ElGamal encryption and ElGamal Proxy Re-Encryption in node.js for https://stackoverflow.com/q/45222849/1816580

elgamal_enc.js

var forge = require('node-forge');
var bigInt = require("big-integer");

var bits = 160;
forge.prime.generateProbablePrime(bits, function(err, num) {
  // Create prime factor and convert to bigInt
  var factor = bigInt(num.toString(10));
  // Find a larger prime of which factor is prime factor
  // Determine a large even number as a co-factor
  var coFactor = bigInt.randBetween("2e260", "3e260"); // should be bitLength(prime) - bitLength(factor)
  var prime = 4;
  while(!coFactor.isEven() || !prime.isPrime()) {
    coFactor = bigInt.randBetween("2e260", "3e260"); // should be bitLength(prime) - bitLength(factor)
    prime = coFactor.multiply(factor);
    prime = prime.add(1);
  }
  // Get a generator g for the multiplicative group mod factor
  var j = prime.minus(1).divide(factor);
  var h = bigInt.randBetween(2, prime.minus(1));
  var g = h.modPow(j, factor);
  // Alice's keys
  // Secret key
  var a = bigInt.randBetween(2, factor.minus(2));
  // Public key
  var A = g.modPow(a, prime);
  // Bob's keys
  // Secret key
  var b = bigInt.randBetween(2, factor.minus(2));
  // Public key
  var B = g.modPow(b, prime);
  // Shared secret
  // Calculated by Alice
  var Sa = B.modPow(a, prime);
  // Calculated by Bob
  var Sb = A.modPow(b, prime);
  // Check
  // Encryption by Alice
  var k = bigInt.randBetween(1, factor.minus(1));
  var c1 = g.modPow(k, prime);
  // Using Bob's public key
  var m = bigInt(2234266) // our message
  var c2 = m.multiply(B.modPow(k, prime));
  // Decryption by Bob
  var decrypt = c1.modPow((prime.minus(b).minus(bigInt(1))), prime).multiply(c2).mod(prime);
  console.log(decrypt); // should be 2234266
});

elgamal_pre.js

var forge = require('node-forge');
var bigInt = require("big-integer");

var bits = 160;
forge.prime.generateProbablePrime(bits, function(err, num) {
  // Create prime factor and convert to bigInt
  var factor = bigInt(num.toString(10));
  // Find a larger prime of which factor is prime factor
  // Determine a large even number as a co-factor
  var coFactor = bigInt.randBetween("2e260", "3e260"); // should be bitLength(prime) - bitLength(factor)
  var prime = 4;
  while(!coFactor.isEven() || !prime.isPrime()) {
    coFactor = bigInt.randBetween("2e260", "3e260"); // should be bitLength(prime) - bitLength(factor)
    prime = coFactor.multiply(factor);
    prime = prime.add(1);
  }
  // Get a generator g for the multiplicative group mod factor
  var j = prime.minus(1).divide(factor);
  var h = bigInt.randBetween(2, prime.minus(1));
  var g = h.modPow(j, factor);
  // Alice's keys
  // Secret key
  var a = bigInt.randBetween(2, factor.minus(2));
  // Public key
  var A = g.modPow(a, prime);
  // Bob's keys
  // Secret key
  var b = bigInt.randBetween(2, factor.minus(2));
  // Public key
  var B = g.modPow(b, prime);
  // Shared secret
  // Calculated by Alice
  var Sa = B.modPow(a, prime);
  // Calculated by Bob
  var Sb = A.modPow(b, prime);
  // Check
  // Encryption by Alice
  var k = bigInt.randBetween(1, factor.minus(1));
  var c1 = g.modPow(k, prime);
  // Using Bob's public key
  var m = bigInt(2234266) // our message
  var c2 = m.multiply(B.modPow(k, prime)).mod(prime);
  // Decryption by Bob
  var decrypt = c1.modPow((prime.minus(b).minus(bigInt(1))), prime).multiply(c2).mod(prime);
  console.log(decrypt); // should be 2234266
  
  
  // Proxy re-encryption test
  // x is secret key
  var x = bigInt.randBetween(1, factor.minus(1));
  var x1 = bigInt.randBetween(1, x);
  var x2 = x.minus(x1);
  // y is public key
  var y = g.modPow(x, prime);
  var r = bigInt.randBetween(1, factor.minus(1));
  var c3 = g.modPow(r, prime);
  // mg^xr
  var c4 = m.multiply(y.modPow(r, prime)).mod(prime);

  var _decryptP = c4.multiply(c3.modPow(x1, prime).modInv(prime)).mod(prime);
  var _decryptF = _decryptP.multiply(c3.modPow(x2, prime).modInv(prime)).mod(prime);
  console.log(_decryptF); // should be 2234266
});