circomlib/circuits/poseidon.circom

include "./poseidon_constants.circom";

template Sigma() {
    signal input in;
    signal output out;

    signal in2;
    signal in4;

    in2 <== in*in;
    in4 <== in2*in2;

    out <== in4*in;
}

template Ark(t, C, r) {
    signal input in[t];
    signal output out[t];

    for (var i=0; i<t; i++) {
        out[i] <== in[i] + C[i + r];
    }
}

template Mix(t, M) {
    signal input in[t];
    signal output out[t];

    var lc;
    for (var i=0; i<t; i++) {
        lc = 0;
        for (var j=0; j<t; j++) {
            lc += M[j][i]*in[j];
        }
        out[i] <== lc;
    }
}

template Poseidon(nInputs) {
    signal input inputs[nInputs];
    signal output out;

		// Using recommended parameters from whitepaper https://eprint.iacr.org/2019/458.pdf (table 2, table 8)
		// Generated by https://extgit.iaik.tugraz.at/krypto/hadeshash/-/blob/master/code/calc_round_numbers.py
		// And rounded up to nearest integer that divides by t
    var t = nInputs + 1;
    var nRoundsF = 8;
    var nRoundsP = 35;
    var C[t*(nRoundsF + nRoundsP)] = POSEIDON_C(t);
    var M[t][t] = POSEIDON_M(t);

    component ark[nRoundsF + nRoundsP - 1];
    component sigmaF[nRoundsF - 1][t];
    component sigmaP[nRoundsP];
    component mix[nRoundsF + nRoundsP - 1];

    var k;

    for (var i=0; i<nRoundsF + nRoundsP - 1; i++) {
        ark[i] = Ark(t, C, t*i);
        for (var j=0; j<t; j++) {
            if (i==0) {
                if (j<nInputs) {
                    ark[i].in[j] <== inputs[j];
                } else {
                    ark[i].in[j] <== 0;
                }
            } else {
                ark[i].in[j] <== mix[i-1].out[j];
            }
        }

        if (i < nRoundsF/2 || i >= nRoundsP + nRoundsF/2) {
            k = i < nRoundsF/2 ? i : i - nRoundsP;
            mix[i] = Mix(t, M);
            for (var j=0; j<t; j++) {
                sigmaF[k][j] = Sigma();
                sigmaF[k][j].in <== ark[i].out[j];
                mix[i].in[j] <== sigmaF[k][j].out;
            }
        } else {
            k = i - nRoundsF/2;
            mix[i] = Mix(t, M);
            sigmaP[k] = Sigma();
            sigmaP[k].in <== ark[i].out[0];
            mix[i].in[0] <== sigmaP[k].out;
            for (var j=1; j<t; j++) {
                mix[i].in[j] <== ark[i].out[j];
            }
        }
    }

    // last round is done only for the first word, so we do it manually to save constraints
    component lastSigmaF = Sigma();
    lastSigmaF.in <== mix[nRoundsF + nRoundsP - 2].out[0] + C[t*(nRoundsF + nRoundsP - 1)];
    out <== lastSigmaF.out;
}