poseidon.go

package main

import (
	"github.com/consensys/gnark/frontend"
	"github.com/reilabs/gnark-lean-extractor/abstractor"
	"math/big"
)

func hex(s string) big.Int {
	var bi big.Int
	bi.SetString(s, 0)
	return bi
}

var MDS_2 = [][]frontend.Variable{
	{
		hex("0x066f6f85d6f68a85ec10345351a23a3aaf07f38af8c952a7bceca70bd2af7ad5"),
		hex("0x2b9d4b4110c9ae997782e1509b1d0fdb20a7c02bbd8bea7305462b9f8125b1e8"),
	}, {
		hex("0x0cc57cdbb08507d62bf67a4493cc262fb6c09d557013fff1f573f431221f8ff9"),
		hex("0x1274e649a32ed355a31a6ed69724e1adade857e86eb5c3a121bcd147943203c8"),
	},
}

var CONSTANTS_2 = [][]frontend.Variable{
	{
		hex("0x09c46e9ec68e9bd4fe1faaba294cba38a71aa177534cdd1b6c7dc0dbd0abd7a7"),
		hex("0x0c0356530896eec42a97ed937f3135cfc5142b3ae405b8343c1d83ffa604cb81"),
	}, {
		hex("0x1e28a1d935698ad1142e51182bb54cf4a00ea5aabd6268bd317ea977cc154a30"),
		hex("0x27af2d831a9d2748080965db30e298e40e5757c3e008db964cf9e2b12b91251f"),
	}, {
		hex("0x1e6f11ce60fc8f513a6a3cfe16ae175a41291462f214cd0879aaf43545b74e03"),
		hex("0x2a67384d3bbd5e438541819cb681f0be04462ed14c3613d8f719206268d142d3"),
	}, {
		hex("0x0b66fdf356093a611609f8e12fbfecf0b985e381f025188936408f5d5c9f45d0"),
		hex("0x012ee3ec1e78d470830c61093c2ade370b26c83cc5cebeeddaa6852dbdb09e21"),
	}, {
		hex("0x0252ba5f6760bfbdfd88f67f8175e3fd6cd1c431b099b6bb2d108e7b445bb1b9"),
		hex("0x179474cceca5ff676c6bec3cef54296354391a8935ff71d6ef5aeaad7ca932f1"),
	}, {
		hex("0x2c24261379a51bfa9228ff4a503fd4ed9c1f974a264969b37e1a2589bbed2b91"),
		hex("0x1cc1d7b62692e63eac2f288bd0695b43c2f63f5001fc0fc553e66c0551801b05"),
	}, {
		hex("0x255059301aada98bb2ed55f852979e9600784dbf17fbacd05d9eff5fd9c91b56"),
		hex("0x28437be3ac1cb2e479e1f5c0eccd32b3aea24234970a8193b11c29ce7e59efd9"),
	}, {
		hex("0x28216a442f2e1f711ca4fa6b53766eb118548da8fb4f78d4338762c37f5f2043"),
		hex("0x2c1f47cd17fa5adf1f39f4e7056dd03feee1efce03094581131f2377323482c9"),
	}, {
		hex("0x07abad02b7a5ebc48632bcc9356ceb7dd9dafca276638a63646b8566a621afc9"),
		hex("0x0230264601ffdf29275b33ffaab51dfe9429f90880a69cd137da0c4d15f96c3c"),
	}, {
		hex("0x1bc973054e51d905a0f168656497ca40a864414557ee289e717e5d66899aa0a9"),
		hex("0x2e1c22f964435008206c3157e86341edd249aff5c2d8421f2a6b22288f0a67fc"),
	}, {
		hex("0x1224f38df67c5378121c1d5f461bbc509e8ea1598e46c9f7a70452bc2bba86b8"),
		hex("0x02e4e69d8ba59e519280b4bd9ed0068fd7bfe8cd9dfeda1969d2989186cde20e"),
	}, {
		hex("0x1f1eccc34aaba0137f5df81fc04ff3ee4f19ee364e653f076d47e9735d98018e"),
		hex("0x1672ad3d709a353974266c3039a9a7311424448032cd1819eacb8a4d4284f582"),
	}, {
		hex("0x283e3fdc2c6e420c56f44af5192b4ae9cda6961f284d24991d2ed602df8c8fc7"),
		hex("0x1c2a3d120c550ecfd0db0957170fa013683751f8fdff59d6614fbd69ff394bcc"),
	}, {
		hex("0x216f84877aac6172f7897a7323456efe143a9a43773ea6f296cb6b8177653fbd"),
		hex("0x2c0d272becf2a75764ba7e8e3e28d12bceaa47ea61ca59a411a1f51552f94788"),
	}, {
		hex("0x16e34299865c0e28484ee7a74c454e9f170a5480abe0508fcb4a6c3d89546f43"),
		hex("0x175ceba599e96f5b375a232a6fb9cc71772047765802290f48cd939755488fc5"),
	}, {
		hex("0x0c7594440dc48c16fead9e1758b028066aa410bfbc354f54d8c5ffbb44a1ee32"),
		hex("0x1a3c29bc39f21bb5c466db7d7eb6fd8f760e20013ccf912c92479882d919fd8d"),
	}, {
		hex("0x0ccfdd906f3426e5c0986ea049b253400855d349074f5a6695c8eeabcd22e68f"),
		hex("0x14f6bc81d9f186f62bdb475ce6c9411866a7a8a3fd065b3ce0e699b67dd9e796"),
	}, {
		hex("0x0962b82789fb3d129702ca70b2f6c5aacc099810c9c495c888edeb7386b97052"),
		hex("0x1a880af7074d18b3bf20c79de25127bc13284ab01ef02575afef0c8f6a31a86d"),
	}, {
		hex("0x10cba18419a6a332cd5e77f0211c154b20af2924fc20ff3f4c3012bb7ae9311b"),
		hex("0x057e62a9a8f89b3ebdc76ba63a9eaca8fa27b7319cae3406756a2849f302f10d"),
	}, {
		hex("0x287c971de91dc0abd44adf5384b4988cb961303bbf65cff5afa0413b44280cee"),
		hex("0x21df3388af1687bbb3bca9da0cca908f1e562bc46d4aba4e6f7f7960e306891d"),
	}, {
		hex("0x1be5c887d25bce703e25cc974d0934cd789df8f70b498fd83eff8b560e1682b3"),
		hex("0x268da36f76e568fb68117175cea2cd0dd2cb5d42fda5acea48d59c2706a0d5c1"),
	}, {
		hex("0x0e17ab091f6eae50c609beaf5510ececc5d8bb74135ebd05bd06460cc26a5ed6"),
		hex("0x04d727e728ffa0a67aee535ab074a43091ef62d8cf83d270040f5caa1f62af40"),
	}, {
		hex("0x0ddbd7bf9c29341581b549762bc022ed33702ac10f1bfd862b15417d7e39ca6e"),
		hex("0x2790eb3351621752768162e82989c6c234f5b0d1d3af9b588a29c49c8789654b"),
	}, {
		hex("0x1e457c601a63b73e4471950193d8a570395f3d9ab8b2fd0984b764206142f9e9"),
		hex("0x21ae64301dca9625638d6ab2bbe7135ffa90ecd0c43ff91fc4c686fc46e091b0"),
	}, {
		hex("0x0379f63c8ce3468d4da293166f494928854be9e3432e09555858534eed8d350b"),
		hex("0x002d56420359d0266a744a080809e054ca0e4921a46686ac8c9f58a324c35049"),
	}, {
		hex("0x123158e5965b5d9b1d68b3cd32e10bbeda8d62459e21f4090fc2c5af963515a6"),
		hex("0x0be29fc40847a941661d14bbf6cbe0420fbb2b6f52836d4e60c80eb49cad9ec1"),
	}, {
		hex("0x1ac96991dec2bb0557716142015a453c36db9d859cad5f9a233802f24fdf4c1a"),
		hex("0x1596443f763dbcc25f4964fc61d23b3e5e12c9fa97f18a9251ca3355bcb0627e"),
	}, {
		hex("0x12e0bcd3654bdfa76b2861d4ec3aeae0f1857d9f17e715aed6d049eae3ba3212"),
		hex("0x0fc92b4f1bbea82b9ea73d4af9af2a50ceabac7f37154b1904e6c76c7cf964ba"),
	}, {
		hex("0x1f9c0b1610446442d6f2e592a8013f40b14f7c7722236f4f9c7e965233872762"),
		hex("0x0ebd74244ae72675f8cde06157a782f4050d914da38b4c058d159f643dbbf4d3"),
	}, {
		hex("0x2cb7f0ed39e16e9f69a9fafd4ab951c03b0671e97346ee397a839839dccfc6d1"),
		hex("0x1a9d6e2ecff022cc5605443ee41bab20ce761d0514ce526690c72bca7352d9bf"),
	}, {
		hex("0x2a115439607f335a5ea83c3bc44a9331d0c13326a9a7ba3087da182d648ec72f"),
		hex("0x23f9b6529b5d040d15b8fa7aee3e3410e738b56305cd44f29535c115c5a4c060"),
	}, {
		hex("0x05872c16db0f72a2249ac6ba484bb9c3a3ce97c16d58b68b260eb939f0e6e8a7"),
		hex("0x1300bdee08bb7824ca20fb80118075f40219b6151d55b5c52b624a7cdeddf6a7"),
	}, {
		hex("0x19b9b63d2f108e17e63817863a8f6c288d7ad29916d98cb1072e4e7b7d52b376"),
		hex("0x015bee1357e3c015b5bda237668522f613d1c88726b5ec4224a20128481b4f7f"),
	}, {
		hex("0x2953736e94bb6b9f1b9707a4f1615e4efe1e1ce4bab218cbea92c785b128ffd1"),
		hex("0x0b069353ba091618862f806180c0385f851b98d372b45f544ce7266ed6608dfc"),
	}, {
		hex("0x304f74d461ccc13115e4e0bcfb93817e55aeb7eb9306b64e4f588ac97d81f429"),
		hex("0x15bbf146ce9bca09e8a33f5e77dfe4f5aad2a164a4617a4cb8ee5415cde913fc"),
	}, {
		hex("0x0ab4dfe0c2742cde44901031487964ed9b8f4b850405c10ca9ff23859572c8c6"),
		hex("0x0e32db320a044e3197f45f7649a19675ef5eedfea546dea9251de39f9639779a"),
	}, {
		hex("0x0a1756aa1f378ca4b27635a78b6888e66797733a82774896a3078efa516da016"),
		hex("0x044c4a33b10f693447fd17177f952ef895e61d328f85efa94254d6a2a25d93ef"),
	}, {
		hex("0x2ed3611b725b8a70be655b537f66f700fe0879d79a496891d37b07b5466c4b8b"),
		hex("0x1f9ba4e8bab7ce42c8ecc3d722aa2e0eadfdeb9cfdd347b5d8339ea7120858aa"),
	}, {
		hex("0x1b233043052e8c288f7ee907a84e518aa38e82ac4502066db74056f865c5d3da"),
		hex("0x2431e1cc164bb8d074031ab72bd55b4c902053bfc0f14db0ca2f97b020875954"),
	}, {
		hex("0x082f934c91f5aac330cd6953a0a7db45a13e322097583319a791f273965801fd"),
		hex("0x2b9a0a223e7538b0a34be074315542a3c77245e2ae7cbe999ad6bb930c48997c"),
	}, {
		hex("0x0e1cd91edd2cfa2cceb85483b887a9be8164163e75a8a00eb0b589cc70214e7d"),
		hex("0x2e1eac0f2bfdfd63c951f61477e3698999774f19854d00f588d324601cebe2f9"),
	}, {
		hex("0x0cbfa95f37fb74060c76158e769d6d157345784d8efdb33c23d748115b500b83"),
		hex("0x08f05b3be923ed44d65ad49d8a61e9a676d991e3a77513d9980c232dfa4a4f84"),
	}, {
		hex("0x22719e2a070bcd0852bf8e21984d0443e7284925dc0758a325a2dd510c047ef6"),
		hex("0x041f596a9ee1cb2bc060f7fcc3a1ab4c7bdbf036119982c0f41f62b2f26830c0"),
	}, {
		hex("0x233fd35de1be520a87628eb06f6b1d4c021be1c2d0dc464a19fcdd0986b10f89"),
		hex("0x0524b46d1aa87a5e4325e0a423ebc810d31e078aa1b4707eefcb453c61c9c267"),
	}, {
		hex("0x2c34f424c81e5716ce47fcac894b85824227bb954b0f3199cc4486237c515211"),
		hex("0x0b5f2a4b63387819207effc2b5541fb72dd2025b5457cc97f33010327de4915e"),
	}, {
		hex("0x22207856082ccc54c5b72fe439d2cfd6c17435d2f57af6ceaefac41fe05c659f"),
		hex("0x24d57a8bf5da63fe4e24159b7f8950b5cdfb210194caf79f27854048ce2c8171"),
	}, {
		hex("0x0afab181fdd5e0583b371d75bd693f98374ad7097bb01a8573919bb23b79396e"),
		hex("0x2dba9b108f208772998a52efac7cbd5676c0057194c16c0bf16290d62b1128ee"),
	}, {
		hex("0x26349b66edb8b16f56f881c788f53f83cbb83de0bd592b255aff13e6bce420b3"),
		hex("0x25af7ce0e5e10357685e95f92339753ad81a56d28ecc193b235288a3e6f137db"),
	}, {
		hex("0x25b4ce7bd2294390c094d6a55edd68b970eed7aae88b2bff1f7c0187fe35011f"),
		hex("0x22c543f10f6c89ec387e53f1908a88e5de9cef28ebdf30b18cb9d54c1e02b631"),
	}, {
		hex("0x0236f93e7789c4724fc7908a9f191e1e425e906a919d7a34df668e74882f87a9"),
		hex("0x29350b401166ca010e7d27e37d05da99652bdae114eb01659cb497af980c4b52"),
	}, {
		hex("0x0eed787d65820d3f6bd31bbab547f75a65edb75d844ebb89ee1260916652363f"),
		hex("0x07cc1170f13b46f2036a753f520b3291fdcd0e99bd94297d1906f656f4de6fad"),
	}, {
		hex("0x22b939233b1d7205f49bcf613a3d30b1908786d7f9f5d10c2059435689e8acea"),
		hex("0x01451762a0aab81c8aad1dc8bc33e870740f083a5aa85438add650ace60ae5a6"),
	}, {
		hex("0x23506bb5d8727d4461fabf1025d46d1fe32eaa61dec7da57e704fec0892fce89"),
		hex("0x2e484c44e838aea0bac06ae3f71bdd092a3709531e1efea97f8bd68907355522"),
	}, {
		hex("0x0f4bc7d07ebafd64379e78c50bd2e42baf4a594545cedc2545418da26835b54c"),
		hex("0x1f4d3c8f6583e9e5fa76637862faaee851582388725df460e620996d50d8e74e"),
	}, {
		hex("0x093514e0c70711f82660d07be0e4a988fae02abc7b681d9153eb9bcb48fe7389"),
		hex("0x1adab0c8e2b3bad346699a2b5f3bc03643ee83ece47228f24a58e0a347e153d8"),
	}, {
		hex("0x1672b1726057d99dd14709ebb474641a378c1b94b8072bac1a22dbef9e80dad2"),
		hex("0x1dfd53d4576af2e38f44f53fdcab468cc5d8e2fae0acc4ee30d47b239b479c14"),
	}, {
		hex("0x0c6888a10b75b0f3a70a36263a37e17fe6d77d640f6fc3debc7f207753205c60"),
		hex("0x1addb933a65be77092b34a7e77d12fe8611a61e00ee6848b85091ecca9d1e508"),
	}, {
		hex("0x00d7540dcd268a845c10ae18d1de933cf638ff5425f0afff7935628e299d1791"),
		hex("0x140c0e42687e9ead01b2827a5664ca9c26fedde4acd99db1d316939d20b82c0e"),
	}, {
		hex("0x2f0c3a115d4317d191ba89b8d13d1806c20a0f9b24f8c5edc091e2ae56565984"),
		hex("0x0c4ee778ff7c14553006ed220cf9c81008a0cff670b22b82d8c538a1dc958c61"),
	}, {
		hex("0x1704f2766d46f82c3693f00440ccc3609424ed26c0acc66227c3d7485de74c69"),
		hex("0x2f2d19cc3ea5d78ea7a02c1b51d244abf0769c9f8544e40239b66fe9009c3cfa"),
	}, {
		hex("0x1ae03853b75fcaba5053f112e2a8e8dcdd7ee6cb9cfed9c7d6c766a806fc6629"),
		hex("0x0971aabf795241df51d131d0fa61aa5f3556921b2d6f014e4e41a86ddaf056d5"),
	}, {
		hex("0x1408c316e6014e1a91d4cf6b6e0de73eda624f8380df1c875f5c29f7bfe2f646"),
		hex("0x1667f3fe2edbe850248abe42b543093b6c89f1f773ef285341691f39822ef5bd"),
	}, {
		hex("0x13bf7c5d0d2c4376a48b0a03557cdf915b81718409e5c133424c69576500fe37"),
		hex("0x07620a6dfb0b6cec3016adf3d3533c24024b95347856b79719bc0ba743a62c2c"),
	}, {
		hex("0x1574c7ef0c43545f36a8ca08bdbdd8b075d2959e2f322b731675de3e1982b4d0"),
		hex("0x269e4b5b7a2eb21afd567970a717ceec5bd4184571c254fdc06e03a7ff8378f0"),
	},
}

var MDS_3 = [][]frontend.Variable{
	{
		hex("0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b"),
		hex("0x16ed41e13bb9c0c66ae119424fddbcbc9314dc9fdbdeea55d6c64543dc4903e0"),
		hex("0x2b90bba00fca0589f617e7dcbfe82e0df706ab640ceb247b791a93b74e36736d"),
	},
	{
		hex("0x2969f27eed31a480b9c36c764379dbca2cc8fdd1415c3dded62940bcde0bd771"),
		hex("0x2e2419f9ec02ec394c9871c832963dc1b89d743c8c7b964029b2311687b1fe23"),
		hex("0x101071f0032379b697315876690f053d148d4e109f5fb065c8aacc55a0f89bfa"),
	},
	{
		hex("0x143021ec686a3f330d5f9e654638065ce6cd79e28c5b3753326244ee65a1b1a7"),
		hex("0x176cc029695ad02582a70eff08a6fd99d057e12e58e7d7b6b16cdfabc8ee2911"),
		hex("0x19a3fc0a56702bf417ba7fee3802593fa644470307043f7773279cd71d25d5e0"),
	},
}

var CONSTANTS_3 = [][]frontend.Variable{
	{
		hex("0x0ee9a592ba9a9518d05986d656f40c2114c4993c11bb29938d21d47304cd8e6e"),
		hex("0x00f1445235f2148c5986587169fc1bcd887b08d4d00868df5696fff40956e864"),
		hex("0x08dff3487e8ac99e1f29a058d0fa80b930c728730b7ab36ce879f3890ecf73f5"),
	}, {
		hex("0x2f27be690fdaee46c3ce28f7532b13c856c35342c84bda6e20966310fadc01d0"),
		hex("0x2b2ae1acf68b7b8d2416bebf3d4f6234b763fe04b8043ee48b8327bebca16cf2"),
		hex("0x0319d062072bef7ecca5eac06f97d4d55952c175ab6b03eae64b44c7dbf11cfa"),
	}, {
		hex("0x28813dcaebaeaa828a376df87af4a63bc8b7bf27ad49c6298ef7b387bf28526d"),
		hex("0x2727673b2ccbc903f181bf38e1c1d40d2033865200c352bc150928adddf9cb78"),
		hex("0x234ec45ca27727c2e74abd2b2a1494cd6efbd43e340587d6b8fb9e31e65cc632"),
	}, {
		hex("0x15b52534031ae18f7f862cb2cf7cf760ab10a8150a337b1ccd99ff6e8797d428"),
		hex("0x0dc8fad6d9e4b35f5ed9a3d186b79ce38e0e8a8d1b58b132d701d4eecf68d1f6"),
		hex("0x1bcd95ffc211fbca600f705fad3fb567ea4eb378f62e1fec97805518a47e4d9c"),
	}, {
		hex("0x10520b0ab721cadfe9eff81b016fc34dc76da36c2578937817cb978d069de559"),
		hex("0x1f6d48149b8e7f7d9b257d8ed5fbbaf42932498075fed0ace88a9eb81f5627f6"),
		hex("0x1d9655f652309014d29e00ef35a2089bfff8dc1c816f0dc9ca34bdb5460c8705"),
	}, {
		hex("0x04df5a56ff95bcafb051f7b1cd43a99ba731ff67e47032058fe3d4185697cc7d"),
		hex("0x0672d995f8fff640151b3d290cedaf148690a10a8c8424a7f6ec282b6e4be828"),
		hex("0x099952b414884454b21200d7ffafdd5f0c9a9dcc06f2708e9fc1d8209b5c75b9"),
	}, {
		hex("0x052cba2255dfd00c7c483143ba8d469448e43586a9b4cd9183fd0e843a6b9fa6"),
		hex("0x0b8badee690adb8eb0bd74712b7999af82de55707251ad7716077cb93c464ddc"),
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		hex("0x21e5241e12564dd6fd9f1cdd2a0de39eedfefc1466cc568ec5ceb745a0506edc"),
	}, {
		hex("0x1cfb5662e8cf5ac9226a80ee17b36abecb73ab5f87e161927b4349e10e4bdf08"),
		hex("0x0f21177e302a771bbae6d8d1ecb373b62c99af346220ac0129c53f666eb24100"),
		hex("0x1671522374606992affb0dd7f71b12bec4236aede6290546bcef7e1f515c2320"),
	}, {
		hex("0x0fa3ec5b9488259c2eb4cf24501bfad9be2ec9e42c5cc8ccd419d2a692cad870"),
		hex("0x193c0e04e0bd298357cb266c1506080ed36edce85c648cc085e8c57b1ab54bba"),
		hex("0x102adf8ef74735a27e9128306dcbc3c99f6f7291cd406578ce14ea2adaba68f8"),
	}, {
		hex("0x0fe0af7858e49859e2a54d6f1ad945b1316aa24bfbdd23ae40a6d0cb70c3eab1"),
		hex("0x216f6717bbc7dedb08536a2220843f4e2da5f1daa9ebdefde8a5ea7344798d22"),
		hex("0x1da55cc900f0d21f4a3e694391918a1b3c23b2ac773c6b3ef88e2e4228325161"),
	},
}

type cfg struct {
	RF        int
	RP        int
	constants [][]frontend.Variable
	mds       [][]frontend.Variable
}

var CFG_3 = cfg{
	RF:        8,
	RP:        57,
	constants: CONSTANTS_3,
	mds:       MDS_3,
}

var CFG_2 = cfg{
	RF:        8,
	RP:        56,
	constants: CONSTANTS_2,
	mds:       MDS_2,
}

func cfgFor(t int) *cfg {
	switch t {
	case 2:
		return &CFG_2
	case 3:
		return &CFG_3
	}
	panic("Poseidon: unsupported arg count")
}

type Poseidon1 struct {
	In frontend.Variable
}

func (g Poseidon1) DefineGadget(api abstractor.API) []frontend.Variable {
	inp := []frontend.Variable{0, g.In}
	return api.Call(poseidon{inp})[:1]
}

type Poseidon2 struct {
	In1, In2 frontend.Variable
}

func (g Poseidon2) DefineGadget(api abstractor.API) []frontend.Variable {
	inp := []frontend.Variable{0, g.In1, g.In2}
	return api.Call(poseidon{inp})[:1]
}

type poseidon struct {
	Inputs []frontend.Variable
}

func (g poseidon) DefineGadget(api abstractor.API) []frontend.Variable {
	state := g.Inputs
	cfg := cfgFor(len(state))
	for i := 0; i < cfg.RF/2; i += 1 {
		state = api.Call(fullRound{state, cfg.constants[i]})
	}
	for i := 0; i < cfg.RP; i += 1 {
		state = api.Call(halfRound{state, cfg.constants[cfg.RF/2+i]})
	}
	for i := 0; i < cfg.RF/2; i += 1 {
		state = api.Call(fullRound{state, cfg.constants[cfg.RF/2+cfg.RP+i]})
	}
	return state
}

type sbox struct {
	Inp frontend.Variable
}

func (s sbox) DefineGadget(api abstractor.API) []frontend.Variable {
	v2 := api.Mul(s.Inp, s.Inp)
	v4 := api.Mul(v2, v2)
	r := api.Mul(s.Inp, v4)
	return []frontend.Variable{r}
}

type mds struct {
	Inp []frontend.Variable
}

func (m mds) DefineGadget(api abstractor.API) []frontend.Variable {
	var mds = make([]frontend.Variable, len(m.Inp))
	cfg := cfgFor(len(m.Inp))
	for i := 0; i < len(m.Inp); i += 1 {
		var sum frontend.Variable = 0
		for j := 0; j < len(m.Inp); j += 1 {
			sum = api.Add(sum, api.Mul(m.Inp[j], cfg.mds[i][j]))
		}
		mds[i] = sum
	}
	return mds
}

type halfRound struct {
	Inp    []frontend.Variable
	Consts []frontend.Variable
}

func (h halfRound) DefineGadget(api abstractor.API) []frontend.Variable {
	for i := 0; i < len(h.Inp); i += 1 {
		h.Inp[i] = api.Add(h.Inp[i], h.Consts[i])
	}
	h.Inp[0] = api.Call(sbox{h.Inp[0]})[0]
	return api.Call(mds{h.Inp})
}

type fullRound struct {
	Inp    []frontend.Variable
	Consts []frontend.Variable
}

func (h fullRound) DefineGadget(api abstractor.API) []frontend.Variable {
	for i := 0; i < len(h.Inp); i += 1 {
		h.Inp[i] = api.Add(h.Inp[i], h.Consts[i])
	}
	for i := 0; i < len(h.Inp); i += 1 {
		h.Inp[i] = api.Call(sbox{h.Inp[i]})[0]
	}
	return api.Call(mds{h.Inp})
}