Example of additive and multiplicative homomorphic encryption

paillier.js

// Reference: https://radicalrafi.github.io/posts/homomorphic-encryption/
// npm i --save big-integer

const bigInt = require('big-integer');

const L = (x, n) => x.minus(1).divide(n);

function createEncryptor({ n, g }) {
  return (m, r) => g.pow(m).times(r.pow(n)).mod(n.pow(2));
}

function createDecryptor({ lambda, mu }, n) {
  return c => L(c.pow(lambda).mod(n.pow(2)), n).times(mu).mod(n);
}

// Two large primes
const p = new bigInt(97);
const q = new bigInt(29);

const n = p.times(q);
const g = n.plus(1);
const pubKey = { n, g };

const lambda = bigInt.lcm(p.minus(1), q.minus(1));
const mu = lambda.modInv(n);
const privKey = { lambda, mu };

const encrypt = createEncryptor(pubKey);
const decrypt = createDecryptor(privKey, pubKey.n);

const message = new bigInt(42);
const random = new bigInt(23);
const message2 = new bigInt(101);
const random2 = new bigInt(37);

const cipherText = encrypt(message, random);
const cipherText2 = encrypt(message2, random2);

const messageSum = decrypt(cipherText.times(cipherText2));
const messageProduct = decrypt(cipherText2.pow(7));

console.log(messageSum);
// D(E(message) * E(message2)) = message + message2 = 143

console.log(messageProduct);
// D(E(message2)^7) = message2 * 7 = 707