New Version of Poseidon

circuits/README.md

@@ -780,7 +780,7 @@ Implementation of Poseidon hash function (LINK)
     - BENCHMARKS
     - EXAMPLE
 
-- `Ark(t, C)`
+- `Ark(t, C, r)`
 
     - DESCRIPTION
     - SCHEMA
@@ -798,7 +798,7 @@ Implementation of Poseidon hash function (LINK)
     - BENCHMARKS
     - EXAMPLE
 
-- `Poseidon(nInputs, t, nRoundsF, nRoundsP)`
+- `Poseidon(nInputs)`
 
     - DESCRIPTION
     - SCHEMA

circuits/eddsaposeidon.circom

@@ -51,7 +51,7 @@ template EdDSAPoseidonVerifier() {
 
 // Calculate the h = H(R,A, msg)
 
-    component hash = Poseidon(5, 6, 8, 57);
+    component hash = Poseidon(5);
 
     hash.inputs[0] <== R8x;
     hash.inputs[1] <== R8y;

circuits/smt/smthash_poseidon.circom

@@ -29,7 +29,7 @@ template SMTHash1() {
     signal input value;
     signal output out;
 
-    component h = Poseidon(3, 6, 8, 57);   // Constant
+    component h = Poseidon(3);   // Constant
     h.inputs[0] <== key;
     h.inputs[1] <== value;
     h.inputs[2] <== 1;
@@ -48,7 +48,7 @@ template SMTHash2() {
     signal input R;
     signal output out;
 
-    component h = Poseidon(2, 6, 8, 57);   // Constant
+    component h = Poseidon(2);   // Constant
     h.inputs[0] <== L;
     h.inputs[1] <== R;
 

src/eddsa.js

@@ -112,8 +112,7 @@ function signPoseidon(prv, msg) {
     const Fr = new F1Field(babyJub.subOrder);
     r = Fr.e(r);
     const R8 = babyJub.mulPointEscalar(babyJub.Base8, r);
-    const hash = poseidon.createHash(6, 8, 57);
+    const hm = poseidon([R8[0], R8[1], A[0], A[1], msg]);
-    const hm = hash([R8[0], R8[1], A[0], A[1], msg]);
     const S = Fr.add(r , Fr.mul(hm, s));
     return {
         R8: R8,
@@ -180,8 +179,7 @@ function verifyPoseidon(msg, sig, A) {
     if (!babyJub.inCurve(A)) return false;
     if (sig.S>= babyJub.subOrder) return false;
 
-    const hash = poseidon.createHash(6, 8, 57);
+    const hm = poseidon([sig.R8[0], sig.R8[1], A[0], A[1], msg]);
-    const hm = hash([sig.R8[0], sig.R8[1], A[0], A[1], msg]);
 
     const Pleft = babyJub.mulPointEscalar(babyJub.Base8, sig.S);
     let Pright = babyJub.mulPointEscalar(A, Scalar.mul(hm, 8));

src/evmasm.js

@@ -154,6 +154,17 @@ class Contract {
     }
 
     push(data) {
+        if (typeof data === "number") {
+            let isNeg;
+            if (data<0) {
+                isNeg = true;
+                data = -data;
+            }
+            data = data.toString(16);
+            if (data.length % 2 == 1) data = "0" + data;
+            data = "0x" + data;
+            if (isNeg) data = "-"+data;
+        }
         const d = Web3Utils.hexToBytes(Web3Utils.toHex(data));
         if (d.length == 0 || d.length > 32) {
             throw new Error("Assertion failed");

src/poseidon.js

@@ -1,121 +1,49 @@
-const Scalar = require("ffjavascript").Scalar;
-const blake2b = require("blake2b");
 const assert = require("assert");
+const Scalar = require("ffjavascript").Scalar;
 const ZqField = require("ffjavascript").ZqField;
-const utils = require("ffjavascript").utils;
+const { unstringifyBigInts } = require("ffjavascript").utils;
 
+// Prime 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
 const F = new ZqField(Scalar.fromString("21888242871839275222246405745257275088548364400416034343698204186575808495617"));
-exports.F = F;
 
-const SEED = "poseidon";
+// Parameters are generated by a reference script https://extgit.iaik.tugraz.at/krypto/hadeshash/-/blob/master/code/generate_parameters_grain.sage
-const NROUNDSF = 8;
+// Used like so: sage generate_parameters_grain.sage 1 0 254 2 8 56 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
-const NROUNDSP = 57;
+const { C, M } = unstringifyBigInts(require("./poseidon_constants.json"));
-const T = 6;
 
-function getPseudoRandom(seed, n) {
+// Using recommended parameters from whitepaper https://eprint.iacr.org/2019/458.pdf (table 2, table 8)
-    const res = [];
+// Generated by https://extgit.iaik.tugraz.at/krypto/hadeshash/-/blob/master/code/calc_round_numbers.py
-    let input = Buffer.from(seed);
+// And rounded up to nearest integer that divides by t
-    let h = blake2b(32).update(input).digest();
+const N_ROUNDS_F = 8;
-    while (res.length<n) {
+const N_ROUNDS_P = [56, 57, 56, 60, 60, 63, 64, 63];
-        const n = F.normalize(utils.leBuff2int(Buffer.from(h)));
-        res.push(n);
-        h = blake2b(32).update(h).digest();
-    }
 
-    return res;
+const pow5 = a => F.mul(a, F.square(F.square(a, a)));
-}
 
-function allDifferent(v) {
+function poseidon(inputs) {
-    for (let i=0; i<v.length; i++) {
-        if (F.isZero(v[i])) return false;
-        for (let j=i+1; j<v.length; j++) {
-            if (F.eq(v[i],v[j])) return false;
-        }
-    }
-    return true;
-}
-
-exports.getMatrix = (t, seed, nRounds) => {
-    if (typeof seed === "undefined") seed = SEED;
-    if (typeof nRounds === "undefined") nRounds = NROUNDSF + NROUNDSP;
-    if (typeof t === "undefined") t = T;
-    assert(t<=6);  // Force the same matrix for all.
-    t=6;
-    let nonce = "0000";
-    let cmatrix = getPseudoRandom(seed+"_matrix_"+nonce, t*2);
-    while (!allDifferent(cmatrix)) {
-        nonce = (Number(nonce)+1)+"";
-        while(nonce.length<4) nonce = "0"+nonce;
-        cmatrix = getPseudoRandom(seed+"_matrix_"+nonce, t*2);
-    }
-
-    const M = new Array(t);
-    for (let i=0; i<t; i++) {
-        M[i] = new Array(t);
-        for (let j=0; j<t; j++) {
-            M[i][j] = F.normalize(F.inv(F.sub(cmatrix[i], cmatrix[t+j])));
-        }
-    }
-    return M;
-};
-
-exports.getConstants = (t, seed, nRounds) => {
-    if (typeof seed === "undefined") seed = SEED;
-    if (typeof nRounds === "undefined") nRounds = NROUNDSF + NROUNDSP;
-    if (typeof t === "undefined") t = T;
-    const cts = getPseudoRandom(seed+"_constants", nRounds);
-    return cts;
-};
-
-function ark(state, c) {
-    for (let j=0; j<state.length; j++ ) {
-        state[j] = F.add(state[j], c);
-    }
-}
-
-function sigma(a) {
-    return F.mul(a, F.square(F.square(a,a)));
-}
-
-function mix(state, M) {
-    const newState = new Array(state.length);
-    for (let i=0; i<state.length; i++) {
-        newState[i] = F.zero;
-        for (let j=0; j<state.length; j++) {
-            newState[i] = F.add(newState[i], F.mul(M[i][j], state[j]) );
-        }
-    }
-    for (let i=0; i<state.length; i++) state[i] = newState[i];
-}
-
-exports.createHash = (t, nRoundsF, nRoundsP, seed) => {
-
-    if (typeof seed === "undefined") seed = SEED;
-    if (typeof nRoundsF === "undefined") nRoundsF = NROUNDSF;
-    if (typeof nRoundsP === "undefined") nRoundsP = NROUNDSP;
-    if (typeof t === "undefined") t = T;
-
-    assert(nRoundsF % 2 == 0);
-    const C = exports.getConstants(t, seed, nRoundsF + nRoundsP);
-    const M = exports.getMatrix(t, seed, nRoundsF + nRoundsP);
-    return function(inputs) {
-        let state = [];
-        assert(inputs.length <= t);
     assert(inputs.length > 0);
-        for (let i=0; i<inputs.length; i++) state[i] = F.e(inputs[i]);
+    assert(inputs.length < N_ROUNDS_P.length - 1);
-        for (let i=inputs.length; i<t; i++) state[i] = F.zero;
 
-        for (let i=0; i< nRoundsF + nRoundsP; i++) {
+    const t = inputs.length + 1;
-            ark(state, C[i]);
+    const nRoundsF = N_ROUNDS_F;
-            if ((i<nRoundsF/2) || (i >= nRoundsF/2 + nRoundsP)) {
+    const nRoundsP = N_ROUNDS_P[t - 2];
-                for (let j=0; j<t; j++) state[j] = sigma(state[j]);
+
+    let state = [...inputs.map(a => F.e(a)), F.zero];
+    for (let r = 0; r < nRoundsF + nRoundsP; r++) {
+        state = state.map((a, i) => F.add(a, C[t - 2][r * t + i]));
+
+        if (r < nRoundsF / 2 || r >= nRoundsF / 2 + nRoundsP) {
+            state = state.map(a => pow5(a));
         } else {
-                state[0] = sigma(state[0]);
+            state[0] = pow5(state[0]);
+        }
+
+        // no matrix multiplication in the last round
+        if (r < nRoundsF + nRoundsP - 1) {
+            state = state.map((_, i) =>
+                state.reduce((acc, a, j) => F.add(acc, F.mul(M[t - 2][j][i], a)), F.zero)
+            );
         }
-            mix(state, M);
     }
     return F.normalize(state[0]);
-    };
+}
-};
-
 
+module.exports = poseidon;

src/poseidon_gencontract.js

@@ -2,14 +2,13 @@
 // License: LGPL-3.0+
 //
 
-const Poseidon = require("./poseidon.js");
-
 const Contract = require("./evmasm");
+const { unstringifyBigInts } = require("ffjavascript").utils;
 
-const SEED = "poseidon";
+const { C:K, M } = unstringifyBigInts(require("./poseidon_constants.json"));
-const NROUNDSF = 8;
+
-const NROUNDSP = 57;
+const N_ROUNDS_F = 8;
-const T = 6;
+const N_ROUNDS_P = [56, 57, 56, 60, 60, 63, 64, 63];
 
 function toHex256(a) {
     let S = a.toString(16);
@@ -17,38 +16,38 @@ function toHex256(a) {
     return "0x" + S;
 }
 
-function createCode(t, nRoundsF, nRoundsP, seed) {
+function createCode(nInputs) {
-    if (typeof seed === "undefined") seed = SEED;
+
-    if (typeof nRoundsF === "undefined") nRoundsF = NROUNDSF;
+    if (( nInputs<1) || (nInputs>8)) throw new Error("Invalid number of inputs. Must be 1<=nInputs<=8");
-    if (typeof nRoundsP === "undefined") nRoundsP = NROUNDSP;
+    const t = nInputs + 1;
-    if (typeof t === "undefined") t = T;
+    const nRoundsF = N_ROUNDS_F;
+    const nRoundsP = N_ROUNDS_P[t - 2];
+
+//    const nRoundsF = 2;
+//    const nRoundsP = 2;
 
-    const K = Poseidon.getConstants(t, seed, nRoundsP + nRoundsF);
-    const M = Poseidon.getMatrix(t, seed, nRoundsP + nRoundsF);
 
     const C = new Contract();
 
     function saveM() {
         for (let i=0; i<t; i++) {
             for (let j=0; j<t; j++) {
-                C.push(toHex256(M[i][j]));
+                C.push(toHex256(M[t-2][j][i]));
                 C.push((1+i*t+j)*32);
                 C.mstore();
             }
         }
     }
 
-    function ark(r) {
+    function ark(r) {   // st, q
-        C.push(toHex256(K[r])); // K, st, q
         for (let i=0; i<t; i++) {
-            C.dup(1+t); // q, K, st, q
+            C.dup(t); // q, st, q
-            C.dup(1);   // K, q, K, st, q
+            C.push(toHex256(K[t-2][r*t+i]));  // K, q, st, q
-            C.dup(3+i); // st[i], K, q, K, st, q
+            C.dup(2+i); // st[i], K, q, st, q
-            C.addmod(); // newSt[i], K, st, q
+            C.addmod(); // newSt[i], st, q
-            C.swap(2 + i); // xx, K, st, q
+            C.swap(1 + i); // xx, st, q
             C.pop();
         }
-        C.pop();
     }
 
     function sigma(p) {
@@ -115,17 +114,17 @@ function createCode(t, nRoundsF, nRoundsP, seed) {
 
     C.push("0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001");  // q
 
-    // Load 6 values from the call data.
+    // Load t values from the call data.
     // The function has a single array param param
     // [Selector (4)] [Pointer (32)][Length (32)] [data1 (32)] ....
-    // We ignore the pointer and the length and just load 6 values to the state
+    // We ignore the pointer and the length and just load t values to the state
-    // (Stack positions 0-5) If the array is shorter, we just set zeros.
+    // (Stack positions 0-{t-1}) If the array is shorter, we just set zeros.
     for (let i=0; i<t; i++) {
         C.push(0x44+(0x20*(t-1-i)));
         C.calldataload();
     }
 
-    for (let i=0; i<nRoundsF+nRoundsP; i++) {
+    for (let i=0; i<nRoundsF+nRoundsP-1; i++) {
         ark(i);
         if ((i<nRoundsF/2) || (i>=nRoundsP+nRoundsF/2)) {
             for (let j=0; j<t; j++) {
@@ -142,6 +141,13 @@ function createCode(t, nRoundsF, nRoundsP, seed) {
         C.label(strLabel);
     }
 
+    C.push(toHex256(K[t-2][(nRoundsF+nRoundsP-1)*t]));  // K, st, q
+    C.dup(t+1); // q, K, st, q
+    C.swap(2);  // st[0], K, q, st\st[0]
+    C.addmod();  // st q
+
+    sigma(0);
+
     C.push("0x00");
     C.mstore();     // Save it to pos 0;
     C.push("0x20");

src/poseidon_printconstants.js

@@ -1,16 +0,0 @@
-
-
-const Poseidon = require("./poseidon.js");
-
-const C = Poseidon.getConstants();
-
-let S = "[\n";
-
-for (let i=0; i<C.length; i++) {
-    S = S + "    " + C[i].toString();
-    if (i<C.length-1) S = S + ",";
-    S = S + "\n";
-}
-S=S+ "]\n";
-
-console.log(S);

src/poseidon_printcontract.js

@@ -1,5 +1,5 @@
 const poseidonGenContract = require("./poseidon_gencontract");
 
 
-console.log(poseidonGenContract.createCode(6, 8, 57));
+console.log(poseidonGenContract.createCode(5));
 

src/smt_hashes_poseidon.js

@@ -1,13 +1,18 @@
-const Poseidon = require("./poseidon");
 
-const hash = Poseidon.createHash(6, 8, 57);
+const ZqField = require("ffjavascript").ZqField;
+const Scalar = require("ffjavascript").Scalar;
+
+const poseidon = require("./poseidon");
+
+const F = new ZqField(Scalar.fromString("21888242871839275222246405745257275088548364400416034343698204186575808495617"));
+
 
 exports.hash0 = function (left, right) {
-    return hash([left, right]);
+    return poseidon([left, right]);
 };
 
 exports.hash1 = function(key, value) {
-    return hash([key, value, Poseidon.F.one]);
+    return poseidon([key, value, F.one]);
 };
 
-exports.F = Poseidon.F;
+exports.F = F;

src/smt_memdb.js

@@ -1,7 +1,9 @@
 
-const F = require("./poseidon.js").F;
 const Scalar = require("ffjavascript").Scalar;
-const utils = require("ffjavascript").utils;
+const ZqField = require("ffjavascript").ZqField;
+
+// Prime 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+const F = new ZqField(Scalar.fromString("21888242871839275222246405745257275088548364400416034343698204186575808495617"));
 
 class SMTMemDb {
     constructor() {

test/circuits/poseidon3_test.circom

@@ -1,3 +1,3 @@
 include "../../circuits/poseidon.circom"
 
-component main = Poseidon(2, 3, 8, 57);
+component main = Poseidon(2);

test/circuits/poseidon6_test.circom

@@ -1,3 +1,3 @@
 include "../../circuits/poseidon.circom"
 
-component main = Poseidon(2, 6, 8, 57);
+component main = Poseidon(5);

test/eddsa_js.js

@@ -67,12 +67,12 @@ describe("EdDSA js test", function () {
         assert.equal(signature.R8[1].toString(),
             "15383486972088797283337779941324724402501462225528836549661220478783371668959");
         assert.equal(signature.S.toString(),
-            "248298168863866362217836334079793350221620631973732197668910946177382043688");
+            "1398758333392199195742243841591064350253744445503462896781493968760929513778");
 
         const pSignature = eddsa.packSignature(signature);
         assert.equal(pSignature.toString("hex"), ""+
             "dfedb4315d3f2eb4de2d3c510d7a987dcab67089c8ace06308827bf5bcbe02a2"+
-            "28506bce274aa1b3f7e7c2fd7e4fe09bff8f9aa37a42def7994e98f322888c00");
+            "32f16b0f2f4c4e1169aa59685637e1429b6581a9531d058d65f4ab224eab1703");
 
         const uSignature = eddsa.unpackSignature(pSignature);
         assert(eddsa.verifyPoseidon(msg, uSignature, pubKey));

test/poseidoncircuit.js

@@ -1,21 +1,11 @@
 const chai = require("chai");
 const path = require("path");
-var blake2b = require("blake2b");
 const tester = require("circom").tester;
 
 const poseidon = require("../src/poseidon.js");
 
 const assert = chai.assert;
 
-describe("Blake2b version test", function() {
-    it("Should give the expected output for blake2b version", async () => {
-        var output = new Uint8Array(32);
-        var input = Buffer.from("poseidon_constants");
-        const h = blake2b(output.length).update(input).digest("hex");
-        assert.equal("e57ba154fb2c47811dc1a2369b27e25a44915b4e4ece4eb8ec74850cb78e01b1", h);
-    });
-});
-
 describe("Poseidon Circuit test", function () {
     let circuit6;
     let circuit3;
@@ -28,24 +18,20 @@ describe("Poseidon Circuit test", function () {
     });
 
     it("Should check constrain of hash([1, 2]) t=6", async () => {
-        const w = await circuit6.calculateWitness({inputs: [1, 2]}, true);
+        const w = await circuit6.calculateWitness({inputs: [1, 2, 0,0,0]}, true);
 
-        const hash = poseidon.createHash(6, 8, 57);
+        const res2 = poseidon([1,2,0,0,0]);
-
+        assert.equal("3975478831357328722254985704342968745327876719981393787143845259590563829094", res2.toString());
-        const res2 = hash([1,2]);
-        assert.equal("12242166908188651009877250812424843524687801523336557272219921456462821518061", res2.toString());
         await circuit6.assertOut(w, {out : res2});
         await circuit6.checkConstraints(w);
     });
 
     it("Should check constrain of hash([3, 4]) t=6", async () => {
-        const w = await circuit6.calculateWitness({inputs: [3, 4]});
+        const w = await circuit6.calculateWitness({inputs: [3, 4,5,10,23]});
 
-        const hash = poseidon.createHash(6, 8, 57);
+        const res2 = poseidon([3, 4,5,10,23]);
 
-        const res2 = hash([3, 4]);
+        assert.equal("18540626624821144952552691894137986276337186174352554475896834101336254024067", res2.toString());
-
-        assert.equal("17185195740979599334254027721507328033796809509313949281114643312710535000993", res2.toString());
         await circuit6.assertOut(w, {out : res2});
         await circuit6.checkConstraints(w);
     });
@@ -54,10 +40,8 @@ describe("Poseidon Circuit test", function () {
     it("Should check constrain of hash([1, 2]) t=3", async () => {
         const w = await circuit3.calculateWitness({inputs: [1, 2]});
 
-        const hash = poseidon.createHash(3, 8, 57);
+        const res2 = poseidon([1,2]);
-
+        assert.equal("17117985411748610629288516079940078114952304104811071254131751175361957805920", res2.toString());
-        const res2 = hash([1,2]);
-        assert.equal("2104035019328376391822106787753454168168617545136592089411833517434990977743", res2.toString());
         await circuit3.assertOut(w, {out : res2});
         await circuit3.checkConstraints(w);
     });
@@ -65,10 +49,8 @@ describe("Poseidon Circuit test", function () {
     it("Should check constrain of hash([3, 4]) t=3", async () => {
         const w = await circuit3.calculateWitness({inputs: [3, 4]});
 
-        const hash = poseidon.createHash(3, 8, 57);
+        const res2 = poseidon([3, 4]);
-
+        assert.equal("21867347236198497199818917118739170715216974132230970409806500217655788551452", res2.toString());
-        const res2 = hash([3, 4]);
-        assert.equal("12456141564250880945411182508630957604732712316993112736876413121277158512223", res2.toString());
         await circuit3.assertOut(w, {out : res2});
         await circuit3.checkConstraints(w);
     });

test/poseidoncontract.js

@@ -2,7 +2,7 @@ const ganache = require("ganache-cli");
 const Web3 = require("web3");
 const chai = require("chai");
 const poseidonGenContract = require("../src/poseidon_gencontract.js");
-const Poseidon = require("../src/poseidon.js");
+const poseidon = require("../src/poseidon.js");
 
 const assert = chai.assert;
 const log = (msg) => { if (process.env.MOCHA_VERBOSE) console.log(msg); };
@@ -24,28 +24,26 @@ describe("Poseidon Smart contract test", function () {
         const C = new web3.eth.Contract(poseidonGenContract.abi);
 
         poseidon6 = await C.deploy({
-            data: poseidonGenContract.createCode(6)
+            data: poseidonGenContract.createCode(5)
         }).send({
-            gas: 2500000,
+            gas: 5000000,
             from: accounts[0]
         });
         poseidon3 = await C.deploy({
-            data: poseidonGenContract.createCode(3)
+            data: poseidonGenContract.createCode(2)
         }).send({
-            gas: 2500000,
+            gas: 5000000,
             from: accounts[0]
         });
     });
 
     it("Shold calculate the poseidon correctly t=6", async () => {
 
-        const res = await poseidon6.methods.poseidon([1,2]).call();
+        const res = await poseidon6.methods.poseidon([1,2, 0, 0, 0]).call();
 
         // console.log("Cir: " + bigInt(res.toString(16)).toString(16));
 
-        const hash = Poseidon.createHash(6, 8, 57);
+        const res2 = poseidon([1,2, 0, 0, 0]);
-
-        const res2 = hash([1,2]);
         // console.log("Ref: " + bigInt(res2).toString(16));
 
         assert.equal(res.toString(), res2.toString());
@@ -56,9 +54,7 @@ describe("Poseidon Smart contract test", function () {
 
         // console.log("Cir: " + bigInt(res.toString(16)).toString(16));
 
-        const hash = Poseidon.createHash(3, 8, 57);
+        const res2 = poseidon([1,2]);
-
-        const res2 = hash([1,2]);
         // console.log("Ref: " + bigInt(res2).toString(16));
 
         assert.equal(res.toString(), res2.toString());