Differences between Neptune and Ethereum-based implementation of Poseidon

[storojs72]

After playing with Solidity implementation of Poseidon in context of development on-chain Nova verifier, I've noticed couple of differences in implementation between Neptune, which we treat as reference for Nova and Ethereum-based one, which I used as a starting point for a Poseidon building block for Nova. This is the patch for actual contract that uses state with 7 field elements (lines with minuses mean Ethereum-based implementation and lines with pluses are actually influenced by Neptune in order to achieve compatibility with it):

--- poseidon-actual.sol	2023-04-26 14:30:52
+++ poseidon-expected.sol	2023-05-01 19:26:35
@@ -1,18 +1,8 @@
-// SPDX-License-Identifier: Apache-2.0
-// Copyright 2017 Loopring Technology Limited.
-pragma solidity ^0.7.0;
+pragma solidity ^0.8.0;
 
-
-/// @title Poseidon hash function
-///        See: https://eprint.iacr.org/2019/458.pdf
-///        Code auto-generated by generate_poseidon_EVM_code.py
-/// @author Brecht Devos - <brecht@loopring.org>
-library Poseidon
+// This contract is for debugging/testing purposes
+library PoseidonU6
 {
-    //
-    // hash_t7f6p52
-    //
-
     struct HashInputs7
     {
         uint t0;
@@ -27,55 +17,70 @@
     function mix(HashInputs7 memory i, uint q) internal pure
     {
         HashInputs7 memory o;
-        o.t0 = mulmod(i.t0, 14183033936038168803360723133013092560869148726790180682363054735190196956789, q);
-        o.t0 = addmod(o.t0, mulmod(i.t1, 9067734253445064890734144122526450279189023719890032859456830213166173619761, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t2, 16378664841697311562845443097199265623838619398287411428110917414833007677155, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t3, 12968540216479938138647596899147650021419273189336843725176422194136033835172, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t4, 3636162562566338420490575570584278737093584021456168183289112789616069756675, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t5, 8949952361235797771659501126471156178804092479420606597426318793013844305422, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t6, 13586657904816433080148729258697725609063090799921401830545410130405357110367, q), q);
-        o.t1 = mulmod(i.t0, 2799255644797227968811798608332314218966179365168250111693473252876996230317, q);
-        o.t1 = addmod(o.t1, mulmod(i.t1, 2482058150180648511543788012634934806465808146786082148795902594096349483974, q), q);
-        o.t1 = addmod(o.t1, mulmod(i.t2, 16563522740626180338295201738437974404892092704059676533096069531044355099628, q), q);
-        o.t1 = addmod(o.t1, mulmod(i.t3, 10468644849657689537028565510142839489302836569811003546969773105463051947124, q), q);
-        o.t1 = addmod(o.t1, mulmod(i.t4, 3328913364598498171733622353010907641674136720305714432354138807013088636408, q), q);
-        o.t1 = addmod(o.t1, mulmod(i.t5, 8642889650254799419576843603477253661899356105675006557919250564400804756641, q), q);
-        o.t1 = addmod(o.t1, mulmod(i.t6, 14300697791556510113764686242794463641010174685800128469053974698256194076125, q), q);
-        o.t2 = mulmod(i.t0, 8652975463545710606098548415650457376967119951977109072274595329619335974180, q);
-        o.t2 = addmod(o.t2, mulmod(i.t1, 970943815872417895015626519859542525373809485973005165410533315057253476903, q), q);
-        o.t2 = addmod(o.t2, mulmod(i.t2, 19406667490568134101658669326517700199745817783746545889094238643063688871948, q), q);
-        o.t2 = addmod(o.t2, mulmod(i.t3, 17049854690034965250221386317058877242629221002521630573756355118745574274967, q), q);
-        o.t2 = addmod(o.t2, mulmod(i.t4, 4964394613021008685803675656098849539153699842663541444414978877928878266244, q), q);
-        o.t2 = addmod(o.t2, mulmod(i.t5, 15474947305445649466370538888925567099067120578851553103424183520405650587995, q), q);
-        o.t2 = addmod(o.t2, mulmod(i.t6, 1016119095639665978105768933448186152078842964810837543326777554729232767846, q), q);
-        o.t3 = mulmod(i.t0, 9077319817220936628089890431129759976815127354480867310384708941479362824016, q);
-        o.t3 = addmod(o.t3, mulmod(i.t1, 4770370314098695913091200576539533727214143013236894216582648993741910829490, q), q);
-        o.t3 = addmod(o.t3, mulmod(i.t2, 4298564056297802123194408918029088169104276109138370115401819933600955259473, q), q);
-        o.t3 = addmod(o.t3, mulmod(i.t3, 6905514380186323693285869145872115273350947784558995755916362330070690839131, q), q);
-        o.t3 = addmod(o.t3, mulmod(i.t4, 4783343257810358393326889022942241108539824540285247795235499223017138301952, q), q);
-        o.t3 = addmod(o.t3, mulmod(i.t5, 1420772902128122367335354247676760257656541121773854204774788519230732373317, q), q);
-        o.t3 = addmod(o.t3, mulmod(i.t6, 14172871439045259377975734198064051992755748777535789572469924335100006948373, q), q);
-        o.t4 = mulmod(i.t0, 8303849270045876854140023508764676765932043944545416856530551331270859502246, q);
-        o.t4 = addmod(o.t4, mulmod(i.t1, 20218246699596954048529384569730026273241102596326201163062133863539137060414, q), q);
-        o.t4 = addmod(o.t4, mulmod(i.t2, 1712845821388089905746651754894206522004527237615042226559791118162382909269, q), q);
-        o.t4 = addmod(o.t4, mulmod(i.t3, 13001155522144542028910638547179410124467185319212645031214919884423841839406, q), q);
-        o.t4 = addmod(o.t4, mulmod(i.t4, 16037892369576300958623292723740289861626299352695838577330319504984091062115, q), q);
-        o.t4 = addmod(o.t4, mulmod(i.t5, 19189494548480259335554606182055502469831573298885662881571444557262020106898, q), q);
-        o.t4 = addmod(o.t4, mulmod(i.t6, 19032687447778391106390582750185144485341165205399984747451318330476859342654, q), q);
-        o.t5 = mulmod(i.t0, 13272957914179340594010910867091459756043436017766464331915862093201960540910, q);
-        o.t5 = addmod(o.t5, mulmod(i.t1, 9416416589114508529880440146952102328470363729880726115521103179442988482948, q), q);
-        o.t5 = addmod(o.t5, mulmod(i.t2, 8035240799672199706102747147502951589635001418759394863664434079699838251138, q), q);
-        o.t5 = addmod(o.t5, mulmod(i.t3, 21642389080762222565487157652540372010968704000567605990102641816691459811717, q), q);
-        o.t5 = addmod(o.t5, mulmod(i.t4, 20261355950827657195644012399234591122288573679402601053407151083849785332516, q), q);
-        o.t5 = addmod(o.t5, mulmod(i.t5, 14514189384576734449268559374569145463190040567900950075547616936149781403109, q), q);
-        o.t5 = addmod(o.t5, mulmod(i.t6, 19038036134886073991945204537416211699632292792787812530208911676638479944765, q), q);
-        o.t6 = mulmod(i.t0, 15627836782263662543041758927100784213807648787083018234961118439434298020664, q);
-        o.t6 = addmod(o.t6, mulmod(i.t1, 5655785191024506056588710805596292231240948371113351452712848652644610823632, q), q);
-        o.t6 = addmod(o.t6, mulmod(i.t2, 8265264721707292643644260517162050867559314081394556886644673791575065394002, q), q);
-        o.t6 = addmod(o.t6, mulmod(i.t3, 17151144681903609082202835646026478898625761142991787335302962548605510241586, q), q);
-        o.t6 = addmod(o.t6, mulmod(i.t4, 18731644709777529787185361516475509623264209648904603914668024590231177708831, q), q);
-        o.t6 = addmod(o.t6, mulmod(i.t5, 20697789991623248954020701081488146717484139720322034504511115160686216223641, q), q);
-        o.t6 = addmod(o.t6, mulmod(i.t6, 6200020095464686209289974437830528853749866001482481427982839122465470640886, q), q);
+
+        o.t0 = 0;
+        o.t0 = addmod(o.t0, mulmod(i.t0, 0x211f5460e751918257c7624b7077624aaa362edc49241a48db6db6db24924925, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t1, 0x656ff268c469cd9f2cd29d07086d9d04a945ef829ffe907f1fffffff20000001, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t2, 0x19c308bd25b13848eef068e557794c72f62a247271c6bf1c38e38e38aaaaaaab, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t3, 0x22c74bcc2615a595a8f7c0cf3616f401991f4acdb332b532e66666661999999a, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t4, 0x6963af62e003892a5d1d50074e93217934daf23145cff68aba2e8ba200000001, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t5, 0x6a44840c3b7b082cd99fb0b208d45b5a376dd6581553d4546aaaaaa9c0000001, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t6, 0x6217dc5a0f85429f8dce7bb808267bb5bd02ed3d9d88753a3b13b13a3b13b13c, q), q);
+
+        o.t1 = 0;
+        o.t1 = addmod(o.t1, mulmod(i.t0, 0x656ff268c469cd9f2cd29d07086d9d04a945ef829ffe907f1fffffff20000001, q), q);
+        o.t1 = addmod(o.t1, mulmod(i.t1, 0x19c308bd25b13848eef068e557794c72f62a247271c6bf1c38e38e38aaaaaaab, q), q);
+        o.t1 = addmod(o.t1, mulmod(i.t2, 0x22c74bcc2615a595a8f7c0cf3616f401991f4acdb332b532e66666661999999a, q), q);
+        o.t1 = addmod(o.t1, mulmod(i.t3, 0x6963af62e003892a5d1d50074e93217934daf23145cff68aba2e8ba200000001, q), q);
+        o.t1 = addmod(o.t1, mulmod(i.t4, 0x6a44840c3b7b082cd99fb0b208d45b5a376dd6581553d4546aaaaaa9c0000001, q), q);
+        o.t1 = addmod(o.t1, mulmod(i.t5, 0x6217dc5a0f85429f8dce7bb808267bb5bd02ed3d9d88753a3b13b13a3b13b13c, q), q);
+        o.t1 = addmod(o.t1, mulmod(i.t6, 0x4a867dda0877876545809d29bd0c9d27fef9e96fa4913b23edb6db6d12492493, q), q);
+
+        o.t2 = 0;
+        o.t2 = addmod(o.t2, mulmod(i.t0, 0x19c308bd25b13848eef068e557794c72f62a247271c6bf1c38e38e38aaaaaaab, q), q);
+        o.t2 = addmod(o.t2, mulmod(i.t1, 0x22c74bcc2615a595a8f7c0cf3616f401991f4acdb332b532e66666661999999a, q), q);
+        o.t2 = addmod(o.t2, mulmod(i.t2, 0x6963af62e003892a5d1d50074e93217934daf23145cff68aba2e8ba200000001, q), q);
+        o.t2 = addmod(o.t2, mulmod(i.t3, 0x6a44840c3b7b082cd99fb0b208d45b5a376dd6581553d4546aaaaaa9c0000001, q), q);
+        o.t2 = addmod(o.t2, mulmod(i.t4, 0x6217dc5a0f85429f8dce7bb808267bb5bd02ed3d9d88753a3b13b13a3b13b13c, q), q);
+        o.t2 = addmod(o.t2, mulmod(i.t5, 0x4a867dda0877876545809d29bd0c9d27fef9e96fa4913b23edb6db6d12492493, q), q);
+        o.t2 = addmod(o.t2, mulmod(i.t6, 0x3dd414f92742ed7bd70dc88cd1efeaad81febddf77769776eeeeeeee66666667, q), q);
+
+        o.t3 = 0;
+        o.t3 = addmod(o.t3, mulmod(i.t0, 0x22c74bcc2615a595a8f7c0cf3616f401991f4acdb332b532e66666661999999a, q), q);
+        o.t3 = addmod(o.t3, mulmod(i.t1, 0x6963af62e003892a5d1d50074e93217934daf23145cff68aba2e8ba200000001, q), q);
+        o.t3 = addmod(o.t3, mulmod(i.t2, 0x6a44840c3b7b082cd99fb0b208d45b5a376dd6581553d4546aaaaaa9c0000001, q), q);
+        o.t3 = addmod(o.t3, mulmod(i.t3, 0x6217dc5a0f85429f8dce7bb808267bb5bd02ed3d9d88753a3b13b13a3b13b13c, q), q);
+        o.t3 = addmod(o.t3, mulmod(i.t4, 0x4a867dda0877876545809d29bd0c9d27fef9e96fa4913b23edb6db6d12492493, q), q);
+        o.t3 = addmod(o.t3, mulmod(i.t5, 0x3dd414f92742ed7bd70dc88cd1efeaad81febddf77769776eeeeeeee66666667, q), q);
+        o.t3 = addmod(o.t3, mulmod(i.t6, 0x6caeccddf703a573b0063a878907ba84fe81c9c2cffe763f0fffffff10000001, q), q);
+
+        o.t4 = 0;
+        o.t4 = addmod(o.t4, mulmod(i.t0, 0x6963af62e003892a5d1d50074e93217934daf23145cff68aba2e8ba200000001, q), q);
+        o.t4 = addmod(o.t4, mulmod(i.t1, 0x6a44840c3b7b082cd99fb0b208d45b5a376dd6581553d4546aaaaaa9c0000001, q), q);
+        o.t4 = addmod(o.t4, mulmod(i.t2, 0x6217dc5a0f85429f8dce7bb808267bb5bd02ed3d9d88753a3b13b13a3b13b13c, q), q);
+        o.t4 = addmod(o.t4, mulmod(i.t3, 0x4a867dda0877876545809d29bd0c9d27fef9e96fa4913b23edb6db6d12492493, q), q);
+        o.t4 = addmod(o.t4, mulmod(i.t4, 0x3dd414f92742ed7bd70dc88cd1efeaad81febddf77769776eeeeeeee66666667, q), q);
+        o.t4 = addmod(o.t4, mulmod(i.t5, 0x6caeccddf703a573b0063a878907ba84fe81c9c2cffe763f0fffffff10000001, q), q);
+        o.t4 = addmod(o.t4, mulmod(i.t6, 0x1b46fa31af7059b6a2a432d4b6f8e788c868db4bffff9d2cf0f0f0f0b4b4b4b5, q), q);
+
+        o.t5 = 0;
+        o.t5 = addmod(o.t5, mulmod(i.t0, 0x6a44840c3b7b082cd99fb0b208d45b5a376dd6581553d4546aaaaaa9c0000001, q), q);
+        o.t5 = addmod(o.t5, mulmod(i.t1, 0x6217dc5a0f85429f8dce7bb808267bb5bd02ed3d9d88753a3b13b13a3b13b13c, q), q);
+        o.t5 = addmod(o.t5, mulmod(i.t2, 0x4a867dda0877876545809d29bd0c9d27fef9e96fa4913b23edb6db6d12492493, q), q);
+        o.t5 = addmod(o.t5, mulmod(i.t3, 0x3dd414f92742ed7bd70dc88cd1efeaad81febddf77769776eeeeeeee66666667, q), q);
+        o.t5 = addmod(o.t5, mulmod(i.t4, 0x6caeccddf703a573b0063a878907ba84fe81c9c2cffe763f0fffffff10000001, q), q);
+        o.t5 = addmod(o.t5, mulmod(i.t5, 0x1b46fa31af7059b6a2a432d4b6f8e788c868db4bffff9d2cf0f0f0f0b4b4b4b5, q), q);
+        o.t5 = addmod(o.t5, mulmod(i.t6, 0x46d8580827a75ac891152076b08d923c24f3e43ab8e28d8d9c71c71bd5555556, q), q);
+
+        o.t6 = 0;
+        o.t6 = addmod(o.t6, mulmod(i.t0, 0x6217dc5a0f85429f8dce7bb808267bb5bd02ed3d9d88753a3b13b13a3b13b13c, q), q);
+        o.t6 = addmod(o.t6, mulmod(i.t1, 0x4a867dda0877876545809d29bd0c9d27fef9e96fa4913b23edb6db6d12492493, q), q);
+        o.t6 = addmod(o.t6, mulmod(i.t2, 0x3dd414f92742ed7bd70dc88cd1efeaad81febddf77769776eeeeeeee66666667, q), q);
+        o.t6 = addmod(o.t6, mulmod(i.t3, 0x6caeccddf703a573b0063a878907ba84fe81c9c2cffe763f0fffffff10000001, q), q);
+        o.t6 = addmod(o.t6, mulmod(i.t4, 0x1b46fa31af7059b6a2a432d4b6f8e788c868db4bffff9d2cf0f0f0f0b4b4b4b5, q), q);
+        o.t6 = addmod(o.t6, mulmod(i.t5, 0x46d8580827a75ac891152076b08d923c24f3e43ab8e28d8d9c71c71bd5555556, q), q);
+        o.t6 = addmod(o.t6, mulmod(i.t6, 0x6dd3abfdf187ba0e815f38736770e79941dc14a486bb13c9286bca1a00000001, q), q);
+
         i.t0 = o.t0;
         i.t1 = o.t1;
         i.t2 = o.t2;
@@ -85,16 +90,18 @@
         i.t6 = o.t6;
     }
 
-    function ark(HashInputs7 memory i, uint q, uint c) internal pure
+    function ark(HashInputs7 memory i, uint q, HashInputs7 memory c) internal pure
     {
         HashInputs7 memory o;
-        o.t0 = addmod(i.t0, c, q);
-        o.t1 = addmod(i.t1, c, q);
-        o.t2 = addmod(i.t2, c, q);
-        o.t3 = addmod(i.t3, c, q);
-        o.t4 = addmod(i.t4, c, q);
-        o.t5 = addmod(i.t5, c, q);
-        o.t6 = addmod(i.t6, c, q);
+
+        o.t0 = addmod(i.t0, c.t0, q);
+        o.t1 = addmod(i.t1, c.t1, q);
+        o.t2 = addmod(i.t2, c.t2, q);
+        o.t3 = addmod(i.t3, c.t3, q);
+        o.t4 = addmod(i.t4, c.t4, q);
+        o.t5 = addmod(i.t5, c.t5, q);
+        o.t6 = addmod(i.t6, c.t6, q);
+
         i.t0 = o.t0;
         i.t1 = o.t1;
         i.t2 = o.t2;
@@ -107,6 +114,7 @@
     function sbox_full(HashInputs7 memory i, uint q) internal pure
     {
         HashInputs7 memory o;
+
         o.t0 = mulmod(i.t0, i.t0, q);
         o.t0 = mulmod(o.t0, o.t0, q);
         o.t0 = mulmod(i.t0, o.t0, q);
@@ -128,6 +136,7 @@
         o.t6 = mulmod(i.t6, i.t6, q);
         o.t6 = mulmod(o.t6, o.t6, q);
         o.t6 = mulmod(i.t6, o.t6, q);
+
         i.t0 = o.t0;
         i.t1 = o.t1;
         i.t2 = o.t2;
@@ -140,13 +149,15 @@
     function sbox_partial(HashInputs7 memory i, uint q) internal pure
     {
         HashInputs7 memory o;
+
         o.t0 = mulmod(i.t0, i.t0, q);
         o.t0 = mulmod(o.t0, o.t0, q);
         o.t0 = mulmod(i.t0, o.t0, q);
+
         i.t0 = o.t0;
     }
 
-    function hash_t7f6p52(HashInputs7 memory i, uint q) internal pure returns (uint)
+    function hash(HashInputs7 memory i, uint q) internal pure returns (uint)
     {
         // validate inputs
         require(i.t0 < q, "INVALID_INPUT");
@@ -158,238 +169,710 @@
         require(i.t6 < q, "INVALID_INPUT");
 
         // round 0
-        ark(i, q, 14397397413755236225575615486459253198602422701513067526754101844196324375522);
+        ark(i, q, HashInputs7(0x5c72d2cf405b5ee824e54cb1ff5acb1776802428b042df9b59fa85e4eb3e8f6f,
+            0x624229fe6c8a33fdc6adfa1eaefb7a386f2b40c5d594f75d8381bf19d010abdf,
+            0x3f3fb27ffa569ded5564b5ee766a6721716e1c116ecd368f86a7ac621199534d,
+            0x6bc1c463efa733daf6b6894e11420e6bd6dc4e5a733acadc763d5b15d46d232a,
+            0x53aea0de8570cc9f15d9f4583b11b26daadbb93bd8c2baf566aa0a187bcf921c,
+            0x696acc17fb193072de5c433545f0965c9dfb9399ed69610dc1f1bf8cd3fd4307,
+            0x38e4c6a3ba2fae3fdea2e8305a3697d400dede47e9757491dee804cb481ad3ff)
+        );
         sbox_full(i, q);
         mix(i, q);
         // round 1
-        ark(i, q, 10405129301473404666785234951972711717481302463898292859783056520670200613128);
+        ark(i, q, HashInputs7(0x1bedebbaba6bc9813a18893ae03ccc6ae4739f5b8328a0a81dab7520b732c4e4,
+            0x1d872276362e1dfede391e27b07f6f2c7e1b3d16b43d36ca237327cb7bc0cc76,
+            0x42e75f20845bbefe97754318d130eaf9979aa461374ff7b4e9554d3f148a6634,
+            0x1378a0b5a34df9251874462d6e1c52cb1494773b44ba283a0957e8ddbe263e1a,
+            0x616f1b20dc03b8f23d2556bf34fadabc0b16da6e41f2ec9de53a04d803c1fe28,
+            0x0f7dd801d109c0b6ec88aff4cfeebca848d0165ac216817068cf6257b45324fe,
+            0x22b1ac9391e9e5af16cff7d8be66daa4b574c43aab0faa6755a6ec5d794dd49f)
+        );
         sbox_full(i, q);
         mix(i, q);
         
         . . . . . 
         
+        sbox_full(i, q);
+        mix(i, q);
+        // round 63
+        ark(i, q, HashInputs7(0x6ac1bb81c105b2f9ef1d82ca4116b3021fe23f890b5a3243255ccfc779ea9c7c,
+            0x39661628909ad370900218489f94998f6e1a42fc333a3ec398623130178ace64,
+            0x050b292ff4cd04ed85951ef4c5b3975f32fc64f227c6f10a505b44bc87d8a54e,
+            0x5b8ded68b5f14f9c165b21995e1b05b886934122d1f80a9abdbe8caec13d0f2a,
+            0x6b7fa371c3ce3501e920cee9b0097297081368d59ca53aaa4c8e881cc4a4c508,
+            0x67e56fa92dc682a1bf0f200927d654b736979e839ff37a7366c414bd606457ff,
+            0x01a7f67a18ed57241d2b6202db1f222739f2c4b203f86fe0f1aa29d2338d3f38)
+        );
+        sbox_full(i, q);
+        mix(i, q);
 
-        return i.t0;
+        return i.t1;
     }
 }

Also, probably the differences in generator might be more expressive, so let me also show them in this context:

--- generate_poseidon_EVM_code_original.py	2023-05-01 20:19:54
+++ generate_poseidon_EVM_code.py	2023-04-28 16:54:01
@@ -1,11 +1,7 @@
-import sys
-sys.path.insert(0, 'ethsnarks')
-import os.path
+from collections import namedtuple
+
 import json
 
-from ethsnarks.poseidon import poseidon, poseidon_params
-from ethsnarks.field import SNARK_SCALAR_FIELD
-
 def sigma_EVM_asm(o, t):
     it = "i.t" + str(t)
     ot = "o.t" + str(t)
@@ -33,18 +29,24 @@
         for j in range(params.t):
             mulmod = "mulmod(i.t" + str(j) + ", " + str(params.constants_M[i][j]) + ", q)"
             if j == 0:
-                o = o + "o.t" + str(i) + " = " + mulmod + ";\n"
+                o = o + "\no.t" + str(i) + " = 0;\n"
+                o = o + "o.t" + str(i) + " = addmod(o.t" + str(i) + ", " + mulmod + ", q);\n"
             else:
                 o = o + "o.t" + str(i) + " = addmod(o.t" + str(i) + ", " + mulmod + ", q);\n"
+
+    o = o + "\n"
     for i in range(params.t):
         o = o + "i.t" + str(i) + " = o.t" + str(i) + ";\n"
     o = o + "}\n"
     o = o + "\n"
 
-    o = o + "function ark(" + struct + " memory i, uint q, uint c) internal pure \n{\n"
+    o = o + "function ark(" + struct + " memory i, uint q, " + struct + " memory c) internal pure \n{\n"
     o = o + struct + " memory o;\n"
+    o = o + "\n"
     for t in range(params.t):
-        o = o + "o.t" + str(t) + " = addmod(i.t" + str(t) + ", c, q);\n"
+        o = o + "o.t" + str(t) + " = addmod(i.t" + str(t) + ", c.t" + str(t) + ", q);\n"
+
+    o = o + "\n"
     for i in range(params.t):
         o = o + "i.t" + str(i) + " = o.t" + str(i) + ";\n"
     o = o + "}\n"
@@ -52,8 +54,12 @@
 
     o = o + "function sbox_full(" + struct + " memory i, uint q) internal pure \n{\n"
     o = o + struct + " memory o;\n"
+
+    o = o + "\n"
     for j in range(params.t):
         o = sigma_EVM_asm(o, j)
+
+    o = o + "\n"
     for i in range(params.t):
         o = o + "i.t" + str(i) + " = o.t" + str(i) + ";\n"
     o = o + "}\n"
@@ -61,21 +67,31 @@
 
     o = o + "function sbox_partial(" + struct + " memory i, uint q) internal pure \n{\n"
     o = o + struct + " memory o;\n"
+    o = o + "\n"
     o = sigma_EVM_asm(o, 0)
+    o = o + "\n"
     for i in range(1):
         o = o + "i.t" + str(i) + " = o.t" + str(i) + ";\n"
     o = o + "}\n"
     o = o + "\n"
 
-    o = o + "function hash_t6f6p52(" + struct + " memory i, uint q) internal pure returns (uint)\n{\n"
+    o = o + "function hash(" + struct + " memory i, uint q) internal pure returns (uint)\n{\n"
     o = o + "// validate inputs\n"
     for i in range(params.t):
         o = o + "require(i.t" + str(i) + " < q, \"INVALID_INPUT\");\n"
     o = o + "\n"
     for i in range(params.nRoundsF + params.nRoundsP):
         o = o + "// round " + str(i) + "\n"
+
+        constants_C_for_round = ""
+        for j in range(params.t):
+            if j != t:
+                constants_C_for_round = constants_C_for_round + str(params.constants_C[i * (t + 1) + j]) + ",\n"
+            else:
+                constants_C_for_round = constants_C_for_round + str(params.constants_C[i * (t + 1) + j])
+
         # ark
-        o = o + "ark(i, q, " + str(params.constants_C[i]) + ");\n"
+        o = o + "ark(i, q, " + struct + "(" + constants_C_for_round + ")\n);\n"
         # sbox
         if (i < params.nRoundsF/2) or (i >= params.nRoundsF/2 + params.nRoundsP):
             o = o + "sbox_full(i, q);\n"
@@ -83,12 +99,29 @@
             o = o + "sbox_partial(i, q);\n"
         # mix
         o = o + "mix(i, q);\n"
-    o = o + "\nreturn i.t0;\n"
+    o = o + "\nreturn i.t1;\n"
     o = o + "}\n"
     o = o + "\n"
 
     return o
 
-poseidonParamsEVM = poseidon_params(SNARK_SCALAR_FIELD, 6, 6, 52, b'poseidon', 5, security_target=128)
+
+PoseidonParamsType = namedtuple('_PoseidonParams', ('t', 'nRoundsF', 'nRoundsP', 'constants_C', 'constants_M'))
+
+f = open('neptune-generated-u24.json')
+data = json.load(f)
+
+t = int(data['state_size_field_elements'])
+nRoundsF = int(data['full_rounds'])
+nRoundsP = int(data['partial_rounds'])
+constants_C = list(data['round_constants'])
+matrix_M = data['matrix_M']
+
+constants_M = []
+for matrix in matrix_M:
+    constants_M.append(matrix)
+
+poseidonParamsEVM = PoseidonParamsType(t, nRoundsF, nRoundsP, constants_C, constants_M)
+
 data = poseidon_EVM_asm(poseidonParamsEVM)
 print(data)

Essentially, these are the differences:

• in AddRoundConstant (ark) function, Neptune uses multiple constants (different one for each field element in the state) for adding to the state, while Ethereum uses one constant for adding to all elements in the state:

-    function ark(HashInputs7 memory i, uint q, uint c) internal pure
+    function ark(HashInputs7 memory i, uint q, HashInputs7 memory c) internal pure
     {
         HashInputs7 memory o;
-        o.t0 = addmod(i.t0, c, q);
-        o.t1 = addmod(i.t1, c, q);
-        o.t2 = addmod(i.t2, c, q);
-        o.t3 = addmod(i.t3, c, q);
-        o.t4 = addmod(i.t4, c, q);
-        o.t5 = addmod(i.t5, c, q);
-        o.t6 = addmod(i.t6, c, q);
+
+        o.t0 = addmod(i.t0, c.t0, q);
+        o.t1 = addmod(i.t1, c.t1, q);
+        o.t2 = addmod(i.t2, c.t2, q);
+        o.t3 = addmod(i.t3, c.t3, q);
+        o.t4 = addmod(i.t4, c.t4, q);
+        o.t5 = addmod(i.t5, c.t5, q);
+        o.t6 = addmod(i.t6, c.t6, q);

• A bit different initialisation of temporary state in mix function:

-        o.t0 = mulmod(i.t0, 141830339360381688033607 ... 180682363054735190196956789, q);
-        o.t0 = addmod(o.t0, mulmod(i.t1, 9067734253445064890734144122526450279 ... 859456830213166173619761, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t2, 1637866484169731156284544309 ... 7411428110917414833007677155, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t3, 129685402164799381386475968991476 ... 176422194136033835172, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t4, 363616256256633842049057557058427 ... 9112789616069756675, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t5, 894995236123579777165950112647115617 .... 97426318793013844305422, q), q);
-        o.t0 = addmod(o.t0, mulmod(i.t6, 13586657904816433 .... 1830545410130405357110367, q), q);

. . .  

+
+        o.t0 = 0;
+        o.t0 = addmod(o.t0, mulmod(i.t0, 0x211f5460e751918257c7624b7077624aaa362edc49241a48db6db6db24924925, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t1, 0x656ff268c469cd9f2cd29d07086d9d04a945ef829ffe907f1fffffff20000001, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t2, 0x19c308bd25b13848eef068e557794c72f62a247271c6bf1c38e38e38aaaaaaab, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t3, 0x22c74bcc2615a595a8f7c0cf3616f401991f4acdb332b532e66666661999999a, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t4, 0x6963af62e003892a5d1d50074e93217934daf23145cff68aba2e8ba200000001, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t5, 0x6a44840c3b7b082cd99fb0b208d45b5a376dd6581553d4546aaaaaa9c0000001, q), q);
+        o.t0 = addmod(o.t0, mulmod(i.t6, 0x6217dc5a0f85429f8dce7bb808267bb5bd02ed3d9d88753a3b13b13a3b13b13c, q), q);
+

• Ethereum uses randomised constants (based on input seed), while Neptune, uses deterministic constants;
• Ethereum validates input parameters to prevent known Grobner and Interpolation attacks (may be it is the same in Neptune, but I didn't find mentions about that).

I can't judge about cryptographic implications, but would like to pay attention, as soon as security is important.

[porcuquine]

A few quick thoughts:

• If you don't want to use the sparse-matrix optimizations, you can get the 'original' constants from Neptune. That should then allow using the simpler algorithm. This will reduce the size of the constants, but at the cost of more expensive hashing.
• I don't think the validation is important in this context, since the goal is not general-purpose — but rather just to correctly perform Poseidon hashing for parameters already selected for Nova.

[storojs72]

Ok. May be @huitseeker will add more thoughts here. I would probably think over adding randomisation based on some seed data for our constants generation, then we can have different constants for each application that utilises neptune, even if other parameters are same (security level, arity, etc.). it may potentially complicate an statistical cryptanalysis efforts from potential adversaries