var asn = require('asn1.js')
var crypto = require('crypto')
var BN = asn.bignum

var zero = new BN(0)
var one = new BN(1)
var two = new BN(2)

function rand(low, high) {
  do {
    var b = new BN(crypto.randomBytes(high.byteLength()))
  } while(b.cmp(low) <= 0 || b.cmp(high) >= 0)
  return b
}

function odd(n) {
  if (n.cmp(zero) === 0) { return zero }
  var r = n
  while (r.isEven()) {
    r = r.div(two)
  }
  return r
}

function rootOne(x, r, n) {
  var i = x.toRed(BN.red(n)).redPow(r).fromRed()
  var o = zero
  while (i.cmp(one) !== 0) {
    o = i
    i = i.mul(i).mod(n)
  }
  if (o.cmp(n.sub(one)) === 0) {
    return zero
  }
  return o
}

function factor(e, d, n) {
  var k = e.mul(d).sub(one)
  var r = odd(k)
  do {
    var y = rootOne(rand(two, n), r, n)
  } while (y.cmp(zero) === 0)

  var p = y.sub(one).gcd(n)
  return {
    p: p,
    q: n.div(p)
  }
}

module.exports = factor