@cloudflare/zkp-ecdsa/lib/src/proofGK/interpolate.js

zkp-ecdsa: A Typescript Implementation of ZKAttest

import { invMod, posMod } from '../bignum/big.js';
function eval_poly(coeff, x, m) {
    let ret = BigInt(0);
    for (let i = coeff.length - 1; i >= 0; i--) {
        ret = posMod(coeff[i] + x * ret, m);
    }
    return ret;
}
export function interpolate(x, y, m) {
    if (x.length != y.length) {
        throw new Error('inconsistent args');
    }
    const n = x.length, s = [], coeff = [];
    for (let i = 0; i < n; i++) {
        s[i] = BigInt(0);
        coeff[i] = BigInt(0);
    }
    s[n] = BigInt(1);
    s[n - 1] = -x[0] % m;
    for (let i = 1; i < n; i++) {
        for (let j = n - i - 1; j < n - 1; j++) {
            s[j] = (s[j] - x[i] * s[j + 1]) % m;
        }
        s[n - 1] = (s[n - 1] - x[i]) % m;
    }
    for (let i = 0; i < n; i++) {
        let phi = BigInt(0);
        for (let j = n; j >= 1; j--) {
            phi = BigInt(j) * s[j] + x[i] * phi;
        }
        phi = posMod(phi, m);
        const ff = invMod(phi, m) % m;
        let b = BigInt(1);
        for (let j = n - 1; j >= 0; j--) {
            coeff[j] = posMod(coeff[j] + b * ff * y[i], m);
            b = s[j] + x[i] * b;
        }
    }
    for (let i = 0; i < n; i++) {
        if (y[i] != eval_poly(coeff, x[i], m)) {
            throw new Error('incorrect interpolation');
        }
    }
    return coeff;
}
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