ecdh-es/dist/ecdh.js

Elliptic Curve Diffie-Hellman with ephemeral-static keys implementation for NodeJS

!function(e){if("object"==typeof exports&&"undefined"!=typeof module)module.exports=e();else if("function"==typeof define&&define.amd)define([],e);else{var f;"undefined"!=typeof window?f=window:"undefined"!=typeof global?f=global:"undefined"!=typeof self&&(f=self),f.ECDH=e()}}(function(){var define,module,exports;return (function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
// Generated by CoffeeScript 1.8.0
(function() {
  exports.createHash = require('crypto-browserify/create-hash');

  exports.createHmac = require('crypto-browserify/create-hmac');

  require('crypto-browserify/node_modules/browserify-aes/inject')(exports, exports);

}).call(this);

},{"crypto-browserify/create-hash":33,"crypto-browserify/create-hmac":34,"crypto-browserify/node_modules/browserify-aes/inject":44}],2:[function(require,module,exports){
(function (Buffer){
// Generated by CoffeeScript 1.8.0
(function() {
  var BigInt, CHECKSUM_SIZE, PUBKEY_SIZE, Point, buff_eq, create_ecdh, crypto, getCurveByName, get_pub, hmac, k, rand, rand_key, reader, sha256, sha512, v, _ref, _ref1, _ref2;

  crypto = require('crypto');

  BigInt = require('bigi');

  _ref = require('ecurve'), Point = _ref.Point, getCurveByName = _ref.getCurveByName;

  _ref1 = require('./util'), reader = _ref1.reader, sha256 = _ref1.sha256, sha512 = _ref1.sha512, hmac = _ref1.hmac, rand = _ref1.rand, rand_key = _ref1.rand_key, get_pub = _ref1.get_pub, buff_eq = _ref1.buff_eq;

  PUBKEY_SIZE = 33;

  CHECKSUM_SIZE = 32;

  create_ecdh = function(_arg) {
    var cipher_algo, curve, curve_name, iv_size, key_size, shared_secret;
    curve_name = _arg.curve_name, cipher_algo = _arg.cipher_algo, key_size = _arg.key_size, iv_size = _arg.iv_size;
    curve = getCurveByName(curve_name);
    shared_secret = function(d, Q) {
      if (Buffer.isBuffer(d)) {
        d = BigInt.fromBuffer(d);
      }
      if (Buffer.isBuffer(Q)) {
        Q = Point.decodeFrom(curve, Q);
      }
      return sha512(Q.multiply(d).getEncoded(false));
    };
    return {
      encrypt: function(pubkey, msg) {
        var checksum, cipher, ct, eph, eph_p, iv, secret;
        eph = rand_key(curve, pubkey, msg);
        eph_p = get_pub(curve, eph);
        secret = shared_secret(eph, pubkey);
        iv = sha256(eph_p).slice(0, iv_size);
        cipher = crypto.createCipheriv(cipher_algo, secret.slice(0, key_size), iv);
        cipher.setAutoPadding(true);
        ct = cipher.update(msg);
        ct = Buffer.concat([ct, cipher.final()]);
        checksum = hmac(secret.slice(key_size), eph_p, ct);
        return Buffer.concat([eph_p, checksum, ct]);
      },
      decrypt: function(privkey, enc) {
        var checksum, cipher, ct, iv, msg, pubkey, read, secret;
        read = reader(enc);
        pubkey = read(PUBKEY_SIZE);
        checksum = read(CHECKSUM_SIZE);
        ct = read();
        secret = shared_secret(privkey, pubkey);
        iv = sha256(pubkey).slice(0, iv_size);
        if (!buff_eq(checksum, hmac(secret.slice(key_size), pubkey, ct))) {
          throw new Error('Invalid checksum');
        }
        cipher = crypto.createDecipheriv(cipher_algo, secret.slice(0, key_size), iv);
        cipher.setAutoPadding(true);
        msg = cipher.update(ct);
        return Buffer.concat([msg, cipher.final()]);
      }
    };
  };

  module.exports = create_ecdh;

  _ref2 = create_ecdh({
    curve_name: 'secp256k1',
    cipher_algo: 'AES-128-CBC',
    key_size: 16,
    iv_size: 16
  });
  for (k in _ref2) {
    v = _ref2[k];
    module.exports[k] = v;
  }

}).call(this);

}).call(this,require("buffer").Buffer)
},{"./util":3,"bigi":6,"buffer":10,"crypto":1,"ecurve":67}],3:[function(require,module,exports){
// Generated by CoffeeScript 1.8.0
(function() {
  var BigInt, buff_eq, createHash, createHmac, get_pub, hmac, rand, rand_key, randomBuffer, reader, sha256, sha512, _ref,
    __slice = [].slice;

  BigInt = require('bigi');

  _ref = require('crypto'), createHash = _ref.createHash, createHmac = _ref.createHmac;

  randomBuffer = require('secure-random').randomBuffer;

  reader = function(buff, pos) {
    if (pos == null) {
      pos = 0;
    }
    return function(len) {
      if (len != null) {
        return buff.slice(pos, (pos += len));
      } else {
        return buff.slice(pos);
      }
    };
  };

  sha256 = function(d) {
    return createHash('sha256').update(d).digest();
  };

  sha512 = function(d) {
    return createHash('sha512').update(d).digest();
  };

  hmac = function() {
    var d, data, h, key, _i, _len;
    key = arguments[0], data = 2 <= arguments.length ? __slice.call(arguments, 1) : [];
    h = createHmac('sha256', key);
    for (_i = 0, _len = data.length; _i < _len; _i++) {
      d = data[_i];
      h.update(d);
    }
    return h.digest();
  };

  rand = function() {
    var entropy;
    entropy = 1 <= arguments.length ? __slice.call(arguments, 0) : [];
    return hmac.apply(null, [randomBuffer(32)].concat(__slice.call(entropy)));
  };

  rand_key = function() {
    var curve, entropy;
    curve = arguments[0], entropy = 2 <= arguments.length ? __slice.call(arguments, 1) : [];
    return BigInt.fromBuffer(rand.apply(null, entropy)).mod(curve.n);
  };

  get_pub = function(curve, privkey) {
    return curve.G.multiply(privkey).getEncoded(true);
  };

  buff_eq = function(a, b) {
    return a.toString('hex') === b.toString('hex');
  };

  module.exports = {
    reader: reader,
    sha256: sha256,
    sha512: sha512,
    hmac: hmac,
    rand: rand,
    rand_key: rand_key,
    get_pub: get_pub,
    buff_eq: buff_eq
  };

}).call(this);

},{"bigi":6,"crypto":1,"secure-random":70}],4:[function(require,module,exports){
// (public) Constructor
function BigInteger(a, b, c) {
  if (!(this instanceof BigInteger))
    return new BigInteger(a, b, c)

  if (a != null) {
    if ("number" == typeof a) this.fromNumber(a, b, c)
    else if (b == null && "string" != typeof a) this.fromString(a, 256)
    else this.fromString(a, b)
  }
}

var proto = BigInteger.prototype

// duck-typed isBigInteger
proto.__bigi = require('../package.json').version
BigInteger.isBigInteger = function (obj, check_ver) {
  return obj && obj.__bigi && (!check_ver || obj.__bigi === proto.__bigi)
}

// Bits per digit
var dbits

// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.

// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i, x, w, j, c, n) {
  while (--n >= 0) {
    var v = x * this[i++] + w[j] + c
    c = Math.floor(v / 0x4000000)
    w[j++] = v & 0x3ffffff
  }
  return c
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i, x, w, j, c, n) {
  var xl = x & 0x7fff,
    xh = x >> 15
  while (--n >= 0) {
    var l = this[i] & 0x7fff
    var h = this[i++] >> 15
    var m = xh * l + h * xl
    l = xl * l + ((m & 0x7fff) << 15) + w[j] + (c & 0x3fffffff)
    c = (l >>> 30) + (m >>> 15) + xh * h + (c >>> 30)
    w[j++] = l & 0x3fffffff
  }
  return c
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i, x, w, j, c, n) {
  var xl = x & 0x3fff,
    xh = x >> 14
  while (--n >= 0) {
    var l = this[i] & 0x3fff
    var h = this[i++] >> 14
    var m = xh * l + h * xl
    l = xl * l + ((m & 0x3fff) << 14) + w[j] + c
    c = (l >> 28) + (m >> 14) + xh * h
    w[j++] = l & 0xfffffff
  }
  return c
}

// wtf?
BigInteger.prototype.am = am1
dbits = 26

BigInteger.prototype.DB = dbits
BigInteger.prototype.DM = ((1 << dbits) - 1)
var DV = BigInteger.prototype.DV = (1 << dbits)

var BI_FP = 52
BigInteger.prototype.FV = Math.pow(2, BI_FP)
BigInteger.prototype.F1 = BI_FP - dbits
BigInteger.prototype.F2 = 2 * dbits - BI_FP

// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz"
var BI_RC = new Array()
var rr, vv
rr = "0".charCodeAt(0)
for (vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv
rr = "a".charCodeAt(0)
for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv
rr = "A".charCodeAt(0)
for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv

function int2char(n) {
  return BI_RM.charAt(n)
}

function intAt(s, i) {
  var c = BI_RC[s.charCodeAt(i)]
  return (c == null) ? -1 : c
}

// (protected) copy this to r
function bnpCopyTo(r) {
  for (var i = this.t - 1; i >= 0; --i) r[i] = this[i]
  r.t = this.t
  r.s = this.s
}

// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
  this.t = 1
  this.s = (x < 0) ? -1 : 0
  if (x > 0) this[0] = x
  else if (x < -1) this[0] = x + DV
  else this.t = 0
}

// return bigint initialized to value
function nbv(i) {
  var r = new BigInteger()
  r.fromInt(i)
  return r
}

// (protected) set from string and radix
function bnpFromString(s, b) {
  var self = this

  var k
  if (b == 16) k = 4
  else if (b == 8) k = 3
  else if (b == 256) k = 8; // byte array
  else if (b == 2) k = 1
  else if (b == 32) k = 5
  else if (b == 4) k = 2
  else {
    self.fromRadix(s, b)
    return
  }
  self.t = 0
  self.s = 0
  var i = s.length,
    mi = false,
    sh = 0
  while (--i >= 0) {
    var x = (k == 8) ? s[i] & 0xff : intAt(s, i)
    if (x < 0) {
      if (s.charAt(i) == "-") mi = true
      continue
    }
    mi = false
    if (sh == 0)
      self[self.t++] = x
    else if (sh + k > self.DB) {
      self[self.t - 1] |= (x & ((1 << (self.DB - sh)) - 1)) << sh
      self[self.t++] = (x >> (self.DB - sh))
    } else
      self[self.t - 1] |= x << sh
    sh += k
    if (sh >= self.DB) sh -= self.DB
  }
  if (k == 8 && (s[0] & 0x80) != 0) {
    self.s = -1
    if (sh > 0) self[self.t - 1] |= ((1 << (self.DB - sh)) - 1) << sh
  }
  self.clamp()
  if (mi) BigInteger.ZERO.subTo(self, self)
}

// (protected) clamp off excess high words
function bnpClamp() {
  var c = this.s & this.DM
  while (this.t > 0 && this[this.t - 1] == c)--this.t
}

// (public) return string representation in given radix
function bnToString(b) {
  var self = this
  if (self.s < 0) return "-" + self.negate()
    .toString(b)
  var k
  if (b == 16) k = 4
  else if (b == 8) k = 3
  else if (b == 2) k = 1
  else if (b == 32) k = 5
  else if (b == 4) k = 2
  else return self.toRadix(b)
  var km = (1 << k) - 1,
    d, m = false,
    r = "",
    i = self.t
  var p = self.DB - (i * self.DB) % k
  if (i-- > 0) {
    if (p < self.DB && (d = self[i] >> p) > 0) {
      m = true
      r = int2char(d)
    }
    while (i >= 0) {
      if (p < k) {
        d = (self[i] & ((1 << p) - 1)) << (k - p)
        d |= self[--i] >> (p += self.DB - k)
      } else {
        d = (self[i] >> (p -= k)) & km
        if (p <= 0) {
          p += self.DB
          --i
        }
      }
      if (d > 0) m = true
      if (m) r += int2char(d)
    }
  }
  return m ? r : "0"
}

// (public) -this
function bnNegate() {
  var r = new BigInteger()
  BigInteger.ZERO.subTo(this, r)
  return r
}

// (public) |this|
function bnAbs() {
  return (this.s < 0) ? this.negate() : this
}

// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
  var r = this.s - a.s
  if (r != 0) return r
  var i = this.t
  r = i - a.t
  if (r != 0) return (this.s < 0) ? -r : r
  while (--i >= 0)
    if ((r = this[i] - a[i]) != 0) return r
  return 0
}

// returns bit length of the integer x
function nbits(x) {
  var r = 1,
    t
  if ((t = x >>> 16) != 0) {
    x = t
    r += 16
  }
  if ((t = x >> 8) != 0) {
    x = t
    r += 8
  }
  if ((t = x >> 4) != 0) {
    x = t
    r += 4
  }
  if ((t = x >> 2) != 0) {
    x = t
    r += 2
  }
  if ((t = x >> 1) != 0) {
    x = t
    r += 1
  }
  return r
}

// (public) return the number of bits in "this"
function bnBitLength() {
  if (this.t <= 0) return 0
  return this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ (this.s & this.DM))
}

// (public) return the number of bytes in "this"
function bnByteLength() {
  return this.bitLength() >> 3
}

// (protected) r = this << n*DB
function bnpDLShiftTo(n, r) {
  var i
  for (i = this.t - 1; i >= 0; --i) r[i + n] = this[i]
  for (i = n - 1; i >= 0; --i) r[i] = 0
  r.t = this.t + n
  r.s = this.s
}

// (protected) r = this >> n*DB
function bnpDRShiftTo(n, r) {
  for (var i = n; i < this.t; ++i) r[i - n] = this[i]
  r.t = Math.max(this.t - n, 0)
  r.s = this.s
}

// (protected) r = this << n
function bnpLShiftTo(n, r) {
  var self = this
  var bs = n % self.DB
  var cbs = self.DB - bs
  var bm = (1 << cbs) - 1
  var ds = Math.floor(n / self.DB),
    c = (self.s << bs) & self.DM,
    i
  for (i = self.t - 1; i >= 0; --i) {
    r[i + ds + 1] = (self[i] >> cbs) | c
    c = (self[i] & bm) << bs
  }
  for (i = ds - 1; i >= 0; --i) r[i] = 0
  r[ds] = c
  r.t = self.t + ds + 1
  r.s = self.s
  r.clamp()
}

// (protected) r = this >> n
function bnpRShiftTo(n, r) {
  var self = this
  r.s = self.s
  var ds = Math.floor(n / self.DB)
  if (ds >= self.t) {
    r.t = 0
    return
  }
  var bs = n % self.DB
  var cbs = self.DB - bs
  var bm = (1 << bs) - 1
  r[0] = self[ds] >> bs
  for (var i = ds + 1; i < self.t; ++i) {
    r[i - ds - 1] |= (self[i] & bm) << cbs
    r[i - ds] = self[i] >> bs
  }
  if (bs > 0) r[self.t - ds - 1] |= (self.s & bm) << cbs
  r.t = self.t - ds
  r.clamp()
}

// (protected) r = this - a
function bnpSubTo(a, r) {
  var self = this
  var i = 0,
    c = 0,
    m = Math.min(a.t, self.t)
  while (i < m) {
    c += self[i] - a[i]
    r[i++] = c & self.DM
    c >>= self.DB
  }
  if (a.t < self.t) {
    c -= a.s
    while (i < self.t) {
      c += self[i]
      r[i++] = c & self.DM
      c >>= self.DB
    }
    c += self.s
  } else {
    c += self.s
    while (i < a.t) {
      c -= a[i]
      r[i++] = c & self.DM
      c >>= self.DB
    }
    c -= a.s
  }
  r.s = (c < 0) ? -1 : 0
  if (c < -1) r[i++] = self.DV + c
  else if (c > 0) r[i++] = c
  r.t = i
  r.clamp()
}

// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a, r) {
  var x = this.abs(),
    y = a.abs()
  var i = x.t
  r.t = i + y.t
  while (--i >= 0) r[i] = 0
  for (i = 0; i < y.t; ++i) r[i + x.t] = x.am(0, y[i], r, i, 0, x.t)
  r.s = 0
  r.clamp()
  if (this.s != a.s) BigInteger.ZERO.subTo(r, r)
}

// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
  var x = this.abs()
  var i = r.t = 2 * x.t
  while (--i >= 0) r[i] = 0
  for (i = 0; i < x.t - 1; ++i) {
    var c = x.am(i, x[i], r, 2 * i, 0, 1)
    if ((r[i + x.t] += x.am(i + 1, 2 * x[i], r, 2 * i + 1, c, x.t - i - 1)) >= x.DV) {
      r[i + x.t] -= x.DV
      r[i + x.t + 1] = 1
    }
  }
  if (r.t > 0) r[r.t - 1] += x.am(i, x[i], r, 2 * i, 0, 1)
  r.s = 0
  r.clamp()
}

// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m.  q or r may be null.
function bnpDivRemTo(m, q, r) {
  var self = this
  var pm = m.abs()
  if (pm.t <= 0) return
  var pt = self.abs()
  if (pt.t < pm.t) {
    if (q != null) q.fromInt(0)
    if (r != null) self.copyTo(r)
    return
  }
  if (r == null) r = new BigInteger()
  var y = new BigInteger(),
    ts = self.s,
    ms = m.s
  var nsh = self.DB - nbits(pm[pm.t - 1]); // normalize modulus
  if (nsh > 0) {
    pm.lShiftTo(nsh, y)
    pt.lShiftTo(nsh, r)
  } else {
    pm.copyTo(y)
    pt.copyTo(r)
  }
  var ys = y.t
  var y0 = y[ys - 1]
  if (y0 == 0) return
  var yt = y0 * (1 << self.F1) + ((ys > 1) ? y[ys - 2] >> self.F2 : 0)
  var d1 = self.FV / yt,
    d2 = (1 << self.F1) / yt,
    e = 1 << self.F2
  var i = r.t,
    j = i - ys,
    t = (q == null) ? new BigInteger() : q
  y.dlShiftTo(j, t)
  if (r.compareTo(t) >= 0) {
    r[r.t++] = 1
    r.subTo(t, r)
  }
  BigInteger.ONE.dlShiftTo(ys, t)
  t.subTo(y, y); // "negative" y so we can replace sub with am later
  while (y.t < ys) y[y.t++] = 0
  while (--j >= 0) {
    // Estimate quotient digit
    var qd = (r[--i] == y0) ? self.DM : Math.floor(r[i] * d1 + (r[i - 1] + e) * d2)
    if ((r[i] += y.am(0, qd, r, j, 0, ys)) < qd) { // Try it out
      y.dlShiftTo(j, t)
      r.subTo(t, r)
      while (r[i] < --qd) r.subTo(t, r)
    }
  }
  if (q != null) {
    r.drShiftTo(ys, q)
    if (ts != ms) BigInteger.ZERO.subTo(q, q)
  }
  r.t = ys
  r.clamp()
  if (nsh > 0) r.rShiftTo(nsh, r); // Denormalize remainder
  if (ts < 0) BigInteger.ZERO.subTo(r, r)
}

// (public) this mod a
function bnMod(a) {
  var r = new BigInteger()
  this.abs()
    .divRemTo(a, null, r)
  if (this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r, r)
  return r
}

// Modular reduction using "classic" algorithm
function Classic(m) {
  this.m = m
}

function cConvert(x) {
  if (x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m)
  else return x
}

function cRevert(x) {
  return x
}

function cReduce(x) {
  x.divRemTo(this.m, null, x)
}

function cMulTo(x, y, r) {
  x.multiplyTo(y, r)
  this.reduce(r)
}

function cSqrTo(x, r) {
  x.squareTo(r)
  this.reduce(r)
}

Classic.prototype.convert = cConvert
Classic.prototype.revert = cRevert
Classic.prototype.reduce = cReduce
Classic.prototype.mulTo = cMulTo
Classic.prototype.sqrTo = cSqrTo

// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
//         xy == 1 (mod m)
//         xy =  1+km
//   xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
  if (this.t < 1) return 0
  var x = this[0]
  if ((x & 1) == 0) return 0
  var y = x & 3; // y == 1/x mod 2^2
  y = (y * (2 - (x & 0xf) * y)) & 0xf; // y == 1/x mod 2^4
  y = (y * (2 - (x & 0xff) * y)) & 0xff; // y == 1/x mod 2^8
  y = (y * (2 - (((x & 0xffff) * y) & 0xffff))) & 0xffff; // y == 1/x mod 2^16
  // last step - calculate inverse mod DV directly
  // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
  y = (y * (2 - x * y % this.DV)) % this.DV; // y == 1/x mod 2^dbits
  // we really want the negative inverse, and -DV < y < DV
  return (y > 0) ? this.DV - y : -y
}

// Montgomery reduction
function Montgomery(m) {
  this.m = m
  this.mp = m.invDigit()
  this.mpl = this.mp & 0x7fff
  this.mph = this.mp >> 15
  this.um = (1 << (m.DB - 15)) - 1
  this.mt2 = 2 * m.t
}

// xR mod m
function montConvert(x) {
  var r = new BigInteger()
  x.abs()
    .dlShiftTo(this.m.t, r)
  r.divRemTo(this.m, null, r)
  if (x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r, r)
  return r
}

// x/R mod m
function montRevert(x) {
  var r = new BigInteger()
  x.copyTo(r)
  this.reduce(r)
  return r
}

// x = x/R mod m (HAC 14.32)
function montReduce(x) {
  while (x.t <= this.mt2) // pad x so am has enough room later
    x[x.t++] = 0
  for (var i = 0; i < this.m.t; ++i) {
    // faster way of calculating u0 = x[i]*mp mod DV
    var j = x[i] & 0x7fff
    var u0 = (j * this.mpl + (((j * this.mph + (x[i] >> 15) * this.mpl) & this.um) << 15)) & x.DM
    // use am to combine the multiply-shift-add into one call
    j = i + this.m.t
    x[j] += this.m.am(0, u0, x, i, 0, this.m.t)
    // propagate carry
    while (x[j] >= x.DV) {
      x[j] -= x.DV
      x[++j]++
    }
  }
  x.clamp()
  x.drShiftTo(this.m.t, x)
  if (x.compareTo(this.m) >= 0) x.subTo(this.m, x)
}

// r = "x^2/R mod m"; x != r
function montSqrTo(x, r) {
  x.squareTo(r)
  this.reduce(r)
}

// r = "xy/R mod m"; x,y != r
function montMulTo(x, y, r) {
  x.multiplyTo(y, r)
  this.reduce(r)
}

Montgomery.prototype.convert = montConvert
Montgomery.prototype.revert = montRevert
Montgomery.prototype.reduce = montReduce
Montgomery.prototype.mulTo = montMulTo
Montgomery.prototype.sqrTo = montSqrTo

// (protected) true iff this is even
function bnpIsEven() {
  return ((this.t > 0) ? (this[0] & 1) : this.s) == 0
}

// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
function bnpExp(e, z) {
  if (e > 0xffffffff || e < 1) return BigInteger.ONE
  var r = new BigInteger(),
    r2 = new BigInteger(),
    g = z.convert(this),
    i = nbits(e) - 1
  g.copyTo(r)
  while (--i >= 0) {
    z.sqrTo(r, r2)
    if ((e & (1 << i)) > 0) z.mulTo(r2, g, r)
    else {
      var t = r
      r = r2
      r2 = t
    }
  }
  return z.revert(r)
}

// (public) this^e % m, 0 <= e < 2^32
function bnModPowInt(e, m) {
  var z
  if (e < 256 || m.isEven()) z = new Classic(m)
  else z = new Montgomery(m)
  return this.exp(e, z)
}

// protected
proto.copyTo = bnpCopyTo
proto.fromInt = bnpFromInt
proto.fromString = bnpFromString
proto.clamp = bnpClamp
proto.dlShiftTo = bnpDLShiftTo
proto.drShiftTo = bnpDRShiftTo
proto.lShiftTo = bnpLShiftTo
proto.rShiftTo = bnpRShiftTo
proto.subTo = bnpSubTo
proto.multiplyTo = bnpMultiplyTo
proto.squareTo = bnpSquareTo
proto.divRemTo = bnpDivRemTo
proto.invDigit = bnpInvDigit
proto.isEven = bnpIsEven
proto.exp = bnpExp

// public
proto.toString = bnToString
proto.negate = bnNegate
proto.abs = bnAbs
proto.compareTo = bnCompareTo
proto.bitLength = bnBitLength
proto.byteLength = bnByteLength
proto.mod = bnMod
proto.modPowInt = bnModPowInt

// (public)
function bnClone() {
  var r = new BigInteger()
  this.copyTo(r)
  return r
}

// (public) return value as integer
function bnIntValue() {
  if (this.s < 0) {
    if (this.t == 1) return this[0] - this.DV
    else if (this.t == 0) return -1
  } else if (this.t == 1) return this[0]
  else if (this.t == 0) return 0
  // assumes 16 < DB < 32
  return ((this[1] & ((1 << (32 - this.DB)) - 1)) << this.DB) | this[0]
}

// (public) return value as byte
function bnByteValue() {
  return (this.t == 0) ? this.s : (this[0] << 24) >> 24
}

// (public) return value as short (assumes DB>=16)
function bnShortValue() {
  return (this.t == 0) ? this.s : (this[0] << 16) >> 16
}

// (protected) return x s.t. r^x < DV
function bnpChunkSize(r) {
  return Math.floor(Math.LN2 * this.DB / Math.log(r))
}

// (public) 0 if this == 0, 1 if this > 0
function bnSigNum() {
  if (this.s < 0) return -1
  else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0
  else return 1
}

// (protected) convert to radix string
function bnpToRadix(b) {
  if (b == null) b = 10
  if (this.signum() == 0 || b < 2 || b > 36) return "0"
  var cs = this.chunkSize(b)
  var a = Math.pow(b, cs)
  var d = nbv(a),
    y = new BigInteger(),
    z = new BigInteger(),
    r = ""
  this.divRemTo(d, y, z)
  while (y.signum() > 0) {
    r = (a + z.intValue())
      .toString(b)
      .substr(1) + r
    y.divRemTo(d, y, z)
  }
  return z.intValue()
    .toString(b) + r
}

// (protected) convert from radix string
function bnpFromRadix(s, b) {
  var self = this
  self.fromInt(0)
  if (b == null) b = 10
  var cs = self.chunkSize(b)
  var d = Math.pow(b, cs),
    mi = false,
    j = 0,
    w = 0
  for (var i = 0; i < s.length; ++i) {
    var x = intAt(s, i)
    if (x < 0) {
      if (s.charAt(i) == "-" && self.signum() == 0) mi = true
      continue
    }
    w = b * w + x
    if (++j >= cs) {
      self.dMultiply(d)
      self.dAddOffset(w, 0)
      j = 0
      w = 0
    }
  }
  if (j > 0) {
    self.dMultiply(Math.pow(b, j))
    self.dAddOffset(w, 0)
  }
  if (mi) BigInteger.ZERO.subTo(self, self)
}

// (protected) alternate constructor
function bnpFromNumber(a, b, c) {
  var self = this
  if ("number" == typeof b) {
    // new BigInteger(int,int,RNG)
    if (a < 2) self.fromInt(1)
    else {
      self.fromNumber(a, c)
      if (!self.testBit(a - 1)) // force MSB set
        self.bitwiseTo(BigInteger.ONE.shiftLeft(a - 1), op_or, self)
      if (self.isEven()) self.dAddOffset(1, 0); // force odd
      while (!self.isProbablePrime(b)) {
        self.dAddOffset(2, 0)
        if (self.bitLength() > a) self.subTo(BigInteger.ONE.shiftLeft(a - 1), self)
      }
    }
  } else {
    // new BigInteger(int,RNG)
    var x = new Array(),
      t = a & 7
    x.length = (a >> 3) + 1
    b.nextBytes(x)
    if (t > 0) x[0] &= ((1 << t) - 1)
    else x[0] = 0
    self.fromString(x, 256)
  }
}

// (public) convert to bigendian byte array
function bnToByteArray() {
  var self = this
  var i = self.t,
    r = new Array()
  r[0] = self.s
  var p = self.DB - (i * self.DB) % 8,
    d, k = 0
  if (i-- > 0) {
    if (p < self.DB && (d = self[i] >> p) != (self.s & self.DM) >> p)
      r[k++] = d | (self.s << (self.DB - p))
    while (i >= 0) {
      if (p < 8) {
        d = (self[i] & ((1 << p) - 1)) << (8 - p)
        d |= self[--i] >> (p += self.DB - 8)
      } else {
        d = (self[i] >> (p -= 8)) & 0xff
        if (p <= 0) {
          p += self.DB
          --i
        }
      }
      if ((d & 0x80) != 0) d |= -256
      if (k === 0 && (self.s & 0x80) != (d & 0x80))++k
      if (k > 0 || d != self.s) r[k++] = d
    }
  }
  return r
}

function bnEquals(a) {
  return (this.compareTo(a) == 0)
}

function bnMin(a) {
  return (this.compareTo(a) < 0) ? this : a
}

function bnMax(a) {
  return (this.compareTo(a) > 0) ? this : a
}

// (protected) r = this op a (bitwise)
function bnpBitwiseTo(a, op, r) {
  var self = this
  var i, f, m = Math.min(a.t, self.t)
  for (i = 0; i < m; ++i) r[i] = op(self[i], a[i])
  if (a.t < self.t) {
    f = a.s & self.DM
    for (i = m; i < self.t; ++i) r[i] = op(self[i], f)
    r.t = self.t
  } else {
    f = self.s & self.DM
    for (i = m; i < a.t; ++i) r[i] = op(f, a[i])
    r.t = a.t
  }
  r.s = op(self.s, a.s)
  r.clamp()
}

// (public) this & a
function op_and(x, y) {
  return x & y
}

function bnAnd(a) {
  var r = new BigInteger()
  this.bitwiseTo(a, op_and, r)
  return r
}

// (public) this | a
function op_or(x, y) {
  return x | y
}

function bnOr(a) {
  var r = new BigInteger()
  this.bitwiseTo(a, op_or, r)
  return r
}

// (public) this ^ a
function op_xor(x, y) {
  return x ^ y
}

function bnXor(a) {
  var r = new BigInteger()
  this.bitwiseTo(a, op_xor, r)
  return r
}

// (public) this & ~a
function op_andnot(x, y) {
  return x & ~y
}

function bnAndNot(a) {
  var r = new BigInteger()
  this.bitwiseTo(a, op_andnot, r)
  return r
}

// (public) ~this
function bnNot() {
  var r = new BigInteger()
  for (var i = 0; i < this.t; ++i) r[i] = this.DM & ~this[i]
  r.t = this.t
  r.s = ~this.s
  return r
}

// (public) this << n
function bnShiftLeft(n) {
  var r = new BigInteger()
  if (n < 0) this.rShiftTo(-n, r)
  else this.lShiftTo(n, r)
  return r
}

// (public) this >> n
function bnShiftRight(n) {
  var r = new BigInteger()
  if (n < 0) this.lShiftTo(-n, r)
  else this.rShiftTo(n, r)
  return r
}

// return index of lowest 1-bit in x, x < 2^31
function lbit(x) {
  if (x == 0) return -1
  var r = 0
  if ((x & 0xffff) == 0) {
    x >>= 16
    r += 16
  }
  if ((x & 0xff) == 0) {
    x >>= 8
    r += 8
  }
  if ((x & 0xf) == 0) {
    x >>= 4
    r += 4
  }
  if ((x & 3) == 0) {
    x >>= 2
    r += 2
  }
  if ((x & 1) == 0)++r
  return r
}

// (public) returns index of lowest 1-bit (or -1 if none)
function bnGetLowestSetBit() {
  for (var i = 0; i < this.t; ++i)
    if (this[i] != 0) return i * this.DB + lbit(this[i])
  if (this.s < 0) return this.t * this.DB
  return -1
}

// return number of 1 bits in x
function cbit(x) {
  var r = 0
  while (x != 0) {
    x &= x - 1
    ++r
  }
  return r
}

// (public) return number of set bits
function bnBitCount() {
  var r = 0,
    x = this.s & this.DM
  for (var i = 0; i < this.t; ++i) r += cbit(this[i] ^ x)
  return r
}

// (public) true iff nth bit is set
function bnTestBit(n) {
  var j = Math.floor(n / this.DB)
  if (j >= this.t) return (this.s != 0)
  return ((this[j] & (1 << (n % this.DB))) != 0)
}

// (protected) this op (1<<n)
function bnpChangeBit(n, op) {
  var r = BigInteger.ONE.shiftLeft(n)
  this.bitwiseTo(r, op, r)
  return r
}

// (public) this | (1<<n)
function bnSetBit(n) {
  return this.changeBit(n, op_or)
}

// (public) this & ~(1<<n)
function bnClearBit(n) {
  return this.changeBit(n, op_andnot)
}

// (public) this ^ (1<<n)
function bnFlipBit(n) {
  return this.changeBit(n, op_xor)
}

// (protected) r = this + a
function bnpAddTo(a, r) {
  var self = this

  var i = 0,
    c = 0,
    m = Math.min(a.t, self.t)
  while (i < m) {
    c += self[i] + a[i]
    r[i++] = c & self.DM
    c >>= self.DB
  }
  if (a.t < self.t) {
    c += a.s
    while (i < self.t) {
      c += self[i]
      r[i++] = c & self.DM
      c >>= self.DB
    }
    c += self.s
  } else {
    c += self.s
    while (i < a.t) {
      c += a[i]
      r[i++] = c & self.DM
      c >>= self.DB
    }
    c += a.s
  }
  r.s = (c < 0) ? -1 : 0
  if (c > 0) r[i++] = c
  else if (c < -1) r[i++] = self.DV + c
  r.t = i
  r.clamp()
}

// (public) this + a
function bnAdd(a) {
  var r = new BigInteger()
  this.addTo(a, r)
  return r
}

// (public) this - a
function bnSubtract(a) {
  var r = new BigInteger()
  this.subTo(a, r)
  return r
}

// (public) this * a
function bnMultiply(a) {
  var r = new BigInteger()
  this.multiplyTo(a, r)
  return r
}

// (public) this^2
function bnSquare() {
  var r = new BigInteger()
  this.squareTo(r)
  return r
}

// (public) this / a
function bnDivide(a) {
  var r = new BigInteger()
  this.divRemTo(a, r, null)
  return r
}

// (public) this % a
function bnRemainder(a) {
  var r = new BigInteger()
  this.divRemTo(a, null, r)
  return r
}

// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
  var q = new BigInteger(),
    r = new BigInteger()
  this.divRemTo(a, q, r)
  return new Array(q, r)
}

// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
  this[this.t] = this.am(0, n - 1, this, 0, 0, this.t)
  ++this.t
  this.clamp()
}

// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n, w) {
  if (n == 0) return
  while (this.t <= w) this[this.t++] = 0
  this[w] += n
  while (this[w] >= this.DV) {
    this[w] -= this.DV
    if (++w >= this.t) this[this.t++] = 0
    ++this[w]
  }
}

// A "null" reducer
function NullExp() {}

function nNop(x) {
  return x
}

function nMulTo(x, y, r) {
  x.multiplyTo(y, r)
}

function nSqrTo(x, r) {
  x.squareTo(r)
}

NullExp.prototype.convert = nNop
NullExp.prototype.revert = nNop
NullExp.prototype.mulTo = nMulTo
NullExp.prototype.sqrTo = nSqrTo

// (public) this^e
function bnPow(e) {
  return this.exp(e, new NullExp())
}

// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a, n, r) {
  var i = Math.min(this.t + a.t, n)
  r.s = 0; // assumes a,this >= 0
  r.t = i
  while (i > 0) r[--i] = 0
  var j
  for (j = r.t - this.t; i < j; ++i) r[i + this.t] = this.am(0, a[i], r, i, 0, this.t)
  for (j = Math.min(a.t, n); i < j; ++i) this.am(0, a[i], r, i, 0, n - i)
  r.clamp()
}

// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a, n, r) {
  --n
  var i = r.t = this.t + a.t - n
  r.s = 0; // assumes a,this >= 0
  while (--i >= 0) r[i] = 0
  for (i = Math.max(n - this.t, 0); i < a.t; ++i)
    r[this.t + i - n] = this.am(n - i, a[i], r, 0, 0, this.t + i - n)
  r.clamp()
  r.drShiftTo(1, r)
}

// Barrett modular reduction
function Barrett(m) {
  // setup Barrett
  this.r2 = new BigInteger()
  this.q3 = new BigInteger()
  BigInteger.ONE.dlShiftTo(2 * m.t, this.r2)
  this.mu = this.r2.divide(m)
  this.m = m
}

function barrettConvert(x) {
  if (x.s < 0 || x.t > 2 * this.m.t) return x.mod(this.m)
  else if (x.compareTo(this.m) < 0) return x
  else {
    var r = new BigInteger()
    x.copyTo(r)
    this.reduce(r)
    return r
  }
}

function barrettRevert(x) {
  return x
}

// x = x mod m (HAC 14.42)
function barrettReduce(x) {
  var self = this
  x.drShiftTo(self.m.t - 1, self.r2)
  if (x.t > self.m.t + 1) {
    x.t = self.m.t + 1
    x.clamp()
  }
  self.mu.multiplyUpperTo(self.r2, self.m.t + 1, self.q3)
  self.m.multiplyLowerTo(self.q3, self.m.t + 1, self.r2)
  while (x.compareTo(self.r2) < 0) x.dAddOffset(1, self.m.t + 1)
  x.subTo(self.r2, x)
  while (x.compareTo(self.m) >= 0) x.subTo(self.m, x)
}

// r = x^2 mod m; x != r
function barrettSqrTo(x, r) {
  x.squareTo(r)
  this.reduce(r)
}

// r = x*y mod m; x,y != r
function barrettMulTo(x, y, r) {
  x.multiplyTo(y, r)
  this.reduce(r)
}

Barrett.prototype.convert = barrettConvert
Barrett.prototype.revert = barrettRevert
Barrett.prototype.reduce = barrettReduce
Barrett.prototype.mulTo = barrettMulTo
Barrett.prototype.sqrTo = barrettSqrTo

// (public) this^e % m (HAC 14.85)
function bnModPow(e, m) {
  var i = e.bitLength(),
    k, r = nbv(1),
    z
  if (i <= 0) return r
  else if (i < 18) k = 1
  else if (i < 48) k = 3
  else if (i < 144) k = 4
  else if (i < 768) k = 5
  else k = 6
  if (i < 8)
    z = new Classic(m)
  else if (m.isEven())
    z = new Barrett(m)
  else
    z = new Montgomery(m)

  // precomputation
  var g = new Array(),
    n = 3,
    k1 = k - 1,
    km = (1 << k) - 1
  g[1] = z.convert(this)
  if (k > 1) {
    var g2 = new BigInteger()
    z.sqrTo(g[1], g2)
    while (n <= km) {
      g[n] = new BigInteger()
      z.mulTo(g2, g[n - 2], g[n])
      n += 2
    }
  }

  var j = e.t - 1,
    w, is1 = true,
    r2 = new BigInteger(),
    t
  i = nbits(e[j]) - 1
  while (j >= 0) {
    if (i >= k1) w = (e[j] >> (i - k1)) & km
    else {
      w = (e[j] & ((1 << (i + 1)) - 1)) << (k1 - i)
      if (j > 0) w |= e[j - 1] >> (this.DB + i - k1)
    }

    n = k
    while ((w & 1) == 0) {
      w >>= 1
      --n
    }
    if ((i -= n) < 0) {
      i += this.DB
      --j
    }
    if (is1) { // ret == 1, don't bother squaring or multiplying it
      g[w].copyTo(r)
      is1 = false
    } else {
      while (n > 1) {
        z.sqrTo(r, r2)
        z.sqrTo(r2, r)
        n -= 2
      }
      if (n > 0) z.sqrTo(r, r2)
      else {
        t = r
        r = r2
        r2 = t
      }
      z.mulTo(r2, g[w], r)
    }

    while (j >= 0 && (e[j] & (1 << i)) == 0) {
      z.sqrTo(r, r2)
      t = r
      r = r2
      r2 = t
      if (--i < 0) {
        i = this.DB - 1
        --j
      }
    }
  }
  return z.revert(r)
}

// (public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
  var x = (this.s < 0) ? this.negate() : this.clone()
  var y = (a.s < 0) ? a.negate() : a.clone()
  if (x.compareTo(y) < 0) {
    var t = x
    x = y
    y = t
  }
  var i = x.getLowestSetBit(),
    g = y.getLowestSetBit()
  if (g < 0) return x
  if (i < g) g = i
  if (g > 0) {
    x.rShiftTo(g, x)
    y.rShiftTo(g, y)
  }
  while (x.signum() > 0) {
    if ((i = x.getLowestSetBit()) > 0) x.rShiftTo(i, x)
    if ((i = y.getLowestSetBit()) > 0) y.rShiftTo(i, y)
    if (x.compareTo(y) >= 0) {
      x.subTo(y, x)
      x.rShiftTo(1, x)
    } else {
      y.subTo(x, y)
      y.rShiftTo(1, y)
    }
  }
  if (g > 0) y.lShiftTo(g, y)
  return y
}

// (protected) this % n, n < 2^26
function bnpModInt(n) {
  if (n <= 0) return 0
  var d = this.DV % n,
    r = (this.s < 0) ? n - 1 : 0
  if (this.t > 0)
    if (d == 0) r = this[0] % n
    else
      for (var i = this.t - 1; i >= 0; --i) r = (d * r + this[i]) % n
  return r
}

// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
  var ac = m.isEven()
  if ((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO
  var u = m.clone(),
    v = this.clone()
  var a = nbv(1),
    b = nbv(0),
    c = nbv(0),
    d = nbv(1)
  while (u.signum() != 0) {
    while (u.isEven()) {
      u.rShiftTo(1, u)
      if (ac) {
        if (!a.isEven() || !b.isEven()) {
          a.addTo(this, a)
          b.subTo(m, b)
        }
        a.rShiftTo(1, a)
      } else if (!b.isEven()) b.subTo(m, b)
      b.rShiftTo(1, b)
    }
    while (v.isEven()) {
      v.rShiftTo(1, v)
      if (ac) {
        if (!c.isEven() || !d.isEven()) {
          c.addTo(this, c)
          d.subTo(m, d)
        }
        c.rShiftTo(1, c)
      } else if (!d.isEven()) d.subTo(m, d)
      d.rShiftTo(1, d)
    }
    if (u.compareTo(v) >= 0) {
      u.subTo(v, u)
      if (ac) a.subTo(c, a)
      b.subTo(d, b)
    } else {
      v.subTo(u, v)
      if (ac) c.subTo(a, c)
      d.subTo(b, d)
    }
  }
  if (v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO
  if (d.compareTo(m) >= 0) return d.subtract(m)
  if (d.signum() < 0) d.addTo(m, d)
  else return d
  if (d.signum() < 0) return d.add(m)
  else return d
}

var lowprimes = [
  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
  73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
  157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
  239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
  331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
  421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
  509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
  613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
  709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
  821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
  919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
]

var lplim = (1 << 26) / lowprimes[lowprimes.length - 1]

// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
  var i, x = this.abs()
  if (x.t == 1 && x[0] <= lowprimes[lowprimes.length - 1]) {
    for (i = 0; i < lowprimes.length; ++i)
      if (x[0] == lowprimes[i]) return true
    return false
  }
  if (x.isEven()) return false
  i = 1
  while (i < lowprimes.length) {
    var m = lowprimes[i],
      j = i + 1
    while (j < lowprimes.length && m < lplim) m *= lowprimes[j++]
    m = x.modInt(m)
    while (i < j) if (m % lowprimes[i++] == 0) return false
  }
  return x.millerRabin(t)
}

// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
  var n1 = this.subtract(BigInteger.ONE)
  var k = n1.getLowestSetBit()
  if (k <= 0) return false
  var r = n1.shiftRight(k)
  t = (t + 1) >> 1
  if (t > lowprimes.length) t = lowprimes.length
  var a = new BigInteger(null)
  var j, bases = []
  for (var i = 0; i < t; ++i) {
    for (;;) {
      j = lowprimes[Math.floor(Math.random() * lowprimes.length)]
      if (bases.indexOf(j) == -1) break
    }
    bases.push(j)
    a.fromInt(j)
    var y = a.modPow(r, this)
    if (y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
      var j = 1
      while (j++ < k && y.compareTo(n1) != 0) {
        y = y.modPowInt(2, this)
        if (y.compareTo(BigInteger.ONE) == 0) return false
      }
      if (y.compareTo(n1) != 0) return false
    }
  }
  return true
}

// protected
proto.chunkSize = bnpChunkSize
proto.toRadix = bnpToRadix
proto.fromRadix = bnpFromRadix
proto.fromNumber = bnpFromNumber
proto.bitwiseTo = bnpBitwiseTo
proto.changeBit = bnpChangeBit
proto.addTo = bnpAddTo
proto.dMultiply = bnpDMultiply
proto.dAddOffset = bnpDAddOffset
proto.multiplyLowerTo = bnpMultiplyLowerTo
proto.multiplyUpperTo = bnpMultiplyUpperTo
proto.modInt = bnpModInt
proto.millerRabin = bnpMillerRabin

// public
proto.clone = bnClone
proto.intValue = bnIntValue
proto.byteValue = bnByteValue
proto.shortValue = bnShortValue
proto.signum = bnSigNum
proto.toByteArray = bnToByteArray
proto.equals = bnEquals
proto.min = bnMin
proto.max = bnMax
proto.and = bnAnd
proto.or = bnOr
proto.xor = bnXor
proto.andNot = bnAndNot
proto.not = bnNot
proto.shiftLeft = bnShiftLeft
proto.shiftRight = bnShiftRight
proto.getLowestSetBit = bnGetLowestSetBit
proto.bitCount = bnBitCount
proto.testBit = bnTestBit
proto.setBit = bnSetBit
proto.clearBit = bnClearBit
proto.flipBit = bnFlipBit
proto.add = bnAdd
proto.subtract = bnSubtract
proto.multiply = bnMultiply
proto.divide = bnDivide
proto.remainder = bnRemainder
proto.divideAndRemainder = bnDivideAndRemainder
proto.modPow = bnModPow
proto.modInverse = bnModInverse
proto.pow = bnPow
proto.gcd = bnGCD
proto.isProbablePrime = bnIsProbablePrime

// JSBN-specific extension
proto.square = bnSquare

// constants
BigInteger.ZERO = nbv(0)
BigInteger.ONE = nbv(1)
BigInteger.valueOf = nbv

module.exports = BigInteger

},{"../package.json":7}],5:[function(require,module,exports){
(function (Buffer){
// FIXME: Kind of a weird way to throw exceptions, consider removing
var assert = require('assert')
var BigInteger = require('./bigi')

/**
 * Turns a byte array into a big integer.
 *
 * This function will interpret a byte array as a big integer in big
 * endian notation.
 */
BigInteger.fromByteArrayUnsigned = function(byteArray) {
  // BigInteger expects a DER integer conformant byte array
  if (byteArray[0] & 0x80) {
    return new BigInteger([0].concat(byteArray))
  }

  return new BigInteger(byteArray)
}

/**
 * Returns a byte array representation of the big integer.
 *
 * This returns the absolute of the contained value in big endian
 * form. A value of zero results in an empty array.
 */
BigInteger.prototype.toByteArrayUnsigned = function() {
  var byteArray = this.toByteArray()
  return byteArray[0] === 0 ? byteArray.slice(1) : byteArray
}

BigInteger.fromDERInteger = function(byteArray) {
  return new BigInteger(byteArray)
}

/*
 * Converts BigInteger to a DER integer representation.
 *
 * The format for this value uses the most significant bit as a sign
 * bit.  If the most significant bit is already set and the integer is
 * positive, a 0x00 is prepended.
 *
 * Examples:
 *
 *      0 =>     0x00
 *      1 =>     0x01
 *     -1 =>     0xff
 *    127 =>     0x7f
 *   -127 =>     0x81
 *    128 =>   0x0080
 *   -128 =>     0x80
 *    255 =>   0x00ff
 *   -255 =>   0xff01
 *  16300 =>   0x3fac
 * -16300 =>   0xc054
 *  62300 => 0x00f35c
 * -62300 => 0xff0ca4
*/
BigInteger.prototype.toDERInteger = BigInteger.prototype.toByteArray

BigInteger.fromBuffer = function(buffer) {
  // BigInteger expects a DER integer conformant byte array
  if (buffer[0] & 0x80) {
    var byteArray = Array.prototype.slice.call(buffer)

    return new BigInteger([0].concat(byteArray))
  }

  return new BigInteger(buffer)
}

BigInteger.fromHex = function(hex) {
  if (hex === '') return BigInteger.ZERO

  assert.equal(hex, hex.match(/^[A-Fa-f0-9]+/), 'Invalid hex string')
  assert.equal(hex.length % 2, 0, 'Incomplete hex')
  return new BigInteger(hex, 16)
}

BigInteger.prototype.toBuffer = function(size) {
  var byteArray = this.toByteArrayUnsigned()
  var zeros = []

  var padding = size - byteArray.length
  while (zeros.length < padding) zeros.push(0)

  return new Buffer(zeros.concat(byteArray))
}

BigInteger.prototype.toHex = function(size) {
  return this.toBuffer(size).toString('hex')
}

}).call(this,require("buffer").Buffer)
},{"./bigi":4,"assert":8,"buffer":10}],6:[function(require,module,exports){
var BigInteger = require('./bigi')

//addons
require('./convert')

module.exports = BigInteger
},{"./bigi":4,"./convert":5}],7:[function(require,module,exports){
module.exports={
  "name": "bigi",
  "version": "1.4.0",
  "description": "Big integers.",
  "keywords": [
    "cryptography",
    "math",
    "bitcoin",
    "arbitrary",
    "precision",
    "arithmetic",
    "big",
    "integer",
    "int",
    "number",
    "biginteger",
    "bigint",
    "bignumber",
    "decimal",
    "float"
  ],
  "devDependencies": {
    "mocha": "^1.20.1",
    "jshint": "^2.5.1",
    "coveralls": "^2.10.0",
    "istanbul": "^0.2.11"
  },
  "repository": {
    "url": "https://github.com/cryptocoinjs/bigi",
    "type": "git"
  },
  "main": "./lib/index.js",
  "scripts": {
    "test": "_mocha -- test/*.js",
    "jshint": "jshint --config jshint.json lib/*.js ; true",
    "unit": "mocha",
    "coverage": "istanbul cover ./node_modules/.bin/_mocha -- --reporter list test/*.js",
    "coveralls": "npm run-script coverage && node ./node_modules/.bin/coveralls < coverage/lcov.info"
  },
  "dependencies": {},
  "testling": {
    "files": "test/*.js",
    "harness": "mocha",
    "browsers": [
      "ie/9..latest",
      "firefox/latest",
      "chrome/latest",
      "safari/6.0..latest",
      "iphone/6.0..latest",
      "android-browser/4.2..latest"
    ]
  },
  "readme": "bigi\n======\n\n[![build status](https://secure.travis-ci.org/cryptocoinjs/bigi.png)](http://travis-ci.org/cryptocoinjs/bigi)\n[![Coverage Status](https://img.shields.io/coveralls/cryptocoinjs/bigi.svg)](https://coveralls.io/r/cryptocoinjs/bigi)\n[![Version](http://img.shields.io/npm/v/bigi.svg)](https://www.npmjs.org/package/bigi)\n\n[![browser support](https://ci.testling.com/cryptocoinjs/bigi.png)](https://ci.testling.com/cryptocoinjs/bigi)\n\nJavaScript library to manipulate big integers. Based on `jsbn` made by [Tom Wu](http://www-cs-students.stanford.edu/~tjw/jsbn/)\n\nOfficial documentation: \n\nhttp://cryptocoinjs.com/modules/misc/bigi/",
  "readmeFilename": "README.md",
  "bugs": {
    "url": "https://github.com/cryptocoinjs/bigi/issues"
  },
  "homepage": "https://github.com/cryptocoinjs/bigi",
  "_id": "bigi@1.4.0",
  "_from": "bigi@"
}

},{}],8:[function(require,module,exports){
// http://wiki.commonjs.org/wiki/Unit_Testing/1.0
//
// THIS IS NOT TESTED NOR LIKELY TO WORK OUTSIDE V8!
//
// Originally from narwhal.js (http://narwhaljs.org)
// Copyright (c) 2009 Thomas Robinson <280north.com>
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the 'Software'), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
// ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

// when used in node, this will actually load the util module we depend on
// versus loading the builtin util module as happens otherwise
// this is a bug in node module loading as far as I am concerned
var util = require('util/');

var pSlice = Array.prototype.slice;
var hasOwn = Object.prototype.hasOwnProperty;

// 1. The assert module provides functions that throw
// AssertionError's when particular conditions are not met. The
// assert module must conform to the following interface.

var assert = module.exports = ok;

// 2. The AssertionError is defined in assert.
// new assert.AssertionError({ message: message,
//                             actual: actual,
//                             expected: expected })

assert.AssertionError = function AssertionError(options) {
  this.name = 'AssertionError';
  this.actual = options.actual;
  this.expected = options.expected;
  this.operator = options.operator;
  if (options.message) {
    this.message = options.message;
    this.generatedMessage = false;
  } else {
    this.message = getMessage(this);
    this.generatedMessage = true;
  }
  var stackStartFunction = options.stackStartFunction || fail;

  if (Error.captureStackTrace) {
    Error.captureStackTrace(this, stackStartFunction);
  }
  else {
    // non v8 browsers so we can have a stacktrace
    var err = new Error();
    if (err.stack) {
      var out = err.stack;

      // try to strip useless frames
      var fn_name = stackStartFunction.name;
      var idx = out.indexOf('\n' + fn_name);
      if (idx >= 0) {
        // once we have located the function frame
        // we need to strip out everything before it (and its line)
        var next_line = out.indexOf('\n', idx + 1);
        out = out.substring(next_line + 1);
      }

      this.stack = out;
    }
  }
};

// assert.AssertionError instanceof Error
util.inherits(assert.AssertionError, Error);

function replacer(key, value) {
  if (util.isUndefined(value)) {
    return '' + value;
  }
  if (util.isNumber(value) && (isNaN(value) || !isFinite(value))) {
    return value.toString();
  }
  if (util.isFunction(value) || util.isRegExp(value)) {
    return value.toString();
  }
  return value;
}

function truncate(s, n) {
  if (util.isString(s)) {
    return s.length < n ? s : s.slice(0, n);
  } else {
    return s;
  }
}

function getMessage(self) {
  return truncate(JSON.stringify(self.actual, replacer), 128) + ' ' +
         self.operator + ' ' +
         truncate(JSON.stringify(self.expected, replacer), 128);
}

// At present only the three keys mentioned above are used and
// understood by the spec. Implementations or sub modules can pass
// other keys to the AssertionError's constructor - they will be
// ignored.

// 3. All of the following functions must throw an AssertionError
// when a corresponding condition is not met, with a message that
// may be undefined if not provided.  All assertion methods provide
// both the actual and expected values to the assertion error for
// display purposes.

function fail(actual, expected, message, operator, stackStartFunction) {
  throw new assert.AssertionError({
    message: message,
    actual: actual,
    expected: expected,
    operator: operator,
    stackStartFunction: stackStartFunc