miller-rabin/lib/mr.js

var bn = require('bn.js');
var brorand = require('brorand');

function MillerRabin(rand) {
  this.rand = rand || new brorand.Rand();
}
module.exports = MillerRabin;

MillerRabin.create = function create(rand) {
  return new MillerRabin(rand);
};

MillerRabin.prototype._randbelow = function _randbelow(n) {
  var len = n.bitLength();
  var min_bytes = Math.ceil(len / 8);

  // Generage random bytes until a number less than n is found.
  // This ensures that 0..n-1 have an equal probability of being selected.
  do
    var a = new bn(this.rand.generate(min_bytes));
  while (a.cmp(n) >= 0);

  return a;
};

MillerRabin.prototype._randrange = function _randrange(start, stop) {
  // Generate a random number greater than or equal to start and less than stop.
  var size = stop.sub(start);
  return start.add(this._randbelow(size));
};

MillerRabin.prototype.test = function test(n, k, cb) {
  var len = n.bitLength();
  var red = bn.mont(n);
  var rone = new bn(1).toRed(red);

  if (!k)
    k = Math.max(1, (len / 48) | 0);

  // Find d and s, (n - 1) = (2 ^ s) * d;
  var n1 = n.subn(1);
  for (var s = 0; !n1.testn(s); s++) {}
  var d = n.shrn(s);

  var rn1 = n1.toRed(red);

  var prime = true;
  for (; k > 0; k--) {
    var a = this._randrange(new bn(2), n1);
    if (cb)
      cb(a);

    var x = a.toRed(red).redPow(d);
    if (x.cmp(rone) === 0 || x.cmp(rn1) === 0)
      continue;

    for (var i = 1; i < s; i++) {
      x = x.redSqr();

      if (x.cmp(rone) === 0)
        return false;
      if (x.cmp(rn1) === 0)
        break;
    }

    if (i === s)
      return false;
  }

  return prime;
};

MillerRabin.prototype.getDivisor = function getDivisor(n, k) {
  var len = n.bitLength();
  var red = bn.mont(n);
  var rone = new bn(1).toRed(red);

  if (!k)
    k = Math.max(1, (len / 48) | 0);

  // Find d and s, (n - 1) = (2 ^ s) * d;
  var n1 = n.subn(1);
  for (var s = 0; !n1.testn(s); s++) {}
  var d = n.shrn(s);

  var rn1 = n1.toRed(red);

  for (; k > 0; k--) {
    var a = this._randrange(new bn(2), n1);

    var g = n.gcd(a);
    if (g.cmpn(1) !== 0)
      return g;

    var x = a.toRed(red).redPow(d);
    if (x.cmp(rone) === 0 || x.cmp(rn1) === 0)
      continue;

    for (var i = 1; i < s; i++) {
      x = x.redSqr();

      if (x.cmp(rone) === 0)
        return x.fromRed().subn(1).gcd(n);
      if (x.cmp(rn1) === 0)
        break;
    }

    if (i === s) {
      x = x.redSqr();
      return x.fromRed().subn(1).gcd(n);
    }
  }

  return false;
};