r = "556fcff7e03458aba9b3229def4",
	},
	{
		.a = "4f902e3c221d879daae7536c66d0d1e0a",
		.b = "4e2451f07d9559f3c36746cef62cb2ce95525de",
		.r = "5be6e06842ff90445f2d002fdce",
	},
	{
		.a = "1ec50fe3ba8edcdd47cecf6b1e67d2263bee334",
		.b = "20eb4fa3aabacd28aa5126fa29425be14",
		.r = "244d6242059f13924023015b8bc",
	},
	{
		.a = "f85a29486c90172f2fcb0e8f2b9cc357235f8",
		.b = "d988a3b4b5b168ed7ebe15381da5818",
		.r = "fdfee673f1bde9585970c65b8",
	},
	{
		.a = "60ff4616bccb386ab1c8c4fd663afd554f8d8cc",
		.b = "5e4e6ea5e8217e17f69c63ea07d8e93bc",
		.r = "780275e6eaa0fe4bf87a78c9974",
	},
	{
		.a = "1ba4b71fa06394748ad36489d8a1232de12d6f0",
		.b = "1da078788fa13e18814edbf15907ef930",
		.r = "235f9d5de3c2a7b93122d930ad0",
	},
	{
		.a = "3b09f70af16cc8c40573bfffb63750b2c",
		.b = "3d4c9928047325884f90888dee2d64f64dca29c",
		.r = "3fc1e8665f4df4243c2062b6d0c",
	},
	{
		.a = "4d3079fb7639d1e7fdab98015c21c782c4c2b7878",
		.b = "3dfed750b07e2be9e32d2627c31a0a1e3c8",
		.r = "500cd222944614585265eb9f9e958",
	},
	{
		.a = "536e6614ee85be4cba997bceeacd5d87db",
		.b = "48a13d2d2df5788977b9e8ecd434cba45fe3ee1b",
		.r = "549a3e0100b99d244e7f85384439",
	},
	{
		.a = "1d83beadd7fe8d557ee9985f3d4c47b9144",
		.b = "22be84a3090cce29b0b666a7cb049f9ba808cb494",
		.r = "25d4b9fb71a6f79ff05eeabfbd454",
	},
	{
		.a = "5b5bc6dc131ab9f1f765c976c96852f5cb024d121",
		.b = "4c8375dd9a13a1c7d31f2c3fc87dd070075",
		.r = "5ec3c5e03869f4dd4372d274fb553",
	},
	{
		.a = "220220e66a4abb06681151d2a9cdf0d30a0",
		.b = "26002cab182d2500064e1c19184707b9e8ba673e0",
		.r = "2633ad7265ae0db8b891f4459eee0",
	},
	{
		.a = "1e2ff1ff6bd8bee4b18ff6fc09e2b4a82e6",
		.b = "207e14815ccc0a2f5cf3903d7e2bf754356c65676",
		.r = "239e193c1bc65766c6b580dcddcc2",
	},
	{
		.a = "26b7793830e334ac155cc8d480f2f3a6de4",
		.b = "27a0ce62b6c85cd1566cdc532b5b1e322e52996cc",
		.r = "297defac305c3a2f2154541ef1dc4",
	},
	{
		.a = "50fda952177aa819c4042847414f2d2d14e",
		.b = "45255a9ae2fd394ed8b760ce3133fb71f94362a86",
		.r = "56aae2037820936b47d6a9cf771fa",
	},
	{
		.a = "5acedf307d7016ffd7380015df422691ebbf7d97e91",
		.b = "53c6266c3e6520cc40abc70370ad94e8a629d",
		.r = "686ec3910fdac81085a738d1d4799d3",
	},
	{
		.a = "584f15ec6c7e7bfa4ba24e1780fde1511fe12",
		.b = "575a78c8e8bb4f02e57efb0010d86b4a408f150fe7e",
		.r = "6317a26e7ae3218b60d8ef6cfa64186",
	},
	{
		.a = "f617d44caf7dc67791e20feac2c1c27e655f",
		.b = "11542c315141d0c46bae8863c1a945963b91b644603",
		.r = "12f20af110dee02b9bbde9c9431ef47",
	},
	{
		.a = "54538d3df7d85581e923e44291cae3aa3a3fcd20cc5",
		.b = "67eef9400e79570ce246df916892707014bbb",
		.r = "6a00b7b006c767a710fdd8b7652cacd",
	},
	{
		.a = "1d567e0e5af1b4994bd82baf9c601d188107d",
		.b = "1dae559a89e7e21212345a8148689c33da8d28f3fc9",
		.r = "1f41fa99ba8e144971e741732e76cc1",
	},
	{
		.a = "2c3172df78361b326b2c1f83749d1b9e42672",
		.b = "2ff4be223d91f31e03e07fee0c18e082f970191a41a",
		.r = "3693dd9f37613c4a7de1d831f44dd26",
	},
	{
		.a = "32e11a127828647a88f8f7b6d48f475e8e71eda585b",
		.b = "2ddf9f7e0f870347401ce5d93ff70a5a3a9cb",
		.r = "3a4156da31ca81617974669400e3629",
	},
	{
		.a = "47f54df57b2d124be53c0c6603700e8f69829238b49",
		.b = "489167e7ed18db6d541c8a94cf6a58f10836d",
		.r = "5ca417bb8cb42fefd91fd832a89bdb7",
	},
	{
		.a = "8963a8cf862bfeda36412dea185c6984c3acf3b22204",
		.b = "8035daf441d2a728b3dbded074c57e103e58ad65efaf5fe3"
		     "b23c",
		.r = "a7cbf319f110484e28a631c8425609ed72ec",
	},
	{
		.a = "40f583721493abb5ead342942d9e142ce51f7251ecb6a333"
		     "c0888",
		.b = "4cce4f3aff6019192f7e32c372c9e32385b2352d32518",
		.r = "52d94814b2149c815d82619dc02750648e558",
	},
	{
		.a = "34a08b5c152b6bda536ab231199c5de7d8e96ad8814f3",
		.b = "328d23516a0bacc130bcbb9b95965ffdd99827c49f306a6c"
		     "06983",
		.r = "431ef899d79eb5aff9b6aa3759bca625f1317",
	},
	{
		.a = "4765f462b4167b25df009c3d0d710d707dc4e8a990e81",
		.b = "5495c974f06f6f2cf98d285af77a76be3ef32eab77ca815b"
		     "a2031",
		.r = "58ab78d483cc486014fb6ea972c22f7ab7b5d",
	},
	{
		.a = "44ad54c2afc1aeac7ec3511d847cbbee8902ec2ede784",
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		     "010271ac23a1e3beaa6bbe99d4b0123172315084fcf38bb8"
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		     "c0e7b6ecbfecd7df5025aca3ff20424029a0be85400b17a0"
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		     "871540ffbed0a5c71228c9af0",
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		     "233fbcdfcc39d33d381dd2aa085d1213b543264757e01f43"
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		     "4b1807725401d82353e90e44dcefb7d485e7c0e0e8761ddc"
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		     "9",
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		     "8b2c79d15d0f7b83e6c002c8ab93319a004752b9ae65edbb"
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		     "dfade4850b027c4e29361acf1fe",
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		     "9bd301eb085239e0bb81d27a0930f67d31da8e0800fe00c3"
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		     "c03926debba4c1832cec97b05ecd3d1810c7249d15a82dbc"
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		     "1018dfe3754088d6698ef224d63545c0605abf884e979f6d"
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		     "6c4cf6febca1e8164c4244af2def72c61c73b7ee84d2668e"
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		     "9787ade90ce668230fc79d8c9ee37ac58b4ec70d09b2d96a"
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		     "29a251dd0f4709ea1823566ae73218ee7134bfb2dc4f4d71"
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		     "53bc5297b5a9110b104b7785b3ae44efc4bc1f188dec1081"
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		     "dd99708e29f6929c63c7403cdd665b055f066e7a32d27cb9"
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		     "ad423d8a568cf53b8295f18445d5659bdca6546b3bf486d0"
		     "742",
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		     "4c498c7b7c21635da7dd9c6bb1b6c2ca7a1a9a9f8cccad9f"
		     "df7e9692298db418bdce2d0a0b2eef85b0a8bf2e669443e1"
		     "977",
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		     "06f8525bb254618d0f9fb5a7d7b6896118f084ee67e904eb"
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		     "1927ceabf03a4a19f97102ac81607b8448d74ea340017b4f"
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		     "d2f562b4a37f6cf500e67d5d680bff68cf0aa456269c99e5"
		     "92a10b713eb3a2d160f2fc3ad1b66a99e60c441671ef7afc"
		     "fd05380181525eb53b9a86043d4698b2a65f6d",
		.r = "1983b5ae26a2caf8c8e5f67ad020fbb72a97bc8c9a66c070"
		     "b76c857b84fa7679ac539b8478a937d0564d408f643659ca"
		     "5b6e3041eca6c166cd4dfe59acabd1304f2fc9",
	},
	{
		.a = "166ac1610f2feb02a26390da221b50c826931c98e94aa393"
		     "99415c85237f730e65c9c8d0b50043e96e62249e1fb39885"
		     "f4ab8cf2a9b77c1c8cfb95f501052da8e80450f0988967fb"
		     "4df550b692127ea82e10d168d3cb3715595a014",
		.b = "19488565e24ac7c11eeaf77144b3d95508203e931eb9b7e8"
		     "0639b92f0ff337fff07ed97b4722b7f8814d071c5fa09260"
		     "7453069aa9708c431cc4bc2209ae30db76db8f248c5a4592"
		     "76f2438d9a2de0c",
		.r = "1ac1ea1783caf51bf4ab0f40db6810354a0fa44e69770677"
		     "bf04602b02b519f64fbb150019cde0254bacfa365553afa2"
		     "1e1012fe4b5b4596fff33c84ff84cb9d4c047cc",
	},
	{
		.a = "5b75b6143a1c6cbcac489957ac2e43ceb1eaf389d6f40285"
		     "b167f0d6f01ef6dc680c42aa7f4b15c2b970b519cc2a748c"
		     "7d495d7dca200144f7b35490710d90f589c95bae6e2450b9"
		     "96d13d9cc1d1dac",
		.b = "5e9a81924c38ae2f348d6b8d72fe1efdd831a0244801108b"
		     "1f9c37218a167bbcd699ad7709a3a4a6fadd10a2977161f0"
		     "2f4097c4614c904ab0a9cbf6b212505995cd2c369b4494b0"
		     "4e5ba0367b9881ccfa59645b6abeca953699734",
		.r = "69d18f3862bc74145c45a988b81cf48e2cc03bfe96c34f9b"
		     "981012b15fd615c51d585a913340688db34ed8d52f4c52ca"
		     "945d58910fb63e927ca8058d88725ef986e0ec4",
	},
	{
		.a = "674701bcb8b7d1afcdee9861b2523a119593959acd7d16aa"
		     "ef2ad3509ec7e9cc60b91b833ade557d0276185244155ffc"
		     "9065a9341b281f6435b7d26d6caa6b39d475f919b5d8167d"
		     "048d1a5bb433da5bd0d4c5901b71d585c32047047",
		.b = "6215d41d790981f440660c4097750c75c0b6ef765b2fc08f"
		     "d7caed2fc6305e84d751d806a3b469ec3ea6825e8bfc18f9"
		     "acb12ad29d099ad6009a0baa13a2bbb1776a567ab705788c"
		     "555ff3c59cd6848f7",
		.r = "76a0f17a23014c2b2b4d06cd952086837c69c3da36bc8cee"
		     "d0d88a74e50dfefe4a8d294cc6ab52a5cee2859ee8ffb141"
		     "0dd1e4fe363035825401679aeab07ab247b67d431",
	},
	{
		.a = "2ad3d974fa2b64854fba3e82434a1df17390ffe49f984a77"
		     "ce7384a02e7fe7b4c77097187ba049699cfedd4d1372cd1a"
		     "a64f837235ca2f9bec822c822e9981ee9afc4ec4f666b37f"
		     "dba827c818306a34a5ec916857dfaf2b8b128d81a",
		.b = "3353e8614d8b3c5c86c76006ab8fb3f1f0973a57ebe08d81"
		     "93a6712a7d180c6ddb91ba324239e399bb910105bf011f48"
		     "f13a9c6c08a11f963cde4adf41ce4bb88ce2f395b11fe2ec"
		     "b19ceaf98d08b19fa",
		.r = "3848694f56c96a0867df3953f63d8b90a140c15b0922dc17"
		     "173002079a986e669a0f032ccae911a8aef52bea6abc0427"
		     "76d99aeb5cfa27d105bca7e2487d051f113e69782",
	},
	{
		.a = "5f6264c220d6716aaf0c345b02791a38ede3a0ad8a44bc08"
		     "6e2fcf001bfabae0028b2ffea988bf1c2328ff9b01524db1"
		     "659dcf2934c26be9c32205933f5334ff2220de1d7a8333b0"
		     "307ad05cd08b8bde423036e898e400c5e0cc887a0",
		.b = "551ff6ad295ae1bce11f72540ef81f4233d1fb688708c3f8"
		     "2c92695e9f57be321dfb98cb7ece06cee2a191470209cb39"
		     "737f9465747378a2b6a2c01ae0e92b9e5e6d954576f25abe"
		     "957f4ad86a8d73ea0",
		.r = "6b4c3708b48166f86d1701bfd9152d7455ac0b56024fe4d6"
		     "e947813c8c87d343a54a14459804fc951190a17134cee19a"
		     "1d6bcca81480ab030ff2c58f677976bbf96d2e4e0",
	},
	{
		.a = "29dc9a1cc77dad36cb857326121100f546dc63a624fd950a"
		     "5edda4361acc17af684faaf932a8a467233321a6966c3e61"
		     "29f490b98e2d463b9abcd4c34263042b7966953411e6ab95"
		     "4f3dabd1d94baf3",
		.b = "32e7ae042092a898c8de2d016f3c9d9d88d534a11fb0ff37"
		     "dac04057e7093ee68fc6a1a9f2639fe69959d82f0109bd6d"
		     "f470869db5feece762683943c506ee79c7544a56a0da307b"
		     "9a02ffec03ae0b4b2797a5699fda4f17853a12f",
		.r = "3376875790192ffc6c7981d34ce9a79e445ab96df93be276"
		     "a290745feef1f204cf826ab0029074ef42b7a7b207f78d40"
		     "fcf5c639a1fe2492cf0bdbcf69b6d0ce3bb05b3",
	},
	{
		.a = "1e0b1c983532babc965cdedc4aea20127d2110d1c6bf636e"
		     "b5384cb9a67059e3bab8ef56a28dc34630ca37fc126ed7b6"
		     "25fc1164f8dd06e79ac03cd6668dee32834e32abbe29e4b9"
		     "415c34f6b12407369",
		.b = "208f4ba8619b531371a3359236423c217565ad6261992978"
		     "42e96a79b0ad9bc89312da9aba13acc17c7cbd12ee3fc769"
		     "e2473be10228f38e666afaefe868a9a960cff9e20fdc047c"
		     "e44b85d26e523a5acef4507da9c145f335ab3521b",
		.r = "270744a30ad54fcc784ebb3ea9f8bfc50372c09ec5578eb5"
		     "8ff70118681efada3d75394a5ed973df0333a14573418ae2"
		     "42c5585b923bcfc6d10f1ee3fd1ca497553c7de6f",
	},
	{
		.a = "4a83938144f1565d1407f16a811c8fd217b594b210dbc259"
		     "459ec5fdf9769ee85878ebe617c386284285e7354898f5ed"
		     "2236d1f832c606e2e7598680c4d3a103730e32a700895f86"
		     "fa2ab0cf34af11b48",
		.b = "424ee13ea5c95ff7e99889e3912b217b97975227c303f1d1"
		     "57c7f8147e239cbcad6a3dd28ffe8315a60b566b326b2827"
		     "cb21f0da1acb02a8a094415fec55f6a76ca47d7443608703"
		     "21e4db7cd1449892b57ecc2c26d8efd6a6bfab978",
		.r = "4aaf2a59ebfbb0d69ab6e0b867762c3fe76c54757caecc33"
		     "3f2c4fc9d39edda28e1beb4bd7fdf35d27f8189bc8c76a7d"
		     "c1613c932b1b921fea1b1eaf11a8390cacc472b28",
	},
	{
		.a = "6c95db45eae9c3890c716013ac0e8c8093000c0030d6b7eb"
		     "d556e749fd6f253d31622c5b8db0ba41d1a0709e0ed5d2d3"
		     "1406d0cec72e7b78bb4a21c5480bdca95a648e8331a26ca8"
		     "5f67c442d9471860",
		.b = "7de0f00b2f156e38ab5549ff5ba31e16a6cb843823a97044"
		     "7abd7542db53e78e812b4eb58d16df6a614a07bb590d673a"
		     "7208ebb98a0fc80b070c55ecfb0a6590f530daddc5ded569"
		     "b80aae255b9cda0b6058c2971474106319df77e0",
		.r = "7e7ff05971d259d4c99403f85afb3236188d72bf350e2e2d"
		     "4c44be9b3a6c569ebf47e8d0dd55c6157a8846d49a1556fa"
		     "d3bb1e00b077bc2a01eab5a0790e0ffadffe39e0",
	},
	{
		.a = "4394fd57db60ab172f4c909cdb8f3ea434e2bc6adc1ba173"
		     "a087dda50d52ed530384197589a0a66dc3fa5c7e47fbbc77"
		     "bd1bf2064d70f6ae0ab33b8fab6beeb56c985baba93b6ee5"
		     "fe086c99c919e3986",
		.b = "4940242edd9807e4ec93d363187f29ec73623961e851a5f1"
		     "176e62cf1de9d47e95d43fefa3e6e05a7de8ef3eef1fbe0a"
		     "e9ac7bf200f8d5c9dd7eb3acca2f1e5245790065e319f456"
		     "419bb208665aa060009300b9197ffd6000d810876",
		.r = "5360c87629e74983d59adea5ec47b9a198b3c5613afc3926"
		     "b9ccdad58725f4e232b7b5f8963838fb1772338620ba9240"
		     "967ebfdb2e29aef289cfd0d50f7a7036081e42e92",
	},
	{
		.a = "61be17703b62e5adf51e2c388ee77758a80632adab7c3a0d"
		     "d56b86ce827242baeb8a2324490c3c1e1615dcf8518aa7c2"
		     "65983441c7542c896e71dd213fdd04be682f654308c05cec"
		     "3c14c8defff396874763f57687e54e32f4ce9d1434c",
		.b = "522d15c2681543b7bb50d64526e6032bebf8cd452cb06f5f"
		     "0105616cc681eee2d522a86f683cd675082de34844ad7836"
		     "4555c7d2b1e960ae02826cdb4d80937bbfcdfa59d0cdbf2b"
		     "4c9a96dc35b5ecbfbac",
		.r = "6534089f006b049c13da2253ee4057e2aac083ce0610de29"
		     "00b01eddd57f4ed13adda2146fbd37bbb443420a0e7a081a"
		     "015e82b9dc85dd6c2389ce55a139e96f6448a424e6c",
	},
	{
		.a = "b287e8ac4abad5500ebe7739682f6bcf324d1afb32d68b0f"
		     "fd0b689aecdcf61473947ab8cc84a0a8873fce752d7027d3"
		     "403ccc28e522aab65b993883cd781b68b7a7d20bbabbdf3e"
		     "93c02aab4ccc335e4fbff8135d7d55fb5fee349bc8",
		.b = "abf36a5b8c6d09a3db1ed4cc037cb32072fb0812652bebb4"
		     "e7f0e194494017958cce507f64f1270083cf4855c9ea85ed"
		     "cd2f99bcb43dcfdff5e65ff2f6b18878999a646e67b10871"
		     "d767a014cb39c06268",
		.r = "bcfa04e04d226734bb8794716a3a3424893b94724dd5e802"
		     "54adad60ee8cea7cf7e8d798aa1287462a43b9d337b89d2b"
		     "8e2dbda0efe829e8fd784d61f0e09df7cee9d9a108",
	},
	{
		.a = "5805113ca06a22d67bf70a022cb538560f1e48331209ec43"
		     "682117ee841f4b7c425f23ce05b9febfe1ceb76784f6ff8c"
		     "4022df8cf61625b95f02f5f8cbf9a24f885776ee0b10acfb"
		     "e9b6535ceaf6c592243",
		.b = "5e164dba2f2ef870b086ee79a8b37b80aaf4d26c1ab53c1f"
		     "3de828ddc22e1820f5a7857de133684e95d9c0487270ac90"
		     "66bea466dc67a70a6f6f22687f35c159314eef3d5c4ee0e2"
		     "f18f1b8a98f270a71bd45d44de71025b1dc966618d3",
		.r = "679f032203be069cd9d44729aecad54a5fd518f9582cf4be"
		     "a3ef0bd7e62dec0aa124369db4f68ff416700a6f052e83a1"
		     "aaf3dee6d31c8f34192a60eba7eb57c759686b53d3f",
	},
	{
		.a = "6133ca653e55b423bb47988e353d8500c668540f10efeafa"
		     "a08aa8b04894517b1a4ce8b0431c2a219dd6c738b878f3a3"
		     "ec8f55f975b24e3d56b42ac4b087200411afc3c6716402ac"
		     "9d05a3b5c099be9d073cea6b51264fab6b602c76efe",
		.b = "52bca44f91ee3f41b18fd6286b91463c00a50f7ac5131d76"
		     "ac1dcc7fd60340a3f55357a364be360744b8699a83a4ac31"
		     "a5b7a6f9d9bd35da094e2d20a3cfb9d21aa3b573013d8301"
		     "cb8cbad78c811e60f5e",
		.r = "61b7a3d5d104cc66dca872b821dfc45afc88f7e46010b538"
		     "83aff819e90d1406991b3e104c4842db52fe1bc97c8daf37"
		     "a0ae1aaf3faa02ab92645764cf9173160c80cde79ea",
	},
	{
		.a = "5ba6fdd7fbeccfe482b2f57cdac17d53d09a60bb76422fb4"
		     "22b4c7785ce7186c88bf33cba40afa8f74a2d66b195c7d3a"
		     "f49ffc436fffb2e32c4cdfb67253c1afa4898bcb5dcbe39e"
		     "e6288129c59cf16dc177d63d0bf02fe216c1fbeba9b",
		.b = "5a1e35a1fa9ca5d66244af81b6a239d1d7b94841e38413ad"
		     "35b47fafb2d7509a30011e6d7a64360d4ccdb9f86d00a939"
		     "4721575f8fe9e23306ffe3059ef99447d09fd00f5c795d38"
		     "36c1dc663834da34991",
		.r = "70d68f80fbeac749d6f0f718ba5a6bca7ca23dee2b7ee687"
		     "ba0e3be0f45941d0ee637b3e8406ea2aed4f1638bdb47f17"
		     "7beec21cab2e49d832d9bda5a9d3b62003d6429bcbf",
	},
	{
		.a = "58f54f7ea83715900bc82bd5fc183f926f0fef989159bab7"
		     "c3aa18fd186efd7fc79d2a58c0bbd8556c1fabb784975801"
		     "396089ffa82f59eff04a2557b532f99bd39e08f597e00d0c"
		     "c96eccf3618cc02ec57b592d4d019152b686bd84bac",
		.b = "4866326c48b8226bec5aae93bc3b3b3fdac0a60319730efa"
		     "7d9aa373da03f59159d3ccbeb478dbb5393fd91c6daaad8c"
		     "28dc0187a59448847ad960648b8fdfc14f785f09e423c8cb"
		     "1c6cc5862b4ec95a25c",
		.r = "5f4a880841ce22ffd67705b03d965c39517a79f8e8ab6669"
		     "482eef3966895a050c67cce16965f98cd53477aeac38a521"
		     "02a6274dba0f5d2f02f1d5f1dff5653db7ca109a9cc",
	},
	{
		.a = "6a0e2e61d2859ce130d11aff8a8a9cc0672d3cea86da2f31"
		     "4a6a656e13f4830826cd8a6044d1233f7a6d70cae35060ea"
		     "fb66ae062c7f4af5eff978da2c5c29421322ed65293dbe9e"
		     "1855cb2977bec2fbf20",
		.b = "594a63062ee8b0b61f0143ed9237906010c17e6d03cfb2fe"
		     "675f13edc7f8c54770f25dbb275f3236a8fa3bddc10c4fa8"
		     "fe0b704e6c4c0ee29929d2d49500a4254903350cdc72b02e"
		     "dddf83964b5c382b4f12571fc4741fd5b3ac9c24a20",
		.r = "6c4c28b2358329ee65678c92b6e9b31187d4ddd793f9af45"
		     "e780b723f63b82c287e2ab0fb06ccd173a9bec960667a47f"
		     "0ebd5a2ce8d1d0059500be32d67c8ab308e3e08fda0",
	},
	{
		.a = "b37bbec16572713e3cadbcbd2703c48673edde83d6ab5cc0"
		     "02c32dd693950f4c3965506c04cddcbd754f23245ce63f92"
		     "f5dcb926f40bbf08583de1a11047e0c2508b47d0896cc0cb"
		     "fbe031a5e9a148923e",
		.b = "e8cceb9061392e35fd652346312aff143d88fb156695e0a7"
		     "f7b84419ca35214374733457d32517d0cb7c16c31a10f002"
		     "d4f2bd2fd4ee4ded122f1e221dfc989d0c8dd66deb1ac49a"
		     "9199290905db12c064d3376805451b969ee424a59a",
		.r = "e9eb6a282f306af29a28df6d720469568183f136e58813e3"
		     "d61929b91f8538cf0f777fd5fb1672f0bdc4e59ccb9a4f79"
		     "16aabeba3101842a700fa4c08e758ec7169726d682",
	},
};

#define N_GCD_TESTS (sizeof(bn_gcd_tests) / sizeof(bn_gcd_tests[0]))

static int
bn_gcd_test(const struct gcd_test *testcase)
{
	BN_CTX *ctx;
	BIGNUM *a, *b, *want, *got;
	size_t i;
	int signs;
	int failed = 0;

	if ((ctx = BN_CTX_new()) == NULL)
		errx(1, "BN_CTX_new");

	BN_CTX_start(ctx);

	if ((a = BN_CTX_get(ctx)) == NULL)
		errx(1, "a = BN_CTX_get(ctx)");
	if ((b = BN_CTX_get(ctx)) == NULL)
		errx(1, "b = BN_CTX_get(ctx)");
	if ((want = BN_CTX_get(ctx)) == NULL)
		errx(1, "want = BN_CTX_get(ctx)");
	if ((got = BN_CTX_get(ctx)) == NULL)
		errx(1, "got = BN_CTX_get(ctx)");

	if (!BN_hex2bn(&a, testcase->a))
		errx(1, "a = hex2bn(%s)", testcase->a);
	if (!BN_hex2bn(&b, testcase->b))
		errx(1, "b = hex2bn(%s)", testcase->b);
	if (!BN_hex2bn(&want, testcase->r))
		errx(1, "want = hex2bn(%s)", testcase->r);

	for (i = 0; i < N_GCD_FN; i++) {
		for (signs = 0; signs < 4; signs++) {
			const struct gcd_test_fn *test = &gcd_fn[i];

			/* XXX - BN_gcd_ct(a, 0) divides by zero */
			if (test->fails_on_zero && BN_is_zero(b))
				continue;

			BN_set_negative(a, (signs >> 0) & 1);
			BN_set_negative(b, (signs >> 1) & 1);

			if (!test->fn(got, a, b, ctx)) {
				fprintf(stderr, "%s(%s, %s) failed\n",
				    test->name, testcase->a, testcase->b);
				goto err;
			}

			if (BN_cmp(got, want) != 0) {
				fprintf(stderr, "a: %s\n", testcase->a);
				fprintf(stderr, "b: %s\n", testcase->b);
				fprintf(stderr, "%s, i: %zu, signs %d, want %s, got ",
				    test->name, i, signs, testcase->r);
				BN_print_fp(stderr, got);
				fprintf(stderr, "\n");

				failed |= 1;
			}
		}
	}

 err:
	BN_CTX_end(ctx);
	BN_CTX_free(ctx);

	return failed;
}

static int
run_bn_gcd_tests(void)
{
	size_t i;
	int failed = 0;

	for (i = 0; i < N_GCD_TESTS; i++)
		failed |= bn_gcd_test(&bn_gcd_tests[i]);

	return failed;
}

/*
 * This test uses the coprime factorization 2^(2k) - 1 = (2^k - 1) * (2^k + 1).
 */

static int
bn_binomial_gcd_test(const struct gcd_test_fn *test, int k, BIGNUM *a,
    BIGNUM *b, BN_CTX *ctx)
{
	BIGNUM *gcd;
	int shift, signs;
	int failed = 0;

	BN_CTX_start(ctx);

	if ((gcd = BN_CTX_get(ctx)) == NULL)
		errx(1, "%s: gcd = BN_CTX_get(ctx)", test->name);

	for (shift = 0; shift < 16; shift++) {
		for (signs = 0; signs < 4; signs++) {
			/* XXX - BN_gcd_ct(a, 0) divides by zero */
			if (test->fails_on_zero && BN_is_zero(b))
				continue;

			BN_set_negative(a, (signs >> 0) & 1);
			BN_set_negative(b, (signs >> 1) & 1);

			if (!test->fn(gcd, a, b, ctx)) {
				errx(1, "%s(), k: %d, shift: %d, signs %d\n",
				    test->name, k, shift, signs);
			}

			if (BN_is_negative(gcd)) {
				fprintf(stderr, "%s: negative gcd, "
				    "k: %d, shift: %d, signs %d\n",
				    test->name, k, shift, signs);
				failed |= 1;
			}

			if (BN_ucmp(gcd, b) != 0) {
				fprintf(stderr, "%s: BN_ucmp(gcd, b) failed, "
				    "k: %d, shift: %d, signs %d\n",
				    test->name, k, shift, signs);
				BN_print_fp(stderr, gcd);
				fprintf(stderr, "\n");
				BN_print_fp(stderr, b);
				fprintf(stderr, "\n");
				failed |= 1;
			}
		}

		if (!BN_lshift1(a, a))
			errx(1, "%s: BN_lshift1(a, a)", test->name);
		if (!BN_lshift1(b, b))
			errx(1, "%s: BN_lshift1(b, b)", test->name);
	}

	BN_CTX_end(ctx);

	return failed;
}

static int
run_bn_binomial_gcd_tests(void)
{
	BN_CTX *ctx;
	BIGNUM *a, *b;
	size_t i;
	int k;
	int failed = 0;

	if ((ctx = BN_CTX_new()) == NULL)
		errx(1, "%s: BN_CTX_new()", __func__);

	BN_CTX_start(ctx);

	if ((a = BN_CTX_get(ctx)) == NULL)
		errx(1, "%s: a = BN_CTX_get(ctx)", __func__);
	if ((b = BN_CTX_get(ctx)) == NULL)
		errx(1, "%s: b = BN_CTX_get(ctx)", __func__);

	for (i = 0; i < N_GCD_FN; i++) {
		const struct gcd_test_fn *test = &gcd_fn[i];

		for (k = 0; k < 400; k++) {
			BN_zero(a);
			BN_zero(b);

			/* a = 2^(2k) - 1 */
			if (!BN_set_bit(a, 2 * k))
				errx(1, "%s: BN_set_bit(a, 2 * k)", test->name);
			if (!BN_sub_word(a, 1))
				errx(1, "%s: BN_sub_word(a, 1)", test->name);

			/* b = 2^k - 1 */
			if (!BN_set_bit(b, k))
				errx(1, "%s: BN_set_bit(a, k)", test->name);
			if (!BN_sub_word(b, 1))
				errx(1, "%s: BN_sub_word(a, 1)", test->name);

			failed |= bn_binomial_gcd_test(test, k, a, b, ctx);

			BN_zero(a);
			BN_zero(b);

			/* a = 2^(2k) - 1 */
			if (!BN_set_bit(a, 2 * k))
				errx(1, "%s: BN_set_bit(a, 2 * k)", test->name);
			if (!BN_sub_word(a, 1))
				errx(1, "%s: BN_sub_word(a, 1)", test->name);

			/* b = 2^k + 1 */
			if (!BN_set_bit(b, k))
				errx(1, "%s: BN_set_bit(a, k)", test->name);
			if (!BN_add_word(b, 1))
				errx(1, "%s: BN_add_word(a, 1)", test->name);

			failed |= bn_binomial_gcd_test(test, k, a, b, ctx);
		}
	}

	BN_CTX_end(ctx);
	BN_CTX_free(ctx);

	return failed;
}

int
main(void)
{
	int failed = 0;

	failed |= run_bn_gcd_tests();
	failed |= run_bn_binomial_gcd_tests();

	return failed;
}