logos-blockchain-circuits/hash_bn/poseidon2_perm.circom

//
pragma circom 2.1.9;

//
// The Poseidon2 permutation for bn128 and t=3 
//

//------------------------------------------------------------------------------
// The S-box

template SBox() {
  signal input  inp;
  signal output out;

  signal x2 <== inp*inp;
  signal x4 <== x2*x2;

  out <== inp*x4;
}

//------------------------------------------------------------------------------
// partial or internal round

template InternalRound(i) {
  signal input  inp[3];
  signal output out[3];

  var round_consts[56] = 
    [0x1a1d063e54b1e764b63e1855bff015b8cedd192f47308731499573f23597d4b5,
    0x26abc66f3fdf8e68839d10956259063708235dccc1aa3793b91b002c5b257c37,
    0x0c7c64a9d887385381a578cfed5aed370754427aabca92a70b3c2b12ff4d7be8,
    0x1cf5998769e9fab79e17f0b6d08b2d1eba2ebac30dc386b0edd383831354b495,
    0x0f5e3a8566be31b7564ca60461e9e08b19828764a9669bc17aba0b97e66b0109,
    0x18df6a9d19ea90d895e60e4db0794a01f359a53a180b7d4b42bf3d7a531c976e,
    0x04f7bf2c5c0538ac6e4b782c3c6e601ad0ea1d3a3b9d25ef4e324055fa3123dc,
    0x29c76ce22255206e3c40058523748531e770c0584aa2328ce55d54628b89ebe6,
    0x198d425a45b78e85c053659ab4347f5d65b1b8e9c6108dbe00e0e945dbc5ff15,
    0x25ee27ab6296cd5e6af3cc79c598a1daa7ff7f6878b3c49d49d3a9a90c3fdf74,
    0x138ea8e0af41a1e024561001c0b6eb1505845d7d0c55b1b2c0f88687a96d1381,
    0x306197fb3fab671ef6e7c2cba2eefd0e42851b5b9811f2ca4013370a01d95687,
    0x1a0c7d52dc32a4432b66f0b4894d4f1a21db7565e5b4250486419eaf00e8f620,
    0x2b46b418de80915f3ff86a8e5c8bdfccebfbe5f55163cd6caa52997da2c54a9f,
    0x12d3e0dc0085873701f8b777b9673af9613a1af5db48e05bfb46e312b5829f64,
    0x263390cf74dc3a8870f5002ed21d089ffb2bf768230f648dba338a5cb19b3a1f,
    0x0a14f33a5fe668a60ac884b4ca607ad0f8abb5af40f96f1d7d543db52b003dcd,
    0x28ead9c586513eab1a5e86509d68b2da27be3a4f01171a1dd847df829bc683b9,
    0x1c6ab1c328c3c6430972031f1bdb2ac9888f0ea1abe71cffea16cda6e1a7416c,
    0x1fc7e71bc0b819792b2500239f7f8de04f6decd608cb98a932346015c5b42c94,
    0x03e107eb3a42b2ece380e0d860298f17c0c1e197c952650ee6dd85b93a0ddaa8,
    0x2d354a251f381a4669c0d52bf88b772c46452ca57c08697f454505f6941d78cd,
    0x094af88ab05d94baf687ef14bc566d1c522551d61606eda3d14b4606826f794b,
    0x19705b783bf3d2dc19bcaeabf02f8ca5e1ab5b6f2e3195a9d52b2d249d1396f7,
    0x09bf4acc3a8bce3f1fcc33fee54fc5b28723b16b7d740a3e60cef6852271200e,
    0x1803f8200db6013c50f83c0c8fab62843413732f301f7058543a073f3f3b5e4e,
    0x0f80afb5046244de30595b160b8d1f38bf6fb02d4454c0add41f7fef2faf3e5c,
    0x126ee1f8504f15c3d77f0088c1cfc964abcfcf643f4a6fea7dc3f98219529d78,
    0x23c203d10cfcc60f69bfb3d919552ca10ffb4ee63175ddf8ef86f991d7d0a591,
    0x2a2ae15d8b143709ec0d09705fa3a6303dec1ee4eec2cf747c5a339f7744fb94,
    0x07b60dee586ed6ef47e5c381ab6343ecc3d3b3006cb461bbb6b5d89081970b2b,
    0x27316b559be3edfd885d95c494c1ae3d8a98a320baa7d152132cfe583c9311bd,
    0x1d5c49ba157c32b8d8937cb2d3f84311ef834cc2a743ed662f5f9af0c0342e76,
    0x2f8b124e78163b2f332774e0b850b5ec09c01bf6979938f67c24bd5940968488,
    0x1e6843a5457416b6dc5b7aa09a9ce21b1d4cba6554e51d84665f75260113b3d5,
    0x11cdf00a35f650c55fca25c9929c8ad9a68daf9ac6a189ab1f5bc79f21641d4b,
    0x21632de3d3bbc5e42ef36e588158d6d4608b2815c77355b7e82b5b9b7eb560bc,
    0x0de625758452efbd97b27025fbd245e0255ae48ef2a329e449d7b5c51c18498a,
    0x2ad253c053e75213e2febfd4d976cc01dd9e1e1c6f0fb6b09b09546ba0838098,
    0x1d6b169ed63872dc6ec7681ec39b3be93dd49cdd13c813b7d35702e38d60b077,
    0x1660b740a143664bb9127c4941b67fed0be3ea70a24d5568c3a54e706cfef7fe,
    0x0065a92d1de81f34114f4ca2deef76e0ceacdddb12cf879096a29f10376ccbfe,
    0x1f11f065202535987367f823da7d672c353ebe2ccbc4869bcf30d50a5871040d,
    0x26596f5c5dd5a5d1b437ce7b14a2c3dd3bd1d1a39b6759ba110852d17df0693e,
    0x16f49bc727e45a2f7bf3056efcf8b6d38539c4163a5f1e706743db15af91860f,
    0x1abe1deb45b3e3119954175efb331bf4568feaf7ea8b3dc5e1a4e7438dd39e5f,
    0x0e426ccab66984d1d8993a74ca548b779f5db92aaec5f102020d34aea15fba59,
    0x0e7c30c2e2e8957f4933bd1942053f1f0071684b902d534fa841924303f6a6c6,
    0x0812a017ca92cf0a1622708fc7edff1d6166ded6e3528ead4c76e1f31d3fc69d,
    0x21a5ade3df2bc1b5bba949d1db96040068afe5026edd7a9c2e276b47cf010d54,
    0x01f3035463816c84ad711bf1a058c6c6bd101945f50e5afe72b1a5233f8749ce,
    0x0b115572f038c0e2028c2aafc2d06a5e8bf2f9398dbd0fdf4dcaa82b0f0c1c8b,
    0x1c38ec0b99b62fd4f0ef255543f50d2e27fc24db42bc910a3460613b6ef59e2f,
    0x1c89c6d9666272e8425c3ff1f4ac737b2f5d314606a297d4b1d0b254d880c53e,
    0x03326e643580356bf6d44008ae4c042a21ad4880097a5eb38b71e2311bb88f8f,
    0x268076b0054fb73f67cee9ea0e51e3ad50f27a6434b5dceb5bdde2299910a4c9];

  component sb = SBox();
  sb.inp <== inp[0] + round_consts[i];

  out[0] <== 2*sb.out +   inp[1] +   inp[2];
  out[1] <==   sb.out + 2*inp[1] +   inp[2];
  out[2] <==   sb.out +   inp[1] + 3*inp[2];

}

//------------------------------------------------------------------------------
// external rounds

template ExternalRound(i) {
  signal input  inp[3];
  signal output out[3];

  var round_consts[8][3] = 

    [ [ 0x1d066a255517b7fd8bddd3a93f7804ef7f8fcde48bb4c37a59a09a1a97052816
      , 0x29daefb55f6f2dc6ac3f089cebcc6120b7c6fef31367b68eb7238547d32c1610
      , 0x1f2cb1624a78ee001ecbd88ad959d7012572d76f08ec5c4f9e8b7ad7b0b4e1d1 
      ]
    , [ 0x0aad2e79f15735f2bd77c0ed3d14aa27b11f092a53bbc6e1db0672ded84f31e5
      , 0x2252624f8617738cd6f661dd4094375f37028a98f1dece66091ccf1595b43f28
      , 0x1a24913a928b38485a65a84a291da1ff91c20626524b2b87d49f4f2c9018d735
      ]
    , [ 0x22fc468f1759b74d7bfc427b5f11ebb10a41515ddff497b14fd6dae1508fc47a
      , 0x1059ca787f1f89ed9cd026e9c9ca107ae61956ff0b4121d5efd65515617f6e4d
      , 0x02be9473358461d8f61f3536d877de982123011f0bf6f155a45cbbfae8b981ce
      ]
    , [ 0x0ec96c8e32962d462778a749c82ed623aba9b669ac5b8736a1ff3a441a5084a4
      , 0x292f906e073677405442d9553c45fa3f5a47a7cdb8c99f9648fb2e4d814df57e
      , 0x274982444157b86726c11b9a0f5e39a5cc611160a394ea460c63f0b2ffe5657e
      ]
    , [ 0x1acd63c67fbc9ab1626ed93491bda32e5da18ea9d8e4f10178d04aa6f8747ad0
      , 0x19f8a5d670e8ab66c4e3144be58ef6901bf93375e2323ec3ca8c86cd2a28b5a5
      , 0x1c0dc443519ad7a86efa40d2df10a011068193ea51f6c92ae1cfbb5f7b9b6893
      ] 
    , [ 0x14b39e7aa4068dbe50fe7190e421dc19fbeab33cb4f6a2c4180e4c3224987d3d
      , 0x1d449b71bd826ec58f28c63ea6c561b7b820fc519f01f021afb1e35e28b0795e
      , 0x1ea2c9a89baaddbb60fa97fe60fe9d8e89de141689d1252276524dc0a9e987fc
      ] 
    , [ 0x0478d66d43535a8cb57e9c1c3d6a2bd7591f9a46a0e9c058134d5cefdb3c7ff1
      , 0x19272db71eece6a6f608f3b2717f9cd2662e26ad86c400b21cde5e4a7b00bebe
      , 0x14226537335cab33c749c746f09208abb2dd1bd66a87ef75039be846af134166
      ] 
    , [ 0x01fd6af15956294f9dfe38c0d976a088b21c21e4a1c2e823f912f44961f9a9ce
      , 0x18e5abedd626ec307bca190b8b2cab1aaee2e62ed229ba5a5ad8518d4e5f2a57
      , 0x0fc1bbceba0590f5abbdffa6d3b35e3297c021a3a409926d0e2d54dc1c84fda6
      ] 
    ];

  component sb[3];
  for(var j=0; j<3; j++) {
    sb[j] = SBox();
    sb[j].inp <== inp[j] + round_consts[i][j];
  }

  out[0] <== 2*sb[0].out +   sb[1].out +   sb[2].out;
  out[1] <==   sb[0].out + 2*sb[1].out +   sb[2].out;
  out[2] <==   sb[0].out +   sb[1].out + 2*sb[2].out;
}

//------------------------------------------------------------------------------
// the initial linear layer

template LinearLayer() {
  signal input  inp[3];
  signal output out[3];
  out[0] <== 2*inp[0] +   inp[1] +   inp[2];
  out[1] <==   inp[0] + 2*inp[1] +   inp[2];
  out[2] <==   inp[0] +   inp[1] + 2*inp[2]; 
}

//------------------------------------------------------------------------------
// the Poseidon2 permutation for t=3

template Permutation() {
  signal input  inp[3];
  signal output out[3];

  signal aux[65][3];

  component ll = LinearLayer();
  for(var j=0; j<3; j++) { ll.inp[j] <== inp[j];    }
  for(var j=0; j<3; j++) { ll.out[j] ==> aux[0][j]; }

  component ext[8];
  for(var k=0; k<8; k++) { ext[k] = ExternalRound(k); }
 
  component int[56];
  for(var k=0; k<56; k++) { int[k] = InternalRound(k); }

  // first 4 external rounds
  for(var k=0; k<4; k++) {
    for(var j=0; j<3; j++) { ext[k].inp[j] <== aux[k  ][j]; }
    for(var j=0; j<3; j++) { ext[k].out[j] ==> aux[k+1][j]; }
  }

  // the 56 internal rounds
  for(var k=0; k<56; k++) {
    for(var j=0; j<3; j++) { int[k].inp[j] <== aux[k+4][j]; }
    for(var j=0; j<3; j++) { int[k].out[j] ==> aux[k+5][j]; }
  }

  // last 4 external rounds
  for(var k=0; k<4; k++) {
    for(var j=0; j<3; j++) { ext[k+4].inp[j] <== aux[k+60][j]; }
    for(var j=0; j<3; j++) { ext[k+4].out[j] ==> aux[k+61][j]; }
  }

  for(var j=0; j<3; j++) { out[j] <== aux[64][j]; }
}

//------------------------------------------------------------------------------
// the "compression function" takes 2 field elements as input and produces
// 1 field element as output. It is a trivial application of the permutation.

template Compression() {
  signal input  inp[2];
  signal output out;

  component perm = Permutation();
  perm.inp[0] <== inp[0];
  perm.inp[1] <== inp[1];
  perm.inp[2] <== 0;

  perm.out[0] ==> out;
}

//------------------------------------------------------------------------------