/** @fileOverview Javascript cryptography implementation.
 *
 * Crush to remove comments, shorten variable names and
 * generally reduce transmission size.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

"use strict";
/*jslint indent: 2, bitwise: false, nomen: false, plusplus: false, white: false, regexp: false */
/*global document, window, escape, unescape */

/** @namespace The Stanford Javascript Crypto Library, top-level namespace. */
var sjcl = {
  /** @namespace Symmetric ciphers. */
  cipher: {},

  /** @namespace Hash functions.  Right now only SHA256 is implemented. */
  hash: {},

  /** @namespace Key exchange functions.  Right now only SRP is implemented. */
  keyexchange: {},
  
  /** @namespace Block cipher modes of operation. */
  mode: {},

  /** @namespace Miscellaneous.  HMAC and PBKDF2. */
  misc: {},
  
  /**
   * @namespace Bit array encoders and decoders.
   *
   * @description
   * The members of this namespace are functions which translate between
   * SJCL's bitArrays and other objects (usually strings).  Because it
   * isn't always clear which direction is encoding and which is decoding,
   * the method names are "fromBits" and "toBits".
   */
  codec: {},
  
  /** @namespace Exceptions. */
  exception: {
    /** @constructor Ciphertext is corrupt. */
    corrupt: function(message) {
      this.toString = function() { return "CORRUPT: "+this.message; };
      this.message = message;
    },
    
    /** @constructor Invalid parameter. */
    invalid: function(message) {
      this.toString = function() { return "INVALID: "+this.message; };
      this.message = message;
    },
    
    /** @constructor Bug or missing feature in SJCL. @constructor */
    bug: function(message) {
      this.toString = function() { return "BUG: "+this.message; };
      this.message = message;
    },

    /** @constructor Something isn't ready. */
    notReady: function(message) {
      this.toString = function() { return "NOT READY: "+this.message; };
      this.message = message;
    }
  }
};

if(typeof module != 'undefined' && module.exports){
  module.exports = sjcl;
}

/** @fileOverview Low-level AES implementation.
 *
 * This file contains a low-level implementation of AES, optimized for
 * size and for efficiency on several browsers.  It is based on
 * OpenSSL's aes_core.c, a public-domain implementation by Vincent
 * Rijmen, Antoon Bosselaers and Paulo Barreto.
 *
 * An older version of this implementation is available in the public
 * domain, but this one is (c) Emily Stark, Mike Hamburg, Dan Boneh,
 * Stanford University 2008-2010 and BSD-licensed for liability
 * reasons.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/**
 * Schedule out an AES key for both encryption and decryption.  This
 * is a low-level class.  Use a cipher mode to do bulk encryption.
 *
 * @constructor
 * @param {Array} key The key as an array of 4, 6 or 8 words.
 *
 * @class Advanced Encryption Standard (low-level interface)
 */
sjcl.cipher.aes = function (key) {
  if (!this._tables[0][0][0]) {
    this._precompute();
  }
  
  var i, j, tmp,
    encKey, decKey,
    sbox = this._tables[0][4], decTable = this._tables[1],
    keyLen = key.length, rcon = 1;
  
  if (keyLen !== 4 && keyLen !== 6 && keyLen !== 8) {
    throw new sjcl.exception.invalid("invalid aes key size");
  }
  
  this._key = [encKey = key.slice(0), decKey = []];
  
  // schedule encryption keys
  for (i = keyLen; i < 4 * keyLen + 28; i++) {
    tmp = encKey[i-1];
    
    // apply sbox
    if (i%keyLen === 0 || (keyLen === 8 && i%keyLen === 4)) {
      tmp = sbox[tmp>>>24]<<24 ^ sbox[tmp>>16&255]<<16 ^ sbox[tmp>>8&255]<<8 ^ sbox[tmp&255];
      
      // shift rows and add rcon
      if (i%keyLen === 0) {
        tmp = tmp<<8 ^ tmp>>>24 ^ rcon<<24;
        rcon = rcon<<1 ^ (rcon>>7)*283;
      }
    }
    
    encKey[i] = encKey[i-keyLen] ^ tmp;
  }
  
  // schedule decryption keys
  for (j = 0; i; j++, i--) {
    tmp = encKey[j&3 ? i : i - 4];
    if (i<=4 || j<4) {
      decKey[j] = tmp;
    } else {
      decKey[j] = decTable[0][sbox[tmp>>>24      ]] ^
                  decTable[1][sbox[tmp>>16  & 255]] ^
                  decTable[2][sbox[tmp>>8   & 255]] ^
                  decTable[3][sbox[tmp      & 255]];
    }
  }
};

sjcl.cipher.aes.prototype = {
  // public
  /* Something like this might appear here eventually
  name: "AES",
  blockSize: 4,
  keySizes: [4,6,8],
  */
  
  /**
   * Encrypt an array of 4 big-endian words.
   * @param {Array} data The plaintext.
   * @return {Array} The ciphertext.
   */
  encrypt:function (data) { return this._crypt(data,0); },
  
  /**
   * Decrypt an array of 4 big-endian words.
   * @param {Array} data The ciphertext.
   * @return {Array} The plaintext.
   */
  decrypt:function (data) { return this._crypt(data,1); },
  
  /**
   * The expanded S-box and inverse S-box tables.  These will be computed
   * on the client so that we don't have to send them down the wire.
   *
   * There are two tables, _tables[0] is for encryption and
   * _tables[1] is for decryption.
   *
   * The first 4 sub-tables are the expanded S-box with MixColumns.  The
   * last (_tables[01][4]) is the S-box itself.
   *
   * @private
   */
  _tables: [[[],[],[],[],[]],[[],[],[],[],[]]],

  /**
   * Expand the S-box tables.
   *
   * @private
   */
  _precompute: function () {
   var encTable = this._tables[0], decTable = this._tables[1],
       sbox = encTable[4], sboxInv = decTable[4],
       i, x, xInv, d=[], th=[], x2, x4, x8, s, tEnc, tDec;

    // Compute double and third tables
   for (i = 0; i < 256; i++) {
     th[( d[i] = i<<1 ^ (i>>7)*283 )^i]=i;
   }
   
   for (x = xInv = 0; !sbox[x]; x ^= x2 || 1, xInv = th[xInv] || 1) {
     // Compute sbox
     s = xInv ^ xInv<<1 ^ xInv<<2 ^ xInv<<3 ^ xInv<<4;
     s = s>>8 ^ s&255 ^ 99;
     sbox[x] = s;
     sboxInv[s] = x;
     
     // Compute MixColumns
     x8 = d[x4 = d[x2 = d[x]]];
     tDec = x8*0x1010101 ^ x4*0x10001 ^ x2*0x101 ^ x*0x1010100;
     tEnc = d[s]*0x101 ^ s*0x1010100;
     
     for (i = 0; i < 4; i++) {
       encTable[i][x] = tEnc = tEnc<<24 ^ tEnc>>>8;
       decTable[i][s] = tDec = tDec<<24 ^ tDec>>>8;
     }
   }
   
   // Compactify.  Considerable speedup on Firefox.
   for (i = 0; i < 5; i++) {
     encTable[i] = encTable[i].slice(0);
     decTable[i] = decTable[i].slice(0);
   }
  },
  
  /**
   * Encryption and decryption core.
   * @param {Array} input Four words to be encrypted or decrypted.
   * @param dir The direction, 0 for encrypt and 1 for decrypt.
   * @return {Array} The four encrypted or decrypted words.
   * @private
   */
  _crypt:function (input, dir) {
    if (input.length !== 4) {
      throw new sjcl.exception.invalid("invalid aes block size");
    }
    
    var key = this._key[dir],
        // state variables a,b,c,d are loaded with pre-whitened data
        a = input[0]           ^ key[0],
        b = input[dir ? 3 : 1] ^ key[1],
        c = input[2]           ^ key[2],
        d = input[dir ? 1 : 3] ^ key[3],
        a2, b2, c2,
        
        nInnerRounds = key.length/4 - 2,
        i,
        kIndex = 4,
        out = [0,0,0,0],
        table = this._tables[dir],
        
        // load up the tables
        t0    = table[0],
        t1    = table[1],
        t2    = table[2],
        t3    = table[3],
        sbox  = table[4];
 
    // Inner rounds.  Cribbed from OpenSSL.
    for (i = 0; i < nInnerRounds; i++) {
      a2 = t0[a>>>24] ^ t1[b>>16 & 255] ^ t2[c>>8 & 255] ^ t3[d & 255] ^ key[kIndex];
      b2 = t0[b>>>24] ^ t1[c>>16 & 255] ^ t2[d>>8 & 255] ^ t3[a & 255] ^ key[kIndex + 1];
      c2 = t0[c>>>24] ^ t1[d>>16 & 255] ^ t2[a>>8 & 255] ^ t3[b & 255] ^ key[kIndex + 2];
      d  = t0[d>>>24] ^ t1[a>>16 & 255] ^ t2[b>>8 & 255] ^ t3[c & 255] ^ key[kIndex + 3];
      kIndex += 4;
      a=a2; b=b2; c=c2;
    }
        
    // Last round.
    for (i = 0; i < 4; i++) {
      out[dir ? 3&-i : i] =
        sbox[a>>>24      ]<<24 ^ 
        sbox[b>>16  & 255]<<16 ^
        sbox[c>>8   & 255]<<8  ^
        sbox[d      & 255]     ^
        key[kIndex++];
      a2=a; a=b; b=c; c=d; d=a2;
    }
    
    return out;
  }
};


/** @fileOverview Arrays of bits, encoded as arrays of Numbers.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/** @namespace Arrays of bits, encoded as arrays of Numbers.
 *
 * @description
 * <p>
 * These objects are the currency accepted by SJCL's crypto functions.
 * </p>
 *
 * <p>
 * Most of our crypto primitives operate on arrays of 4-byte words internally,
 * but many of them can take arguments that are not a multiple of 4 bytes.
 * This library encodes arrays of bits (whose size need not be a multiple of 8
 * bits) as arrays of 32-bit words.  The bits are packed, big-endian, into an
 * array of words, 32 bits at a time.  Since the words are double-precision
 * floating point numbers, they fit some extra data.  We use this (in a private,
 * possibly-changing manner) to encode the number of bits actually  present
 * in the last word of the array.
 * </p>
 *
 * <p>
 * Because bitwise ops clear this out-of-band data, these arrays can be passed
 * to ciphers like AES which want arrays of words.
 * </p>
 */
sjcl.bitArray = {
  /**
   * Array slices in units of bits.
   * @param {bitArray} a The array to slice.
   * @param {Number} bstart The offset to the start of the slice, in bits.
   * @param {Number} bend The offset to the end of the slice, in bits.  If this is undefined,
   * slice until the end of the array.
   * @return {bitArray} The requested slice.
   */
  bitSlice: function (a, bstart, bend) {
    a = sjcl.bitArray._shiftRight(a.slice(bstart/32), 32 - (bstart & 31)).slice(1);
    return (bend === undefined) ? a : sjcl.bitArray.clamp(a, bend-bstart);
  },

  /**
   * Extract a number packed into a bit array.
   * @param {bitArray} a The array to slice.
   * @param {Number} bstart The offset to the start of the slice, in bits.
   * @param {Number} length The length of the number to extract.
   * @return {Number} The requested slice.
   */
  extract: function(a, bstart, blength) {
    // FIXME: this Math.floor is not necessary at all, but for some reason
    // seems to suppress a bug in the Chromium JIT.
    var x, sh = Math.floor((-bstart-blength) & 31);
    if ((bstart + blength - 1 ^ bstart) & -32) {
      // it crosses a boundary
      x = (a[bstart/32|0] << (32 - sh)) ^ (a[bstart/32+1|0] >>> sh);
    } else {
      // within a single word
      x = a[bstart/32|0] >>> sh;
    }
    return x & ((1<<blength) - 1);
  },

  /**
   * Concatenate two bit arrays.
   * @param {bitArray} a1 The first array.
   * @param {bitArray} a2 The second array.
   * @return {bitArray} The concatenation of a1 and a2.
   */
  concat: function (a1, a2) {
    if (a1.length === 0 || a2.length === 0) {
      return a1.concat(a2);
    }
    
    var out, i, last = a1[a1.length-1], shift = sjcl.bitArray.getPartial(last);
    if (shift === 32) {
      return a1.concat(a2);
    } else {
      return sjcl.bitArray._shiftRight(a2, shift, last|0, a1.slice(0,a1.length-1));
    }
  },

  /**
   * Find the length of an array of bits.
   * @param {bitArray} a The array.
   * @return {Number} The length of a, in bits.
   */
  bitLength: function (a) {
    var l = a.length, x;
    if (l === 0) { return 0; }
    x = a[l - 1];
    return (l-1) * 32 + sjcl.bitArray.getPartial(x);
  },

  /**
   * Truncate an array.
   * @param {bitArray} a The array.
   * @param {Number} len The length to truncate to, in bits.
   * @return {bitArray} A new array, truncated to len bits.
   */
  clamp: function (a, len) {
    if (a.length * 32 < len) { return a; }
    a = a.slice(0, Math.ceil(len / 32));
    var l = a.length;
    len = len & 31;
    if (l > 0 && len) {
      a[l-1] = sjcl.bitArray.partial(len, a[l-1] & 0x80000000 >> (len-1), 1);
    }
    return a;
  },

  /**
   * Make a partial word for a bit array.
   * @param {Number} len The number of bits in the word.
   * @param {Number} x The bits.
   * @param {Number} [0] _end Pass 1 if x has already been shifted to the high side.
   * @return {Number} The partial word.
   */
  partial: function (len, x, _end) {
    if (len === 32) { return x; }
    return (_end ? x|0 : x << (32-len)) + len * 0x10000000000;
  },

  /**
   * Get the number of bits used by a partial word.
   * @param {Number} x The partial word.
   * @return {Number} The number of bits used by the partial word.
   */
  getPartial: function (x) {
    return Math.round(x/0x10000000000) || 32;
  },

  /**
   * Compare two arrays for equality in a predictable amount of time.
   * @param {bitArray} a The first array.
   * @param {bitArray} b The second array.
   * @return {boolean} true if a == b; false otherwise.
   */
  equal: function (a, b) {
    if (sjcl.bitArray.bitLength(a) !== sjcl.bitArray.bitLength(b)) {
      return false;
    }
    var x = 0, i;
    for (i=0; i<a.length; i++) {
      x |= a[i]^b[i];
    }
    return (x === 0);
  },

  /** Shift an array right.
   * @param {bitArray} a The array to shift.
   * @param {Number} shift The number of bits to shift.
   * @param {Number} [carry=0] A byte to carry in
   * @param {bitArray} [out=[]] An array to prepend to the output.
   * @private
   */
  _shiftRight: function (a, shift, carry, out) {
    var i, last2=0, shift2;
    if (out === undefined) { out = []; }
    
    for (; shift >= 32; shift -= 32) {
      out.push(carry);
      carry = 0;
    }
    if (shift === 0) {
      return out.concat(a);
    }
    
    for (i=0; i<a.length; i++) {
      out.push(carry | a[i]>>>shift);
      carry = a[i] << (32-shift);
    }
    last2 = a.length ? a[a.length-1] : 0;
    shift2 = sjcl.bitArray.getPartial(last2);
    out.push(sjcl.bitArray.partial(shift+shift2 & 31, (shift + shift2 > 32) ? carry : out.pop(),1));
    return out;
  },
  
  /** xor a block of 4 words together.
   * @private
   */
  _xor4: function(x,y) {
    return [x[0]^y[0],x[1]^y[1],x[2]^y[2],x[3]^y[3]];
  }
};

/** @fileOverview Bit array codec implementations.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */
 
/** @namespace UTF-8 strings */
sjcl.codec.utf8String = {
  /** Convert from a bitArray to a UTF-8 string. */
  fromBits: function (arr) {
    var out = "", bl = sjcl.bitArray.bitLength(arr), i, tmp;
    for (i=0; i<bl/8; i++) {
      if ((i&3) === 0) {
        tmp = arr[i/4];
      }
      out += String.fromCharCode(tmp >>> 24);
      tmp <<= 8;
    }
    return decodeURIComponent(escape(out));
  },
  
  /** Convert from a UTF-8 string to a bitArray. */
  toBits: function (str) {
    str = unescape(encodeURIComponent(str));
    var out = [], i, tmp=0;
    for (i=0; i<str.length; i++) {
      tmp = tmp << 8 | str.charCodeAt(i);
      if ((i&3) === 3) {
        out.push(tmp);
        tmp = 0;
      }
    }
    if (i&3) {
      out.push(sjcl.bitArray.partial(8*(i&3), tmp));
    }
    return out;
  }
};

/** @fileOverview Bit array codec implementations.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/** @namespace Hexadecimal */
sjcl.codec.hex = {
  /** Convert from a bitArray to a hex string. */
  fromBits: function (arr) {
    var out = "", i, x;
    for (i=0; i<arr.length; i++) {
      out += ((arr[i]|0)+0xF00000000000).toString(16).substr(4);
    }
    return out.substr(0, sjcl.bitArray.bitLength(arr)/4);//.replace(/(.{8})/g, "$1 ");
  },
  /** Convert from a hex string to a bitArray. */
  toBits: function (str) {
    var i, out=[], len;
    str = str.replace(/\s|0x/g, "");
    len = str.length;
    str = str + "00000000";
    for (i=0; i<str.length; i+=8) {
      out.push(parseInt(str.substr(i,8),16)^0);
    }
    return sjcl.bitArray.clamp(out, len*4);
  }
};


/** @fileOverview Bit array codec implementations.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/** @namespace Base64 encoding/decoding */
sjcl.codec.base64 = {
  /** The base64 alphabet.
   * @private
   */
  _chars: "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/",
  
  /** Convert from a bitArray to a base64 string. */
  fromBits: function (arr, _noEquals, _url) {
    var out = "", i, bits=0, c = sjcl.codec.base64._chars, ta=0, bl = sjcl.bitArray.bitLength(arr);
    if (_url) c = c.substr(0,62) + '-_';
    for (i=0; out.length * 6 < bl; ) {
      out += c.charAt((ta ^ arr[i]>>>bits) >>> 26);
      if (bits < 6) {
        ta = arr[i] << (6-bits);
        bits += 26;
        i++;
      } else {
        ta <<= 6;
        bits -= 6;
      }
    }
    while ((out.length & 3) && !_noEquals) { out += "="; }
    return out;
  },
  
  /** Convert from a base64 string to a bitArray */
  toBits: function(str, _url) {
    str = str.replace(/\s|=/g,'');
    var out = [], i, bits=0, c = sjcl.codec.base64._chars, ta=0, x;
    if (_url) c = c.substr(0,62) + '-_';
    for (i=0; i<str.length; i++) {
      x = c.indexOf(str.charAt(i));
      if (x < 0) {
        throw new sjcl.exception.invalid("this isn't base64!");
      }
      if (bits > 26) {
        bits -= 26;
        out.push(ta ^ x>>>bits);
        ta  = x << (32-bits);
      } else {
        bits += 6;
        ta ^= x << (32-bits);
      }
    }
    if (bits&56) {
      out.push(sjcl.bitArray.partial(bits&56, ta, 1));
    }
    return out;
  }
};

sjcl.codec.base64url = {
  fromBits: function (arr) { return sjcl.codec.base64.fromBits(arr,1,1); },
  toBits: function (str) { return sjcl.codec.base64.toBits(str,1); }
};

/** @fileOverview Bit array codec implementations.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/** @namespace Arrays of bytes */
sjcl.codec.bytes = {
  /** Convert from a bitArray to an array of bytes. */
  fromBits: function (arr) {
    var out = [], bl = sjcl.bitArray.bitLength(arr), i, tmp;
    for (i=0; i<bl/8; i++) {
      if ((i&3) === 0) {
        tmp = arr[i/4];
      }
      out.push(tmp >>> 24);
      tmp <<= 8;
    }
    return out;
  },
  /** Convert from an array of bytes to a bitArray. */
  toBits: function (bytes) {
    var out = [], i, tmp=0;
    for (i=0; i<bytes.length; i++) {
      tmp = tmp << 8 | bytes[i];
      if ((i&3) === 3) {
        out.push(tmp);
        tmp = 0;
      }
    }
    if (i&3) {
      out.push(sjcl.bitArray.partial(8*(i&3), tmp));
    }
    return out;
  }
};

/** @fileOverview Javascript SHA-256 implementation.
 *
 * An older version of this implementation is available in the public
 * domain, but this one is (c) Emily Stark, Mike Hamburg, Dan Boneh,
 * Stanford University 2008-2010 and BSD-licensed for liability
 * reasons.
 *
 * Special thanks to Aldo Cortesi for pointing out several bugs in
 * this code.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/**
 * Context for a SHA-256 operation in progress.
 * @constructor
 * @class Secure Hash Algorithm, 256 bits.
 */
sjcl.hash.sha256 = function (hash) {
  if (!this._key[0]) { this._precompute(); }
  if (hash) {
    this._h = hash._h.slice(0);
    this._buffer = hash._buffer.slice(0);
    this._length = hash._length;
  } else {
    this.reset();
  }
};

/**
 * Hash a string or an array of words.
 * @static
 * @param {bitArray|String} data the data to hash.
 * @return {bitArray} The hash value, an array of 16 big-endian words.
 */
sjcl.hash.sha256.hash = function (data) {
  return (new sjcl.hash.sha256()).update(data).finalize();
};

sjcl.hash.sha256.prototype = {
  /**
   * The hash's block size, in bits.
   * @constant
   */
  blockSize: 512,
   
  /**
   * Reset the hash state.
   * @return this
   */
  reset:function () {
    this._h = this._init.slice(0);
    this._buffer = [];
    this._length = 0;
    return this;
  },
  
  /**
   * Input several words to the hash.
   * @param {bitArray|String} data the data to hash.
   * @return this
   */
  update: function (data) {
    if (typeof data === "string") {
      data = sjcl.codec.utf8String.toBits(data);
    }
    var i, b = this._buffer = sjcl.bitArray.concat(this._buffer, data),
        ol = this._length,
        nl = this._length = ol + sjcl.bitArray.bitLength(data);
    for (i = 512+ol & -512; i <= nl; i+= 512) {
      this._block(b.splice(0,16));
    }
    return this;
  },
  
  /**
   * Complete hashing and output the hash value.
   * @return {bitArray} The hash value, an array of 8 big-endian words.
   */
  finalize:function () {
    var i, b = this._buffer, h = this._h;

    // Round out and push the buffer
    b = sjcl.bitArray.concat(b, [sjcl.bitArray.partial(1,1)]);
    
    // Round out the buffer to a multiple of 16 words, less the 2 length words.
    for (i = b.length + 2; i & 15; i++) {
      b.push(0);
    }
    
    // append the length
    b.push(Math.floor(this._length / 0x100000000));
    b.push(this._length | 0);

    while (b.length) {
      this._block(b.splice(0,16));
    }

    this.reset();
    return h;
  },

  /**
   * The SHA-256 initialization vector, to be precomputed.
   * @private
   */
  _init:[],
  /*
  _init:[0x6a09e667,0xbb67ae85,0x3c6ef372,0xa54ff53a,0x510e527f,0x9b05688c,0x1f83d9ab,0x5be0cd19],
  */
  
  /**
   * The SHA-256 hash key, to be precomputed.
   * @private
   */
  _key:[],
  /*
  _key:
    [0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
     0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
     0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
     0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
     0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
     0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
     0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
     0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2],
  */


  /**
   * Function to precompute _init and _key.
   * @private
   */
  _precompute: function () {
    var i = 0, prime = 2, factor;

    function frac(x) { return (x-Math.floor(x)) * 0x100000000 | 0; }

    outer: for (; i<64; prime++) {
      for (factor=2; factor*factor <= prime; factor++) {
        if (prime % factor === 0) {
          // not a prime
          continue outer;
        }
      }
      
      if (i<8) {
        this._init[i] = frac(Math.pow(prime, 1/2));
      }
      this._key[i] = frac(Math.pow(prime, 1/3));
      i++;
    }
  },
  
  /**
   * Perform one cycle of SHA-256.
   * @param {bitArray} words one block of words.
   * @private
   */
  _block:function (words) {  
    var i, tmp, a, b,
      w = words.slice(0),
      h = this._h,
      k = this._key,
      h0 = h[0], h1 = h[1], h2 = h[2], h3 = h[3],
      h4 = h[4], h5 = h[5], h6 = h[6], h7 = h[7];

    /* Rationale for placement of |0 :
     * If a value can overflow is original 32 bits by a factor of more than a few
     * million (2^23 ish), there is a possibility that it might overflow the
     * 53-bit mantissa and lose precision.
     *
     * To avoid this, we clamp back to 32 bits by |'ing with 0 on any value that
     * propagates around the loop, and on the hash state h[].  I don't believe
     * that the clamps on h4 and on h0 are strictly necessary, but it's close
     * (for h4 anyway), and better safe than sorry.
     *
     * The clamps on h[] are necessary for the output to be correct even in the
     * common case and for short inputs.
     */
    for (i=0; i<64; i++) {
      // load up the input word for this round
      if (i<16) {
        tmp = w[i];
      } else {
        a   = w[(i+1 ) & 15];
        b   = w[(i+14) & 15];
        tmp = w[i&15] = ((a>>>7  ^ a>>>18 ^ a>>>3  ^ a<<25 ^ a<<14) + 
                         (b>>>17 ^ b>>>19 ^ b>>>10 ^ b<<15 ^ b<<13) +
                         w[i&15] + w[(i+9) & 15]) | 0;
      }
      
      tmp = (tmp + h7 + (h4>>>6 ^ h4>>>11 ^ h4>>>25 ^ h4<<26 ^ h4<<21 ^ h4<<7) +  (h6 ^ h4&(h5^h6)) + k[i]); // | 0;
      
      // shift register
      h7 = h6; h6 = h5; h5 = h4;
      h4 = h3 + tmp | 0;
      h3 = h2; h2 = h1; h1 = h0;

      h0 = (tmp +  ((h1&h2) ^ (h3&(h1^h2))) + (h1>>>2 ^ h1>>>13 ^ h1>>>22 ^ h1<<30 ^ h1<<19 ^ h1<<10)) | 0;
    }

    h[0] = h[0]+h0 | 0;
    h[1] = h[1]+h1 | 0;
    h[2] = h[2]+h2 | 0;
    h[3] = h[3]+h3 | 0;
    h[4] = h[4]+h4 | 0;
    h[5] = h[5]+h5 | 0;
    h[6] = h[6]+h6 | 0;
    h[7] = h[7]+h7 | 0;
  }
};



/** @fileOverview Javascript SHA-512 implementation.
 *
 * This implementation was written for CryptoJS by Jeff Mott and adapted for
 * SJCL by Stefan Thomas.
 *
 * CryptoJS (c) 2009–2012 by Jeff Mott. All rights reserved.
 * Released with New BSD License
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 * @author Jeff Mott
 * @author Stefan Thomas
 */

/**
 * Context for a SHA-512 operation in progress.
 * @constructor
 * @class Secure Hash Algorithm, 512 bits.
 */
sjcl.hash.sha512 = function (hash) {
  if (!this._key[0]) { this._precompute(); }
  if (hash) {
    this._h = hash._h.slice(0);
    this._buffer = hash._buffer.slice(0);
    this._length = hash._length;
  } else {
    this.reset();
  }
};

/**
 * Hash a string or an array of words.
 * @static
 * @param {bitArray|String} data the data to hash.
 * @return {bitArray} The hash value, an array of 16 big-endian words.
 */
sjcl.hash.sha512.hash = function (data) {
  return (new sjcl.hash.sha512()).update(data).finalize();
};

sjcl.hash.sha512.prototype = {
  /**
   * The hash's block size, in bits.
   * @constant
   */
  blockSize: 1024,
   
  /**
   * Reset the hash state.
   * @return this
   */
  reset:function () {
    this._h = this._init.slice(0);
    this._buffer = [];
    this._length = 0;
    return this;
  },
  
  /**
   * Input several words to the hash.
   * @param {bitArray|String} data the data to hash.
   * @return this
   */
  update: function (data) {
    if (typeof data === "string") {
      data = sjcl.codec.utf8String.toBits(data);
    }
    var i, b = this._buffer = sjcl.bitArray.concat(this._buffer, data),
        ol = this._length,
        nl = this._length = ol + sjcl.bitArray.bitLength(data);
    for (i = 1024+ol & -1024; i <= nl; i+= 1024) {
      this._block(b.splice(0,32));
    }
    return this;
  },
  
  /**
   * Complete hashing and output the hash value.
   * @return {bitArray} The hash value, an array of 16 big-endian words.
   */
  finalize:function () {
    var i, b = this._buffer, h = this._h;

    // Round out and push the buffer
    b = sjcl.bitArray.concat(b, [sjcl.bitArray.partial(1,1)]);

    // Round out the buffer to a multiple of 32 words, less the 4 length words.
    for (i = b.length + 4; i & 31; i++) {
      b.push(0);
    }

    // append the length
    b.push(0);
    b.push(0);
    b.push(Math.floor(this._length / 0x100000000));
    b.push(this._length | 0);

    while (b.length) {
      this._block(b.splice(0,32));
    }

    this.reset();
    return h;
  },

  /**
   * The SHA-512 initialization vector, to be precomputed.
   * @private
   */
  _init:[],

  /**
   * Least significant 24 bits of SHA512 initialization values.
   *
   * Javascript only has 53 bits of precision, so we compute the 40 most
   * significant bits and add the remaining 24 bits as constants.
   *
   * @private
   */
  _initr: [ 0xbcc908, 0xcaa73b, 0x94f82b, 0x1d36f1, 0xe682d1, 0x3e6c1f, 0x41bd6b, 0x7e2179 ],

  /*
  _init:
  [0x6a09e667, 0xf3bcc908, 0xbb67ae85, 0x84caa73b, 0x3c6ef372, 0xfe94f82b, 0xa54ff53a, 0x5f1d36f1,
   0x510e527f, 0xade682d1, 0x9b05688c, 0x2b3e6c1f, 0x1f83d9ab, 0xfb41bd6b, 0x5be0cd19, 0x137e2179],
  */

  /**
   * The SHA-512 hash key, to be precomputed.
   * @private
   */
  _key:[],

  /**
   * Least significant 24 bits of SHA512 key values.
   * @private
   */
  _keyr:
  [0x28ae22, 0xef65cd, 0x4d3b2f, 0x89dbbc, 0x48b538, 0x05d019, 0x194f9b, 0x6d8118,
   0x030242, 0x706fbe, 0xe4b28c, 0xffb4e2, 0x7b896f, 0x1696b1, 0xc71235, 0x692694,
   0xf14ad2, 0x4f25e3, 0x8cd5b5, 0xac9c65, 0x2b0275, 0xa6e483, 0x41fbd4, 0x1153b5,
   0x66dfab, 0xb43210, 0xfb213f, 0xef0ee4, 0xa88fc2, 0x0aa725, 0x03826f, 0x0e6e70,
   0xd22ffc, 0x26c926, 0xc42aed, 0x95b3df, 0xaf63de, 0x77b2a8, 0xedaee6, 0x82353b,
   0xf10364, 0x423001, 0xf89791, 0x54be30, 0xef5218, 0x65a910, 0x71202a, 0xbbd1b8,
   0xd2d0c8, 0x41ab53, 0x8eeb99, 0x9b48a8, 0xc95a63, 0x418acb, 0x63e373, 0xb2b8a3,
   0xefb2fc, 0x172f60, 0xf0ab72, 0x6439ec, 0x631e28, 0x82bde9, 0xc67915, 0x72532b,
   0x26619c, 0xc0c207, 0xe0eb1e, 0x6ed178, 0x176fba, 0xc898a6, 0xf90dae, 0x1c471b,
   0x047d84, 0xc72493, 0xc9bebc, 0x100d4c, 0x3e42b6, 0x657e2a, 0xd6faec, 0x475817],

  /*
  _key:
  [0x428a2f98, 0xd728ae22, 0x71374491, 0x23ef65cd, 0xb5c0fbcf, 0xec4d3b2f, 0xe9b5dba5, 0x8189dbbc,
   0x3956c25b, 0xf348b538, 0x59f111f1, 0xb605d019, 0x923f82a4, 0xaf194f9b, 0xab1c5ed5, 0xda6d8118,
   0xd807aa98, 0xa3030242, 0x12835b01, 0x45706fbe, 0x243185be, 0x4ee4b28c, 0x550c7dc3, 0xd5ffb4e2,
   0x72be5d74, 0xf27b896f, 0x80deb1fe, 0x3b1696b1, 0x9bdc06a7, 0x25c71235, 0xc19bf174, 0xcf692694,
   0xe49b69c1, 0x9ef14ad2, 0xefbe4786, 0x384f25e3, 0x0fc19dc6, 0x8b8cd5b5, 0x240ca1cc, 0x77ac9c65,
   0x2de92c6f, 0x592b0275, 0x4a7484aa, 0x6ea6e483, 0x5cb0a9dc, 0xbd41fbd4, 0x76f988da, 0x831153b5,
   0x983e5152, 0xee66dfab, 0xa831c66d, 0x2db43210, 0xb00327c8, 0x98fb213f, 0xbf597fc7, 0xbeef0ee4,
   0xc6e00bf3, 0x3da88fc2, 0xd5a79147, 0x930aa725, 0x06ca6351, 0xe003826f, 0x14292967, 0x0a0e6e70,
   0x27b70a85, 0x46d22ffc, 0x2e1b2138, 0x5c26c926, 0x4d2c6dfc, 0x5ac42aed, 0x53380d13, 0x9d95b3df,
   0x650a7354, 0x8baf63de, 0x766a0abb, 0x3c77b2a8, 0x81c2c92e, 0x47edaee6, 0x92722c85, 0x1482353b,
   0xa2bfe8a1, 0x4cf10364, 0xa81a664b, 0xbc423001, 0xc24b8b70, 0xd0f89791, 0xc76c51a3, 0x0654be30,
   0xd192e819, 0xd6ef5218, 0xd6990624, 0x5565a910, 0xf40e3585, 0x5771202a, 0x106aa070, 0x32bbd1b8,
   0x19a4c116, 0xb8d2d0c8, 0x1e376c08, 0x5141ab53, 0x2748774c, 0xdf8eeb99, 0x34b0bcb5, 0xe19b48a8,
   0x391c0cb3, 0xc5c95a63, 0x4ed8aa4a, 0xe3418acb, 0x5b9cca4f, 0x7763e373, 0x682e6ff3, 0xd6b2b8a3,
   0x748f82ee, 0x5defb2fc, 0x78a5636f, 0x43172f60, 0x84c87814, 0xa1f0ab72, 0x8cc70208, 0x1a6439ec,
   0x90befffa, 0x23631e28, 0xa4506ceb, 0xde82bde9, 0xbef9a3f7, 0xb2c67915, 0xc67178f2, 0xe372532b,
   0xca273ece, 0xea26619c, 0xd186b8c7, 0x21c0c207, 0xeada7dd6, 0xcde0eb1e, 0xf57d4f7f, 0xee6ed178,
   0x06f067aa, 0x72176fba, 0x0a637dc5, 0xa2c898a6, 0x113f9804, 0xbef90dae, 0x1b710b35, 0x131c471b,
   0x28db77f5, 0x23047d84, 0x32caab7b, 0x40c72493, 0x3c9ebe0a, 0x15c9bebc, 0x431d67c4, 0x9c100d4c,
   0x4cc5d4be, 0xcb3e42b6, 0x597f299c, 0xfc657e2a, 0x5fcb6fab, 0x3ad6faec, 0x6c44198c, 0x4a475817],
  */

  /**
   * Function to precompute _init and _key.
   * @private
   */
  _precompute: function () {
    // XXX: This code is for precomputing the SHA256 constants, change for
    //      SHA512 and re-enable.
    var i = 0, prime = 2, factor;

    function frac(x)  { return (x-Math.floor(x)) * 0x100000000 | 0; }
    function frac2(x) { return (x-Math.floor(x)) * 0x10000000000 & 0xff; }

    outer: for (; i<80; prime++) {
      for (factor=2; factor*factor <= prime; factor++) {
        if (prime % factor === 0) {
          // not a prime
          continue outer;
        }
      }

      if (i<8) {
        this._init[i*2] = frac(Math.pow(prime, 1/2));
        this._init[i*2+1] = (frac2(Math.pow(prime, 1/2)) << 24) | this._initr[i];
      }
      this._key[i*2] = frac(Math.pow(prime, 1/3));
      this._key[i*2+1] = (frac2(Math.pow(prime, 1/3)) << 24) | this._keyr[i];
      i++;
    }
  },

  /**
   * Perform one cycle of SHA-512.
   * @param {bitArray} words one block of words.
   * @private
   */
  _block:function (words) {
    var i, wrh, wrl,
        w = words.slice(0),
        h = this._h,
        k = this._key,
        h0h = h[ 0], h0l = h[ 1], h1h = h[ 2], h1l = h[ 3],
        h2h = h[ 4], h2l = h[ 5], h3h = h[ 6], h3l = h[ 7],
        h4h = h[ 8], h4l = h[ 9], h5h = h[10], h5l = h[11],
        h6h = h[12], h6l = h[13], h7h = h[14], h7l = h[15];

    // Working variables
    var ah = h0h, al = h0l, bh = h1h, bl = h1l,
        ch = h2h, cl = h2l, dh = h3h, dl = h3l,
        eh = h4h, el = h4l, fh = h5h, fl = h5l,
        gh = h6h, gl = h6l, hh = h7h, hl = h7l;

    for (i=0; i<80; i++) {
      // load up the input word for this round
      if (i<16) {
        wrh = w[i * 2];
        wrl = w[i * 2 + 1];
      } else {
        // Gamma0
        var gamma0xh = w[(i-15) * 2];
        var gamma0xl = w[(i-15) * 2 + 1];
        var gamma0h =
          ((gamma0xl << 31) | (gamma0xh >>> 1)) ^
          ((gamma0xl << 24) | (gamma0xh >>> 8)) ^
           (gamma0xh >>> 7);
        var gamma0l =
          ((gamma0xh << 31) | (gamma0xl >>> 1)) ^
          ((gamma0xh << 24) | (gamma0xl >>> 8)) ^
          ((gamma0xh << 25) | (gamma0xl >>> 7));

        // Gamma1
        var gamma1xh = w[(i-2) * 2];
        var gamma1xl = w[(i-2) * 2 + 1];
        var gamma1h =
          ((gamma1xl << 13) | (gamma1xh >>> 19)) ^
          ((gamma1xh << 3)  | (gamma1xl >>> 29)) ^
           (gamma1xh >>> 6);
        var gamma1l =
          ((gamma1xh << 13) | (gamma1xl >>> 19)) ^
          ((gamma1xl << 3)  | (gamma1xh >>> 29)) ^
          ((gamma1xh << 26) | (gamma1xl >>> 6));

        // Shortcuts
        var wr7h = w[(i-7) * 2];
        var wr7l = w[(i-7) * 2 + 1];

        var wr16h = w[(i-16) * 2];
        var wr16l = w[(i-16) * 2 + 1];

        // W(round) = gamma0 + W(round - 7) + gamma1 + W(round - 16)
        wrl = gamma0l + wr7l;
        wrh = gamma0h + wr7h + ((wrl >>> 0) < (gamma0l >>> 0) ? 1 : 0);
        wrl += gamma1l;
        wrh += gamma1h + ((wrl >>> 0) < (gamma1l >>> 0) ? 1 : 0);
        wrl += wr16l;
        wrh += wr16h + ((wrl >>> 0) < (wr16l >>> 0) ? 1 : 0);
      }

      w[i*2]     = wrh |= 0;
      w[i*2 + 1] = wrl |= 0;

      // Ch
      var chh = (eh & fh) ^ (~eh & gh);
      var chl = (el & fl) ^ (~el & gl);

      // Maj
      var majh = (ah & bh) ^ (ah & ch) ^ (bh & ch);
      var majl = (al & bl) ^ (al & cl) ^ (bl & cl);

      // Sigma0
      var sigma0h = ((al << 4) | (ah >>> 28)) ^ ((ah << 30) | (al >>> 2)) ^ ((ah << 25) | (al >>> 7));
      var sigma0l = ((ah << 4) | (al >>> 28)) ^ ((al << 30) | (ah >>> 2)) ^ ((al << 25) | (ah >>> 7));

      // Sigma1
      var sigma1h = ((el << 18) | (eh >>> 14)) ^ ((el << 14) | (eh >>> 18)) ^ ((eh << 23) | (el >>> 9));
      var sigma1l = ((eh << 18) | (el >>> 14)) ^ ((eh << 14) | (el >>> 18)) ^ ((el << 23) | (eh >>> 9));

      // K(round)
      var krh = k[i*2];
      var krl = k[i*2+1];

      // t1 = h + sigma1 + ch + K(round) + W(round)
      var t1l = hl + sigma1l;
      var t1h = hh + sigma1h + ((t1l >>> 0) < (hl >>> 0) ? 1 : 0);
      t1l += chl;
      t1h += chh + ((t1l >>> 0) < (chl >>> 0) ? 1 : 0);
      t1l += krl;
      t1h += krh + ((t1l >>> 0) < (krl >>> 0) ? 1 : 0);
      t1l += wrl;
      t1h += wrh + ((t1l >>> 0) < (wrl >>> 0) ? 1 : 0);

      // t2 = sigma0 + maj
      var t2l = sigma0l + majl;
      var t2h = sigma0h + majh + ((t2l >>> 0) < (sigma0l >>> 0) ? 1 : 0);

      // Update working variables
      hh = gh;
      hl = gl;
      gh = fh;
      gl = fl;
      fh = eh;
      fl = el;
      el = (dl + t1l) | 0;
      eh = (dh + t1h + ((el >>> 0) < (dl >>> 0) ? 1 : 0)) | 0;
      dh = ch;
      dl = cl;
      ch = bh;
      cl = bl;
      bh = ah;
      bl = al;
      al = (t1l + t2l) | 0;
      ah = (t1h + t2h + ((al >>> 0) < (t1l >>> 0) ? 1 : 0)) | 0;
    }

    // Intermediate hash
    h0l = h[1] = (h0l + al) | 0;
    h[0] = (h0h + ah + ((h0l >>> 0) < (al >>> 0) ? 1 : 0)) | 0;
    h1l = h[3] = (h1l + bl) | 0;
    h[2] = (h1h + bh + ((h1l >>> 0) < (bl >>> 0) ? 1 : 0)) | 0;
    h2l = h[5] = (h2l + cl) | 0;
    h[4] = (h2h + ch + ((h2l >>> 0) < (cl >>> 0) ? 1 : 0)) | 0;
    h3l = h[7] = (h3l + dl) | 0;
    h[6] = (h3h + dh + ((h3l >>> 0) < (dl >>> 0) ? 1 : 0)) | 0;
    h4l = h[9] = (h4l + el) | 0;
    h[8] = (h4h + eh + ((h4l >>> 0) < (el >>> 0) ? 1 : 0)) | 0;
    h5l = h[11] = (h5l + fl) | 0;
    h[10] = (h5h + fh + ((h5l >>> 0) < (fl >>> 0) ? 1 : 0)) | 0;
    h6l = h[13] = (h6l + gl) | 0;
    h[12] = (h6h + gh + ((h6l >>> 0) < (gl >>> 0) ? 1 : 0)) | 0;
    h7l = h[15] = (h7l + hl) | 0;
    h[14] = (h7h + hh + ((h7l >>> 0) < (hl >>> 0) ? 1 : 0)) | 0;
  }
};



/** @fileOverview Javascript SHA-1 implementation.
 *
 * Based on the implementation in RFC 3174, method 1, and on the SJCL
 * SHA-256 implementation.
 *
 * @author Quinn Slack
 */

/**
 * Context for a SHA-1 operation in progress.
 * @constructor
 * @class Secure Hash Algorithm, 160 bits.
 */
sjcl.hash.sha1 = function (hash) {
  if (hash) {
    this._h = hash._h.slice(0);
    this._buffer = hash._buffer.slice(0);
    this._length = hash._length;
  } else {
    this.reset();
  }
};

/**
 * Hash a string or an array of words.
 * @static
 * @param {bitArray|String} data the data to hash.
 * @return {bitArray} The hash value, an array of 5 big-endian words.
 */
sjcl.hash.sha1.hash = function (data) {
  return (new sjcl.hash.sha1()).update(data).finalize();
};

sjcl.hash.sha1.prototype = {
  /**
   * The hash's block size, in bits.
   * @constant
   */
  blockSize: 512,
   
  /**
   * Reset the hash state.
   * @return this
   */
  reset:function () {
    this._h = this._init.slice(0);
    this._buffer = [];
    this._length = 0;
    return this;
  },
  
  /**
   * Input several words to the hash.
   * @param {bitArray|String} data the data to hash.
   * @return this
   */
  update: function (data) {
    if (typeof data === "string") {
      data = sjcl.codec.utf8String.toBits(data);
    }
    var i, b = this._buffer = sjcl.bitArray.concat(this._buffer, data),
        ol = this._length,
        nl = this._length = ol + sjcl.bitArray.bitLength(data);
    for (i = this.blockSize+ol & -this.blockSize; i <= nl;
         i+= this.blockSize) {
      this._block(b.splice(0,16));
    }
    return this;
  },
  
  /**
   * Complete hashing and output the hash value.
   * @return {bitArray} The hash value, an array of 5 big-endian words. TODO
   */
  finalize:function () {
    var i, b = this._buffer, h = this._h;

    // Round out and push the buffer
    b = sjcl.bitArray.concat(b, [sjcl.bitArray.partial(1,1)]);
    // Round out the buffer to a multiple of 16 words, less the 2 length words.
    for (i = b.length + 2; i & 15; i++) {
      b.push(0);
    }

    // append the length
    b.push(Math.floor(this._length / 0x100000000));
    b.push(this._length | 0);

    while (b.length) {
      this._block(b.splice(0,16));
    }

    this.reset();
    return h;
  },

  /**
   * The SHA-1 initialization vector.
   * @private
   */
  _init:[0x67452301, 0xEFCDAB89, 0x98BADCFE, 0x10325476, 0xC3D2E1F0],

  /**
   * The SHA-1 hash key.
   * @private
   */
  _key:[0x5A827999, 0x6ED9EBA1, 0x8F1BBCDC, 0xCA62C1D6],

  /**
   * The SHA-1 logical functions f(0), f(1), ..., f(79).
   * @private
   */
  _f:function(t, b, c, d) {
    if (t <= 19) {
      return (b & c) | (~b & d);
    } else if (t <= 39) {
      return b ^ c ^ d;
    } else if (t <= 59) {
      return (b & c) | (b & d) | (c & d);
    } else if (t <= 79) {
      return b ^ c ^ d;
    }
  },

  /**
   * Circular left-shift operator.
   * @private
   */
  _S:function(n, x) {
    return (x << n) | (x >>> 32-n);
  },
  
  /**
   * Perform one cycle of SHA-1.
   * @param {bitArray} words one block of words.
   * @private
   */
  _block:function (words) {  
    var t, tmp, a, b, c, d, e,
    w = words.slice(0),
    h = this._h,
    k = this._key;
   
    a = h[0]; b = h[1]; c = h[2]; d = h[3]; e = h[4]; 

    for (t=0; t<=79; t++) {
      if (t >= 16) {
        w[t] = this._S(1, w[t-3] ^ w[t-8] ^ w[t-14] ^ w[t-16]);
      }
      tmp = (this._S(5, a) + this._f(t, b, c, d) + e + w[t] +
             this._key[Math.floor(t/20)]) | 0;
      e = d;
      d = c;
      c = this._S(30, b);
      b = a;
      a = tmp;
   }

   h[0] = (h[0]+a) |0;
   h[1] = (h[1]+b) |0;
   h[2] = (h[2]+c) |0;
   h[3] = (h[3]+d) |0;
   h[4] = (h[4]+e) |0;
  }
};

/** @fileOverview CCM mode implementation.
 *
 * Special thanks to Roy Nicholson for pointing out a bug in our
 * implementation.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/** @namespace CTR mode with CBC MAC. */
sjcl.mode.ccm = {
  /** The name of the mode.
   * @constant
   */
  name: "ccm",
  
  /** Encrypt in CCM mode.
   * @static
   * @param {Object} prf The pseudorandom function.  It must have a block size of 16 bytes.
   * @param {bitArray} plaintext The plaintext data.
   * @param {bitArray} iv The initialization value.
   * @param {bitArray} [adata=[]] The authenticated data.
   * @param {Number} [tlen=64] the desired tag length, in bits.
   * @return {bitArray} The encrypted data, an array of bytes.
   */
  encrypt: function(prf, plaintext, iv, adata, tlen) {
    var L, i, out = plaintext.slice(0), tag, w=sjcl.bitArray, ivl = w.bitLength(iv) / 8, ol = w.bitLength(out) / 8;
    tlen = tlen || 64;
    adata = adata || [];
    
    if (ivl < 7) {
      throw new sjcl.exception.invalid("ccm: iv must be at least 7 bytes");
    }
    
    // compute the length of the length
    for (L=2; L<4 && ol >>> 8*L; L++) {}
    if (L < 15 - ivl) { L = 15-ivl; }
    iv = w.clamp(iv,8*(15-L));
    
    // compute the tag
    tag = sjcl.mode.ccm._computeTag(prf, plaintext, iv, adata, tlen, L);
    
    // encrypt
    out = sjcl.mode.ccm._ctrMode(prf, out, iv, tag, tlen, L);
    
    return w.concat(out.data, out.tag);
  },
  
  /** Decrypt in CCM mode.
   * @static
   * @param {Object} prf The pseudorandom function.  It must have a block size of 16 bytes.
   * @param {bitArray} ciphertext The ciphertext data.
   * @param {bitArray} iv The initialization value.
   * @param {bitArray} [[]] adata The authenticated data.
   * @param {Number} [64] tlen the desired tag length, in bits.
   * @return {bitArray} The decrypted data.
   */
  decrypt: function(prf, ciphertext, iv, adata, tlen) {
    tlen = tlen || 64;
    adata = adata || [];
    var L, i, 
        w=sjcl.bitArray,
        ivl = w.bitLength(iv) / 8,
        ol = w.bitLength(ciphertext), 
        out = w.clamp(ciphertext, ol - tlen),
        tag = w.bitSlice(ciphertext, ol - tlen), tag2;
    

    ol = (ol - tlen) / 8;
        
    if (ivl < 7) {
      throw new sjcl.exception.invalid("ccm: iv must be at least 7 bytes");
    }
    
    // compute the length of the length
    for (L=2; L<4 && ol >>> 8*L; L++) {}
    if (L < 15 - ivl) { L = 15-ivl; }
    iv = w.clamp(iv,8*(15-L));
    
    // decrypt
    out = sjcl.mode.ccm._ctrMode(prf, out, iv, tag, tlen, L);
    
    // check the tag
    tag2 = sjcl.mode.ccm._computeTag(prf, out.data, iv, adata, tlen, L);
    if (!w.equal(out.tag, tag2)) {
      throw new sjcl.exception.corrupt("ccm: tag doesn't match");
    }
    
    return out.data;
  },

  /* Compute the (unencrypted) authentication tag, according to the CCM specification
   * @param {Object} prf The pseudorandom function.
   * @param {bitArray} plaintext The plaintext data.
   * @param {bitArray} iv The initialization value.
   * @param {bitArray} adata The authenticated data.
   * @param {Number} tlen the desired tag length, in bits.
   * @return {bitArray} The tag, but not yet encrypted.
   * @private
   */
  _computeTag: function(prf, plaintext, iv, adata, tlen, L) {
    // compute B[0]
    var q, mac, field = 0, offset = 24, tmp, i, macData = [], w=sjcl.bitArray, xor = w._xor4;

    tlen /= 8;
  
    // check tag length and message length
    if (tlen % 2 || tlen < 4 || tlen > 16) {
      throw new sjcl.exception.invalid("ccm: invalid tag length");
    }
  
    if (adata.length > 0xFFFFFFFF || plaintext.length > 0xFFFFFFFF) {
      // I don't want to deal with extracting high words from doubles.
      throw new sjcl.exception.bug("ccm: can't deal with 4GiB or more data");
    }

    // mac the flags
    mac = [w.partial(8, (adata.length ? 1<<6 : 0) | (tlen-2) << 2 | L-1)];

    // mac the iv and length
    mac = w.concat(mac, iv);
    mac[3] |= w.bitLength(plaintext)/8;
    mac = prf.encrypt(mac);
    
  
    if (adata.length) {
      // mac the associated data.  start with its length...
      tmp = w.bitLength(adata)/8;
      if (tmp <= 0xFEFF) {
        macData = [w.partial(16, tmp)];
      } else if (tmp <= 0xFFFFFFFF) {
        macData = w.concat([w.partial(16,0xFFFE)], [tmp]);
      } // else ...
    
      // mac the data itself
      macData = w.concat(macData, adata);
      for (i=0; i<macData.length; i += 4) {
        mac = prf.encrypt(xor(mac, macData.slice(i,i+4).concat([0,0,0])));
      }
    }
  
    // mac the plaintext
    for (i=0; i<plaintext.length; i+=4) {
      mac = prf.encrypt(xor(mac, plaintext.slice(i,i+4).concat([0,0,0])));
    }

    return w.clamp(mac, tlen * 8);
  },

  /** CCM CTR mode.
   * Encrypt or decrypt data and tag with the prf in CCM-style CTR mode.
   * May mutate its arguments.
   * @param {Object} prf The PRF.
   * @param {bitArray} data The data to be encrypted or decrypted.
   * @param {bitArray} iv The initialization vector.
   * @param {bitArray} tag The authentication tag.
   * @param {Number} tlen The length of th etag, in bits.
   * @param {Number} L The CCM L value.
   * @return {Object} An object with data and tag, the en/decryption of data and tag values.
   * @private
   */
  _ctrMode: function(prf, data, iv, tag, tlen, L) {
    var enc, i, w=sjcl.bitArray, xor = w._xor4, ctr, b, l = data.length, bl=w.bitLength(data);

    // start the ctr
    ctr = w.concat([w.partial(8,L-1)],iv).concat([0,0,0]).slice(0,4);
    
    // en/decrypt the tag
    tag = w.bitSlice(xor(tag,prf.encrypt(ctr)), 0, tlen);
  
    // en/decrypt the data
    if (!l) { return {tag:tag, data:[]}; }
    
    for (i=0; i<l; i+=4) {
      ctr[3]++;
      enc = prf.encrypt(ctr);
      data[i]   ^= enc[0];
      data[i+1] ^= enc[1];
      data[i+2] ^= enc[2];
      data[i+3] ^= enc[3];
    }
    return { tag:tag, data:w.clamp(data,bl) };
  }
};

/** @fileOverview HMAC implementation.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/** HMAC with the specified hash function.
 * @constructor
 * @param {bitArray} key the key for HMAC.
 * @param {Object} [hash=sjcl.hash.sha256] The hash function to use.
 */
sjcl.misc.hmac = function (key, Hash) {
  this._hash = Hash = Hash || sjcl.hash.sha256;
  var exKey = [[],[]], i,
      bs = Hash.prototype.blockSize / 32;
  this._baseHash = [new Hash(), new Hash()];

  if (key.length > bs) {
    key = Hash.hash(key);
  }
  
  for (i=0; i<bs; i++) {
    exKey[0][i] = key[i]^0x36363636;
    exKey[1][i] = key[i]^0x5C5C5C5C;
  }
  
  this._baseHash[0].update(exKey[0]);
  this._baseHash[1].update(exKey[1]);
};

/** HMAC with the specified hash function.  Also called encrypt since it's a prf.
 * @param {bitArray|String} data The data to mac.
 */
sjcl.misc.hmac.prototype.encrypt = sjcl.misc.hmac.prototype.mac = function (data) {
  var w = new (this._hash)(this._baseHash[0]).update(data).finalize();
  return new (this._hash)(this._baseHash[1]).update(w).finalize();
};


/** @fileOverview Password-based key-derivation function, version 2.0.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/** Password-Based Key-Derivation Function, version 2.0.
 *
 * Generate keys from passwords using PBKDF2-HMAC-SHA256.
 *
 * This is the method specified by RSA's PKCS #5 standard.
 *
 * @param {bitArray|String} password  The password.
 * @param {bitArray} salt The salt.  Should have lots of entropy.
 * @param {Number} [count=1000] The number of iterations.  Higher numbers make the function slower but more secure.
 * @param {Number} [length] The length of the derived key.  Defaults to the
                            output size of the hash function.
 * @param {Object} [Prff=sjcl.misc.hmac] The pseudorandom function family.
 * @return {bitArray} the derived key.
 */
sjcl.misc.pbkdf2 = function (password, salt, count, length, Prff) {
  count = count || 1000;
  
  if (length < 0 || count < 0) {
    throw sjcl.exception.invalid("invalid params to pbkdf2");
  }
  
  if (typeof password === "string") {
    password = sjcl.codec.utf8String.toBits(password);
  }
  
  Prff = Prff || sjcl.misc.hmac;
  
  var prf = new Prff(password),
      u, ui, i, j, k, out = [], b = sjcl.bitArray;

  for (k = 1; 32 * out.length < (length || 1); k++) {
    u = ui = prf.encrypt(b.concat(salt,[k]));
    
    for (i=1; i<count; i++) {
      ui = prf.encrypt(ui);
      for (j=0; j<ui.length; j++) {
        u[j] ^= ui[j];
      }
    }
    
    out = out.concat(u);
  }

  if (length) { out = b.clamp(out, length); }

  return out;
};

/** @fileOverview Random number generator.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */

/** @constructor
 * @class Random number generator
 *
 * @description
 * <p>
 * This random number generator is a derivative of Ferguson and Schneier's
 * generator Fortuna.  It collects entropy from various events into several
 * pools, implemented by streaming SHA-256 instances.  It differs from
 * ordinary Fortuna in a few ways, though.
 * </p>
 *
 * <p>
 * Most importantly, it has an entropy estimator.  This is present because
 * there is a strong conflict here between making the generator available
 * as soon as possible, and making sure that it doesn't "run on empty".
 * In Fortuna, there is a saved state file, and the system is likely to have
 * time to warm up.
 * </p>
 *
 * <p>
 * Second, because users are unlikely to stay on the page for very long,
 * and to speed startup time, the number of pools increases logarithmically:
 * a new pool is created when the previous one is actually used for a reseed.
 * This gives the same asymptotic guarantees as Fortuna, but gives more
 * entropy to early reseeds.
 * </p>
 *
 * <p>
 * The entire mechanism here feels pretty klunky.  Furthermore, there are
 * several improvements that should be made, including support for
 * dedicated cryptographic functions that may be present in some browsers;
 * state files in local storage; cookies containing randomness; etc.  So
 * look for improvements in future versions.
 * </p>
 */
sjcl.prng = function(defaultParanoia) {
  
  /* private */
  this._pools                   = [new sjcl.hash.sha256()];
  this._poolEntropy             = [0];
  this._reseedCount             = 0;
  this._robins                  = {};
  this._eventId                 = 0;
  
  this._collectorIds            = {};
  this._collectorIdNext         = 0;
  
  this._strength                = 0;
  this._poolStrength            = 0;
  this._nextReseed              = 0;
  this._key                     = [0,0,0,0,0,0,0,0];
  this._counter                 = [0,0,0,0];
  this._cipher                  = undefined;
  this._defaultParanoia         = defaultParanoia;
  
  /* event listener stuff */
  this._collectorsStarted       = false;
  this._callbacks               = {progress: {}, seeded: {}};
  this._callbackI               = 0;
  
  /* constants */
  this._NOT_READY               = 0;
  this._READY                   = 1;
  this._REQUIRES_RESEED         = 2;

  this._MAX_WORDS_PER_BURST     = 65536;
  this._PARANOIA_LEVELS         = [0,48,64,96,128,192,256,384,512,768,1024];
  this._MILLISECONDS_PER_RESEED = 30000;
  this._BITS_PER_RESEED         = 80;
}
 
sjcl.prng.prototype = {
  /** Generate several random words, and return them in an array
   * @param {Number} nwords The number of words to generate.
   */
  randomWords: function (nwords, paranoia) {
    var out = [], i, readiness = this.isReady(paranoia), g;
  
    if (readiness === this._NOT_READY) {
      throw new sjcl.exception.notReady("generator isn't seeded");
    } else if (readiness & this._REQUIRES_RESEED) {
      this._reseedFromPools(!(readiness & this._READY));
    }
  
    for (i=0; i<nwords; i+= 4) {
      if ((i+1) % this._MAX_WORDS_PER_BURST === 0) {
        this._gate();
      }
   
      g = this._gen4words();
      out.push(g[0],g[1],g[2],g[3]);
    }
    this._gate();
  
    return out.slice(0,nwords);
  },
  
  setDefaultParanoia: function (paranoia) {
    this._defaultParanoia = paranoia;
  },
  
  /**
   * Add entropy to the pools.
   * @param data The entropic value.  Should be a 32-bit integer, array of 32-bit integers, or string
   * @param {Number} estimatedEntropy The estimated entropy of data, in bits
   * @param {String} source The source of the entropy, eg "mouse"
   */
  addEntropy: function (data, estimatedEntropy, source) {
    source = source || "user";
  
    var id,
      i, tmp,
      t = (new Date()).valueOf(),
      robin = this._robins[source],
      oldReady = this.isReady(), err = 0;
      
    id = this._collectorIds[source];
    if (id === undefined) { id = this._collectorIds[source] = this._collectorIdNext ++; }
      
    if (robin === undefined) { robin = this._robins[source] = 0; }
    this._robins[source] = ( this._robins[source] + 1 ) % this._pools.length;
  
    switch(typeof(data)) {
      
    case "number":
      if (estimatedEntropy === undefined) {
        estimatedEntropy = 1;
      }
      this._pools[robin].update([id,this._eventId++,1,estimatedEntropy,t,1,data|0]);
      break;
      
    case "object":
      var objName = Object.prototype.toString.call(data);
      if (objName === "[object Uint32Array]") {
        tmp = [];
        for (i = 0; i < data.length; i++) {
          tmp.push(data[i]);
        }
        data = tmp;
      } else {
        if (objName !== "[object Array]") {
          err = 1;
        }
        for (i=0; i<data.length && !err; i++) {
          if (typeof(data[i]) != "number") {
            err = 1;
          }
        }
      }
      if (!err) {
        if (estimatedEntropy === undefined) {
          /* horrible entropy estimator */
          estimatedEntropy = 0;
          for (i=0; i<data.length; i++) {
            tmp= data[i];
            while (tmp>0) {
              estimatedEntropy++;
              tmp = tmp >>> 1;
            }
          }
        }
        this._pools[robin].update([id,this._eventId++,2,estimatedEntropy,t,data.length].concat(data));
      }
      break;
      
    case "string":
      if (estimatedEntropy === undefined) {
       /* English text has just over 1 bit per character of entropy.
        * But this might be HTML or something, and have far less
        * entropy than English...  Oh well, let's just say one bit.
        */
       estimatedEntropy = data.length;
      }
      this._pools[robin].update([id,this._eventId++,3,estimatedEntropy,t,data.length]);
      this._pools[robin].update(data);
      break;
      
    default:
      err=1;
    }
    if (err) {
      throw new sjcl.exception.bug("random: addEntropy only supports number, array of numbers or string");
    }
  
    /* record the new strength */
    this._poolEntropy[robin] += estimatedEntropy;
    this._poolStrength += estimatedEntropy;
  
    /* fire off events */
    if (oldReady === this._NOT_READY) {
      if (this.isReady() !== this._NOT_READY) {
        this._fireEvent("seeded", Math.max(this._strength, this._poolStrength));
      }
      this._fireEvent("progress", this.getProgress());
    }
  },
  
  /** Is the generator ready? */
  isReady: function (paranoia) {
    var entropyRequired = this._PARANOIA_LEVELS[ (paranoia !== undefined) ? paranoia : this._defaultParanoia ];
  
    if (this._strength && this._strength >= entropyRequired) {
      return (this._poolEntropy[0] > this._BITS_PER_RESEED && (new Date()).valueOf() > this._nextReseed) ?
        this._REQUIRES_RESEED | this._READY :
        this._READY;
    } else {
      return (this._poolStrength >= entropyRequired) ?
        this._REQUIRES_RESEED | this._NOT_READY :
        this._NOT_READY;
    }
  },
  
  /** Get the generator's progress toward readiness, as a fraction */
  getProgress: function (paranoia) {
    var entropyRequired = this._PARANOIA_LEVELS[ paranoia ? paranoia : this._defaultParanoia ];
  
    if (this._strength >= entropyRequired) {
      return 1.0;
    } else {
      return (this._poolStrength > entropyRequired) ?
        1.0 :
        this._poolStrength / entropyRequired;
    }
  },
  
  /** start the built-in entropy collectors */
  startCollectors: function () {
    if (this._collectorsStarted) { return; }
  
    if (window.addEventListener) {
      window.addEventListener("load", this._loadTimeCollector, false);
      window.addEventListener("mousemove", this._mouseCollector, false);
    } else if (document.attachEvent) {
      document.attachEvent("onload", this._loadTimeCollector);
      document.attachEvent("onmousemove", this._mouseCollector);
    }
    else {
      throw new sjcl.exception.bug("can't attach event");
    }
  
    this._collectorsStarted = true;
  },
  
  /** stop the built-in entropy collectors */
  stopCollectors: function () {
    if (!this._collectorsStarted) { return; }
  
    if (window.removeEventListener) {
      window.removeEventListener("load", this._loadTimeCollector, false);
      window.removeEventListener("mousemove", this._mouseCollector, false);
    } else if (window.detachEvent) {
      window.detachEvent("onload", this._loadTimeCollector);
      window.detachEvent("onmousemove", this._mouseCollector);
    }
    this._collectorsStarted = false;
  },
  
  /* use a cookie to store entropy.
  useCookie: function (all_cookies) {
      throw new sjcl.exception.bug("random: useCookie is unimplemented");
  },*/
  
  /** add an event listener for progress or seeded-ness. */
  addEventListener: function (name, callback) {
    this._callbacks[name][this._callbackI++] = callback;
  },
  
  /** remove an event listener for progress or seeded-ness */
  removeEventListener: function (name, cb) {
    var i, j, cbs=this._callbacks[name], jsTemp=[];
  
    /* I'm not sure if this is necessary; in C++, iterating over a
     * collection and modifying it at the same time is a no-no.
     */
  
    for (j in cbs) {
	if (cbs.hasOwnProperty(j) && cbs[j] === cb) {
        jsTemp.push(j);
      }
    }
  
    for (i=0; i<jsTemp.length; i++) {
      j = jsTemp[i];
      delete cbs[j];
    }
  },
  
  /** Generate 4 random words, no reseed, no gate.
   * @private
   */
  _gen4words: function () {
    for (var i=0; i<4; i++) {
      this._counter[i] = this._counter[i]+1 | 0;
      if (this._counter[i]) { break; }
    }
    return this._cipher.encrypt(this._counter);
  },
  
  /* Rekey the AES instance with itself after a request, or every _MAX_WORDS_PER_BURST words.
   * @private
   */
  _gate: function () {
    this._key = this._gen4words().concat(this._gen4words());
    this._cipher = new sjcl.cipher.aes(this._key);
  },
  
  /** Reseed the generator with the given words
   * @private
   */
  _reseed: function (seedWords) {
    this._key = sjcl.hash.sha256.hash(this._key.concat(seedWords));
    this._cipher = new sjcl.cipher.aes(this._key);
    for (var i=0; i<4; i++) {
      this._counter[i] = this._counter[i]+1 | 0;
      if (this._counter[i]) { break; }
    }
  },
  
  /** reseed the data from the entropy pools
   * @param full If set, use all the entropy pools in the reseed.
   */
  _reseedFromPools: function (full) {
    var reseedData = [], strength = 0, i;
  
    this._nextReseed = reseedData[0] =
      (new Date()).valueOf() + this._MILLISECONDS_PER_RESEED;
    
    for (i=0; i<16; i++) {
      /* On some browsers, this is cryptographically random.  So we might
       * as well toss it in the pot and stir...
       */
      reseedData.push(Math.random()*0x100000000|0);
    }
    
    for (i=0; i<this._pools.length; i++) {
     reseedData = reseedData.concat(this._pools[i].finalize());
     strength += this._poolEntropy[i];
     this._poolEntropy[i] = 0;
   
     if (!full && (this._reseedCount & (1<<i))) { break; }
    }
  
    /* if we used the last pool, push a new one onto the stack */
    if (this._reseedCount >= 1 << this._pools.length) {
     this._pools.push(new sjcl.hash.sha256());
     this._poolEntropy.push(0);
    }
  
    /* how strong was this reseed? */
    this._poolStrength -= strength;
    if (strength > this._strength) {
      this._strength = strength;
    }
  
    this._reseedCount ++;
    this._reseed(reseedData);
  },
  
  _mouseCollector: function (ev) {
    var x = ev.x || ev.clientX || ev.offsetX || 0, y = ev.y || ev.clientY || ev.offsetY || 0;
    sjcl.random.addEntropy([x,y], 2, "mouse");
  },
  
  _loadTimeCollector: function (ev) {
    sjcl.random.addEntropy((new Date()).valueOf(), 2, "loadtime");
  },
  
  _fireEvent: function (name, arg) {
    var j, cbs=sjcl.random._callbacks[name], cbsTemp=[];
    /* TODO: there is a race condition between removing collectors and firing them */ 

    /* I'm not sure if this is necessary; in C++, iterating over a
     * collection and modifying it at the same time is a no-no.
     */
  
    for (j in cbs) {
     if (cbs.hasOwnProperty(j)) {
        cbsTemp.push(cbs[j]);
     }
    }
  
    for (j=0; j<cbsTemp.length; j++) {
     cbsTemp[j](arg);
    }
  }
};

sjcl.random = new sjcl.prng(6);

(function(){
  try {
    // get cryptographically strong entropy in Webkit
    var ab = new Uint32Array(32);
    crypto.getRandomValues(ab);
    sjcl.random.addEntropy(ab, 1024, "crypto.getRandomValues");
  } catch (e) {
    // no getRandomValues :-(
  }
})();

/** @fileOverview Convenince functions centered around JSON encapsulation.
 *
 * @author Emily Stark
 * @author Mike Hamburg
 * @author Dan Boneh
 */
 
 /** @namespace JSON encapsulation */
 sjcl.json = {
  /** Default values for encryption */
  defaults: { v:1, iter:1000, ks:128, ts:64, mode:"ccm", adata:"", cipher:"aes" },

  /** Simple encryption function.
   * @param {String|bitArray} password The password or key.
   * @param {String} plaintext The data to encrypt.
   * @param {Object} [params] The parameters including tag, iv and salt.
   * @param {Object} [rp] A returned version with filled-in parameters.
   * @return {String} The ciphertext.
   * @throws {sjcl.exception.invalid} if a parameter is invalid.
   */
  encrypt: function (password, plaintext, params, rp) {
    params = params || {};
    rp = rp || {};
    
    var j = sjcl.json, p = j._add({ iv: sjcl.random.randomWords(4,0) },
                                  j.defaults), tmp, prp, adata;
    j._add(p, params);
    adata = p.adata;
    if (typeof p.salt === "string") {
      p.salt = sjcl.codec.base64.toBits(p.salt);
    }
    if (typeof p.iv === "string") {
      p.iv = sjcl.codec.base64.toBits(p.iv);
    }
    
    if (!sjcl.mode[p.mode] ||
        !sjcl.cipher[p.cipher] ||
        (typeof password === "string" && p.iter <= 100) ||
        (p.ts !== 64 && p.ts !== 96 && p.ts !== 128) ||
        (p.ks !== 128 && p.ks !== 192 && p.ks !== 256) ||
        (p.iv.length < 2 || p.iv.length > 4)) {
      throw new sjcl.exception.invalid("json encrypt: invalid parameters");
    }
    
    if (typeof password === "string") {
      tmp = sjcl.misc.cachedPbkdf2(password, p);
      password = tmp.key.slice(0,p.ks/32);
      p.salt = tmp.salt;
    } else if (sjcl.ecc && password instanceof sjcl.ecc.elGamal.publicKey) {
      tmp = password.kem();
      p.kemtag = tmp.tag;
      password = tmp.key.slice(0,p.ks/32);
    }
    if (typeof plaintext === "string") {
      plaintext = sjcl.codec.utf8String.toBits(plaintext);
    }
    if (typeof adata === "string") {
      adata = sjcl.codec.utf8String.toBits(adata);
    }
    prp = new sjcl.cipher[p.cipher](password);
    
    /* return the json data */
    j._add(rp, p);
    rp.key = password;
    
    /* do the encryption */
    p.ct = sjcl.mode[p.mode].encrypt(prp, plaintext, p.iv, adata, p.ts);
    
    //return j.encode(j._subtract(p, j.defaults));
    return j.encode(p);
  },
  
  /** Simple decryption function.
   * @param {String|bitArray} password The password or key.
   * @param {String} ciphertext The ciphertext to decrypt.
   * @param {Object} [params] Additional non-default parameters.
   * @param {Object} [rp] A returned object with filled parameters.
   * @return {String} The plaintext.
   * @throws {sjcl.exception.invalid} if a parameter is invalid.
   * @throws {sjcl.exception.corrupt} if the ciphertext is corrupt.
   */
  decrypt: function (password, ciphertext, params, rp) {
    params = params || {};
    rp = rp || {};
    
    var j = sjcl.json, p = j._add(j._add(j._add({},j.defaults),j.decode(ciphertext)), params, true), ct, tmp, prp, adata=p.adata;
    if (typeof p.salt === "string") {
      p.salt = sjcl.codec.base64.toBits(p.salt);
    }
    if (typeof p.iv === "string") {
      p.iv = sjcl.codec.base64.toBits(p.iv);
    }
    
    if (!sjcl.mode[p.mode] ||
        !sjcl.cipher[p.cipher] ||
        (typeof password === "string" && p.iter <= 100) ||
        (p.ts !== 64 && p.ts !== 96 && p.ts !== 128) ||
        (p.ks !== 128 && p.ks !== 192 && p.ks !== 256) ||
        (!p.iv) ||
        (p.iv.length < 2 || p.iv.length > 4)) {
      throw new sjcl.exception.invalid("json decrypt: invalid parameters");
    }
    
    if (typeof password === "string") {
      tmp = sjcl.misc.cachedPbkdf2(password, p);
      password = tmp.key.slice(0,p.ks/32);
      p.salt  = tmp.salt;
    } else if (sjcl.ecc && password instanceof sjcl.ecc.elGamal.secretKey) {
      password = password.unkem(sjcl.codec.base64.toBits(p.kemtag)).slice(0,p.ks/32);
    }
    if (typeof adata === "string") {
      adata = sjcl.codec.utf8String.toBits(adata);
    }
    prp = new sjcl.cipher[p.cipher](password);
    
    /* do the decryption */
    ct = sjcl.mode[p.mode].decrypt(prp, p.ct, p.iv, adata, p.ts);
    
    /* return the json data */
    j._add(rp, p);
    rp.key = password;
    
    return sjcl.codec.utf8String.fromBits(ct);
  },
  
  /** Encode a flat structure into a JSON string.
   * @param {Object} obj The structure to encode.
   * @return {String} A JSON string.
   * @throws {sjcl.exception.invalid} if obj has a non-alphanumeric property.
   * @throws {sjcl.exception.bug} if a parameter has an unsupported type.
   */
  encode: function (obj) {
    var i, out='{', comma='';
    for (i in obj) {
      if (obj.hasOwnProperty(i)) {
        if (!i.match(/^[a-z0-9]+$/i)) {
          throw new sjcl.exception.invalid("json encode: invalid property name");
        }
        out += comma + '"' + i + '":';
        comma = ',';
        
        switch (typeof obj[i]) {
        case 'number':
        case 'boolean':
          out += obj[i];
          break;
          
        case 'string':
          out += '"' + escape(obj[i]) + '"';
          break;
        
        case 'object':
          out += '"' + sjcl.codec.base64.fromBits(obj[i],0) + '"';
          break;
        
        default:
          throw new sjcl.exception.bug("json encode: unsupported type");
        }
      }
    }
    return out+'}';
  },
  
  /** Decode a simple (flat) JSON string into a structure.  The ciphertext,
   * adata, salt and iv will be base64-decoded.
   * @param {String} str The string.
   * @return {Object} The decoded structure.
   * @throws {sjcl.exception.invalid} if str isn't (simple) JSON.
   */
  decode: function (str) {
    str = str.replace(/\s/g,'');
    if (!str.match(/^\{.*\}$/)) { 
      throw new sjcl.exception.invalid("json decode: this isn't json!");
    }
    var a = str.replace(/^\{|\}$/g, '').split(/,/), out={}, i, m;
    for (i=0; i<a.length; i++) {
      if (!(m=a[i].match(/^(?:(["']?)([a-z][a-z0-9]*)\1):(?:(\d+)|"([a-z0-9+\/%*_.@=\-]*)")$/i))) {
        throw new sjcl.exception.invalid("json decode: this isn't json!");
      }
      if (m[3]) {
        out[m[2]] = parseInt(m[3],10);
      } else {
        out[m[2]] = m[2].match(/^(ct|salt|iv)$/) ? sjcl.codec.base64.toBits(m[4]) : unescape(m[4]);
      }
    }
    return out;
  },
  
  /** Insert all elements of src into target, modifying and returning target.
   * @param {Object} target The object to be modified.
   * @param {Object} src The object to pull data from.
   * @param {boolean} [requireSame=false] If true, throw an exception if any field of target differs from corresponding field of src.
   * @return {Object} target.
   * @private
   */
  _add: function (target, src, requireSame) {
    if (target === undefined) { target = {}; }
    if (src === undefined) { return target; }
    var i;
    for (i in src) {
      if (src.hasOwnProperty(i)) {
        if (requireSame && target[i] !== undefined && target[i] !== src[i]) {
          throw new sjcl.exception.invalid("required parameter overridden");
        }
        target[i] = src[i];
      }
    }
    return target;
  },
  
  /** Remove all elements of minus from plus.  Does not modify plus.
   * @private
   */
  _subtract: function (plus, minus) {
    var out = {}, i;
    
    for (i in plus) {
      if (plus.hasOwnProperty(i) && plus[i] !== minus[i]) {
        out[i] = plus[i];
      }
    }
    
    return out;
  },
  
  /** Return only the specified elements of src.
   * @private
   */
  _filter: function (src, filter) {
    var out = {}, i;
    for (i=0; i<filter.length; i++) {
      if (src[filter[i]] !== undefined) {
        out[filter[i]] = src[filter[i]];
      }
    }
    return out;
  }
};

/** Simple encryption function; convenient shorthand for sjcl.json.encrypt.
 * @param {String|bitArray} password The password or key.
 * @param {String} plaintext The data to encrypt.
 * @param {Object} [params] The parameters including tag, iv and salt.
 * @param {Object} [rp] A returned version with filled-in parameters.
 * @return {String} The ciphertext.
 */
sjcl.encrypt = sjcl.json.encrypt;

/** Simple decryption function; convenient shorthand for sjcl.json.decrypt.
 * @param {String|bitArray} password The password or key.
 * @param {String} ciphertext The ciphertext to decrypt.
 * @param {Object} [params] Additional non-default parameters.
 * @param {Object} [rp] A returned object with filled parameters.
 * @return {String} The plaintext.
 */
sjcl.decrypt = sjcl.json.decrypt;

/** The cache for cachedPbkdf2.
 * @private
 */
sjcl.misc._pbkdf2Cache = {};

/** Cached PBKDF2 key derivation.
 * @param {String} password The password.
 * @param {Object} [params] The derivation params (iteration count and optional salt).
 * @return {Object} The derived data in key, the salt in salt.
 */
sjcl.misc.cachedPbkdf2 = function (password, obj) {
  var cache = sjcl.misc._pbkdf2Cache, c, cp, str, salt, iter;
  
  obj = obj || {};
  iter = obj.iter || 1000;
  
  /* open the cache for this password and iteration count */
  cp = cache[password] = cache[password] || {};
  c = cp[iter] = cp[iter] || { firstSalt: (obj.salt && obj.salt.length) ?
                     obj.salt.slice(0) : sjcl.random.randomWords(2,0) };
          
  salt = (obj.salt === undefined) ? c.firstSalt : obj.salt;
  
  c[salt] = c[salt] || sjcl.misc.pbkdf2(password, salt, obj.iter);
  return { key: c[salt].slice(0), salt:salt.slice(0) };
};



/**
 * @constructor
 * Constructs a new bignum from another bignum, a number or a hex string.
 */
sjcl.bn = function(it) {
  this.initWith(it);
};

sjcl.bn.prototype = {
  radix: 24,
  maxMul: 8,
  _class: sjcl.bn,
  
  copy: function() {
    return new this._class(this);
  },

  /**
   * Initializes this with it, either as a bn, a number, or a hex string.
   */
  initWith: function(it) {
    var i=0, k, n, l;
    switch(typeof it) {
    case "object":
      this.limbs = it.limbs.slice(0);
      break;
      
    case "number":
      this.limbs = [it];
      this.normalize();
      break;
      
    case "string":
      it = it.replace(/^0x/, '');
      this.limbs = [];
      // hack
      k = this.radix / 4;
      for (i=0; i < it.length; i+=k) {
        this.limbs.push(parseInt(it.substring(Math.max(it.length - i - k, 0), it.length - i),16));
      }
      break;

    default:
      this.limbs = [0];
    }
    return this;
  },

  /**
   * Returns true if "this" and "that" are equal.  Calls fullReduce().
   * Equality test is in constant time.
   */
  equals: function(that) {
    if (typeof that === "number") { that = new this._class(that); }
    var difference = 0, i;
    this.fullReduce();
    that.fullReduce();
    for (i = 0; i < this.limbs.length || i < that.limbs.length; i++) {
      difference |= this.getLimb(i) ^ that.getLimb(i);
    }
    return (difference === 0);
  },
  
  /**
   * Get the i'th limb of this, zero if i is too large.
   */
  getLimb: function(i) {
    return (i >= this.limbs.length) ? 0 : this.limbs[i];
  },
  
  /**
   * Constant time comparison function.
   * Returns 1 if this >= that, or zero otherwise.
   */
  greaterEquals: function(that) {
    if (typeof that === "number") { that = new this._class(that); }
    var less = 0, greater = 0, i, a, b;
    i = Math.max(this.limbs.length, that.limbs.length) - 1;
    for (; i>= 0; i--) {
      a = this.getLimb(i);
      b = that.getLimb(i);
      greater |= (b - a) & ~less;
      less |= (a - b) & ~greater;
    }
    return (greater | ~less) >>> 31;
  },
  
  /**
   * Convert to a hex string.
   */
  toString: function() {
    this.fullReduce();
    var out="", i, s, l = this.limbs;
    for (i=0; i < this.limbs.length; i++) {
      s = l[i].toString(16);
      while (i < this.limbs.length - 1 && s.length < 6) {
        s = "0" + s;
      }
      out = s + out;
    }
    return "0x"+out;
  },
  
  /** this += that.  Does not normalize. */
  addM: function(that) {
    if (typeof(that) !== "object") { that = new this._class(that); }
    var i, l=this.limbs, ll=that.limbs;
    for (i=l.length; i<ll.length; i++) {
      l[i] = 0;
    }
    for (i=0; i<ll.length; i++) {
      l[i] += ll[i];
    }
    return this;
  },
  
  /** this *= 2.  Requires normalized; ends up normalized. */
  doubleM: function() {
    var i, carry=0, tmp, r=this.radix, m=this.radixMask, l=this.limbs;
    for (i=0; i<l.length; i++) {
      tmp = l[i];
      tmp = tmp+tmp+carry;
      l[i] = tmp & m;
      carry = tmp >> r;
    }
    if (carry) {
      l.push(carry);
    }
    return this;
  },
  
  /** this /= 2, rounded down.  Requires normalized; ends up normalized. */
  halveM: function() {
    var i, carry=0, tmp, r=this.radix, l=this.limbs;
    for (i=l.length-1; i>=0; i--) {
      tmp = l[i];
      l[i] = (tmp+carry)>>1;
      carry = (tmp&1) << r;
    }
    if (!l[l.length-1]) {
      l.pop();
    }
    return this;
  },

  /** this -= that.  Does not normalize. */
  subM: function(that) {
    if (typeof(that) !== "object") { that = new this._class(that); }
    var i, l=this.limbs, ll=that.limbs;
    for (i=l.length; i<ll.length; i++) {
      l[i] = 0;
    }
    for (i=0; i<ll.length; i++) {
      l[i] -= ll[i];
    }
    return this;
  },
  
  mod: function(that) {
    var neg = !this.greaterEquals(new sjcl.bn(0));
    
    that = new sjcl.bn(that).normalize(); // copy before we begin
    var out = new sjcl.bn(this).normalize(), ci=0;
    
    if (neg) out = (new sjcl.bn(0)).subM(out).normalize();
    
    for (; out.greaterEquals(that); ci++) {
      that.doubleM();
    }
    
    if (neg) out = that.sub(out).normalize();
    
    for (; ci > 0; ci--) {
      that.halveM();
      if (out.greaterEquals(that)) {
        out.subM(that).normalize();
      }
    }
    return out.trim();
  },
  
  /** return inverse mod prime p.  p must be odd. Binary extended Euclidean algorithm mod p. */
  inverseMod: function(p) {
    var a = new sjcl.bn(1), b = new sjcl.bn(0), x = new sjcl.bn(this), y = new sjcl.bn(p), tmp, i, nz=1;
    
    if (!(p.limbs[0] & 1)) {
      throw (new sjcl.exception.invalid("inverseMod: p must be odd"));
    }
    
    // invariant: y is odd
    do {
      if (x.limbs[0] & 1) {
        if (!x.greaterEquals(y)) {
          // x < y; swap everything
          tmp = x; x = y; y = tmp;
          tmp = a; a = b; b = tmp;
        }
        x.subM(y);
        x.normalize();
        
        if (!a.greaterEquals(b)) {
          a.addM(p);
        }
        a.subM(b);
      }
      
      // cut everything in half
      x.halveM();
      if (a.limbs[0] & 1) {
        a.addM(p);
      }
      a.normalize();
      a.halveM();
      
      // check for termination: x ?= 0
      for (i=nz=0; i<x.limbs.length; i++) {
        nz |= x.limbs[i];
      }
    } while(nz);
    
    if (!y.equals(1)) {
      throw (new sjcl.exception.invalid("inverseMod: p and x must be relatively prime"));
    }
    
    return b;
  },
  
  /** this + that.  Does not normalize. */
  add: function(that) {
    return this.copy().addM(that);
  },

  /** this - that.  Does not normalize. */
  sub: function(that) {
    return this.copy().subM(that);
  },
  
  /** this * that.  Normalizes and reduces. */
  mul: function(that) {
    if (typeof(that) === "number") { that = new this._class(that); }
    var i, j, a = this.limbs, b = that.limbs, al = a.length, bl = b.length, out = new this._class(), c = out.limbs, ai, ii=this.maxMul;

    for (i=0; i < this.limbs.length + that.limbs.length + 1; i++) {
      c[i] = 0;
    }
    for (i=0; i<al; i++) {
      ai = a[i];
      for (j=0; j<bl; j++) {
        c[i+j] += ai * b[j];
      }
     
      if (!--ii) {
        ii = this.maxMul;
        out.cnormalize();
      }
    }
    return out.cnormalize().reduce();
  },

  /** this ^ 2.  Normalizes and reduces. */
  square: function() {
    return this.mul(this);
  },

  /** this ^ n.  Uses square-and-multiply.  Normalizes and reduces. */
  power: function(l) {
    if (typeof(l) === "number") {
      l = [l];
    } else if (l.limbs !== undefined) {
      l = l.normalize().limbs;
    }
    var i, j, out = new this._class(1), pow = this;

    for (i=0; i<l.length; i++) {
      for (j=0; j<this.radix; j++) {
        if (l[i] & (1<<j)) {
          out = out.mul(pow);
        }
        pow = pow.square();
      }
    }
    
    return out;
  },

  /** this * that mod N */
  mulmod: function(that, N) {
    return this.mod(N).mul(that.mod(N)).mod(N);
  },

  /** this ^ x mod N */
  powermod: function(x, N) {
    var result = new sjcl.bn(1), a = new sjcl.bn(this), k = new sjcl.bn(x);
    while (true) {
      if (k.limbs[0] & 1) { result = result.mulmod(a, N); }
      k.halveM();
      if (k.equals(0)) { break; }
      a = a.mulmod(a, N);
    }
    return result.normalize().reduce();
  },

  trim: function() {
    var l = this.limbs, p;
    do {
      p = l.pop();
    } while (l.length && p === 0);
    l.push(p);
    return this;
  },
  
  /** Reduce mod a modulus.  Stubbed for subclassing. */
  reduce: function() {
    return this;
  },

  /** Reduce and normalize. */
  fullReduce: function() {
    return this.normalize();
  },
  
  /** Propagate carries. */
  normalize: function() {
    var carry=0, i, pv = this.placeVal, ipv = this.ipv, l, m, limbs = this.limbs, ll = limbs.length, mask = this.radixMask;
    for (i=0; i < ll || (carry !== 0 && carry !== -1); i++) {
      l = (limbs[i]||0) + carry;
      m = limbs[i] = l & mask;
      carry = (l-m)*ipv;
    }
    if (carry === -1) {
      limbs[i-1] -= this.placeVal;
    }
    return this;
  },

  /** Constant-time normalize. Does not allocate additional space. */
  cnormalize: function() {
    var carry=0, i, ipv = this.ipv, l, m, limbs = this.limbs, ll = limbs.length, mask = this.radixMask;
    for (i=0; i < ll-1; i++) {
      l = limbs[i] + carry;
      m = limbs[i] = l & mask;
      carry = (l-m)*ipv;
    }
    limbs[i] += carry;
    return this;
  },
  
  /** Serialize to a bit array */
  toBits: function(len) {
    this.fullReduce();
    len = len || this.exponent || this.bitLength();
    var i = Math.floor((len-1)/24), w=sjcl.bitArray, e = (len + 7 & -8) % this.radix || this.radix,
        out = [w.partial(e, this.getLimb(i))];
    for (i--; i >= 0; i--) {
      out = w.concat(out, [w.partial(Math.min(this.radix,len), this.getLimb(i))]);
      len -= this.radix;
    }
    return out;
  },
  
  /** Return the length in bits, rounded up to the nearest byte. */
  bitLength: function() {
    this.fullReduce();
    var out = this.radix * (this.limbs.length - 1),
        b = this.limbs[this.limbs.length - 1];
    for (; b; b >>>= 1) {
      out ++;
    }
    return out+7 & -8;
  }
};

/** @this { sjcl.bn } */
sjcl.bn.fromBits = function(bits) {
  var Class = this, out = new Class(), words=[], w=sjcl.bitArray, t = this.prototype,
      l = Math.min(this.bitLength || 0x100000000, w.bitLength(bits)), e = l % t.radix || t.radix;
  
  words[0] = w.extract(bits, 0, e);
  for (; e < l; e += t.radix) {
    words.unshift(w.extract(bits, e, t.radix));
  }

  out.limbs = words;
  return out;
};



sjcl.bn.prototype.ipv = 1 / (sjcl.bn.prototype.placeVal = Math.pow(2,sjcl.bn.prototype.radix));
sjcl.bn.prototype.radixMask = (1 << sjcl.bn.prototype.radix) - 1;

/**
 * Creates a new subclass of bn, based on reduction modulo a pseudo-Mersenne prime,
 * i.e. a prime of the form 2^e + sum(a * 2^b),where the sum is negative and sparse.
 */
sjcl.bn.pseudoMersennePrime = function(exponent, coeff) {
  /** @constructor */
  function p(it) {
    this.initWith(it);
    /*if (this.limbs[this.modOffset]) {
      this.reduce();
    }*/
  }

  var ppr = p.prototype = new sjcl.bn(), i, tmp, mo;
  mo = ppr.modOffset = Math.ceil(tmp = exponent / ppr.radix);
  ppr.exponent = exponent;
  ppr.offset = [];
  ppr.factor = [];
  ppr.minOffset = mo;
  ppr.fullMask = 0;
  ppr.fullOffset = [];
  ppr.fullFactor = [];
  ppr.modulus = p.modulus = new sjcl.bn(Math.pow(2,exponent));
  
  ppr.fullMask = 0|-Math.pow(2, exponent % ppr.radix);

  for (i=0; i<coeff.length; i++) {
    ppr.offset[i] = Math.floor(coeff[i][0] / ppr.radix - tmp);
    ppr.fullOffset[i] = Math.ceil(coeff[i][0] / ppr.radix - tmp);
    ppr.factor[i] = coeff[i][1] * Math.pow(1/2, exponent - coeff[i][0] + ppr.offset[i] * ppr.radix);
    ppr.fullFactor[i] = coeff[i][1] * Math.pow(1/2, exponent - coeff[i][0] + ppr.fullOffset[i] * ppr.radix);
    ppr.modulus.addM(new sjcl.bn(Math.pow(2,coeff[i][0])*coeff[i][1]));
    ppr.minOffset = Math.min(ppr.minOffset, -ppr.offset[i]); // conservative
  }
  ppr._class = p;
  ppr.modulus.cnormalize();

  /** Approximate reduction mod p.  May leave a number which is negative or slightly larger than p.
   * @this {sjcl.bn}
   */
  ppr.reduce = function() {
    var i, k, l, mo = this.modOffset, limbs = this.limbs, aff, off = this.offset, ol = this.offset.length, fac = this.factor, ll;

    i = this.minOffset;
    while (limbs.length > mo) {
      l = limbs.pop();
      ll = limbs.length;
      for (k=0; k<ol; k++) {
        limbs[ll+off[k]] -= fac[k] * l;
      }
      
      i--;
      if (!i) {
        limbs.push(0);
        this.cnormalize();
        i = this.minOffset;
      }
    }
    this.cnormalize();

    return this;
  };
  
  /** @this {sjcl.bn} */
  ppr._strongReduce = (ppr.fullMask === -1) ? ppr.reduce : function() {
    var limbs = this.limbs, i = limbs.length - 1, k, l;
    this.reduce();
    if (i === this.modOffset - 1) {
      l = limbs[i] & this.fullMask;
      limbs[i] -= l;
      for (k=0; k<this.fullOffset.length; k++) {
        limbs[i+this.fullOffset[k]] -= this.fullFactor[k] * l;
      }
      this.normalize();
    }
  };

  /** mostly constant-time, very expensive full reduction.
   * @this {sjcl.bn}
   */
  ppr.fullReduce = function() {
    var greater, i;
    // massively above the modulus, may be negative
    
    this._strongReduce();
    // less than twice the modulus, may be negative

    this.addM(this.modulus);
    this.addM(this.modulus);
    this.normalize();
    // probably 2-3x the modulus
    
    this._strongReduce();
    // less than the power of 2.  still may be more than
    // the modulus

    // HACK: pad out to this length
    for (i=this.limbs.length; i<this.modOffset; i++) {
      this.limbs[i] = 0;
    }
    
    // constant-time subtract modulus
    greater = this.greaterEquals(this.modulus);
    for (i=0; i<this.limbs.length; i++) {
      this.limbs[i] -= this.modulus.limbs[i] * greater;
    }
    this.cnormalize();

    return this;
  };


  /** @this {sjcl.bn} */
  ppr.inverse = function() {
    return (this.power(this.modulus.sub(2)));
  };

  p.fromBits = sjcl.bn.fromBits;

  return p;
};

// a small Mersenne prime
sjcl.bn.prime = {
  p127: sjcl.bn.pseudoMersennePrime(127, [[0,-1]]),

  // Bernstein's prime for Curve25519
  p25519: sjcl.bn.pseudoMersennePrime(255, [[0,-19]]),

  // NIST primes
  p192: sjcl.bn.pseudoMersennePrime(192, [[0,-1],[64,-1]]),
  p224: sjcl.bn.pseudoMersennePrime(224, [[0,1],[96,-1]]),
  p256: sjcl.bn.pseudoMersennePrime(256, [[0,-1],[96,1],[192,1],[224,-1]]),
  p384: sjcl.bn.pseudoMersennePrime(384, [[0,-1],[32,1],[96,-1],[128,-1]]),
  p521: sjcl.bn.pseudoMersennePrime(521, [[0,-1]])
};

sjcl.bn.random = function(modulus, paranoia) {
  if (typeof modulus !== "object") { modulus = new sjcl.bn(modulus); }
  var words, i, l = modulus.limbs.length, m = modulus.limbs[l-1]+1, out = new sjcl.bn();
  while (true) {
    // get a sequence whose first digits make sense
    do {
      words = sjcl.random.randomWords(l, paranoia);
      if (words[l-1] < 0) { words[l-1] += 0x100000000; }
    } while (Math.floor(words[l-1] / m) === Math.floor(0x100000000 / m));
    words[l-1] %= m;

    // mask off all the limbs
    for (i=0; i<l-1; i++) {
      words[i] &= modulus.radixMask;
    }

    // check the rest of the digitssj
    out.limbs = words;
    if (!out.greaterEquals(modulus)) {
      return out;
    }
  }
};


sjcl.ecc = {};

/**
 * Represents a point on a curve in affine coordinates.
 * @constructor
 * @param {sjcl.ecc.curve} curve The curve that this point lies on.
 * @param {bigInt} x The x coordinate.
 * @param {bigInt} y The y coordinate.
 */
sjcl.ecc.point = function(curve,x,y) {
  if (x === undefined) {
    this.isIdentity = true;
  } else {
    if (x instanceof sjcl.bn) {
      x = new curve.field(x);
    }
    if (y instanceof sjcl.bn) {
      y = new curve.field(y);
    }

    this.x = x;
    this.y = y;

    this.isIdentity = false;
  }
  this.curve = curve;
};



sjcl.ecc.point.prototype = {
  toJac: function() {
    return new sjcl.ecc.pointJac(this.curve, this.x, this.y, new this.curve.field(1));
  },

  mult: function(k) {
    return this.toJac().mult(k, this).toAffine();
  },
  
  /**
   * Multiply this point by k, added to affine2*k2, and return the answer in Jacobian coordinates.
   * @param {bigInt} k The coefficient to multiply this by.
   * @param {bigInt} k2 The coefficient to multiply affine2 this by.
   * @param {sjcl.ecc.point} affine The other point in affine coordinates.
   * @return {sjcl.ecc.pointJac} The result of the multiplication and addition, in Jacobian coordinates.
   */
  mult2: function(k, k2, affine2) {
    return this.toJac().mult2(k, this, k2, affine2).toAffine();
  },
  
  multiples: function() {
    var m, i, j;
    if (this._multiples === undefined) {
      j = this.toJac().doubl();
      m = this._multiples = [new sjcl.ecc.point(this.curve), this, j.toAffine()];
      for (i=3; i<16; i++) {
        j = j.add(this);
        m.push(j.toAffine());
      }
    }
    return this._multiples;
  },

  isValid: function() {
    return this.y.square().equals(this.curve.b.add(this.x.mul(this.curve.a.add(this.x.square()))));
  },

  toBits: function() {
    return sjcl.bitArray.concat(this.x.toBits(), this.y.toBits());
  }
};

/**
 * Represents a point on a curve in Jacobian coordinates. Coordinates can be specified as bigInts or strings (which
 * will be converted to bigInts).
 *
 * @constructor
 * @param {bigInt/string} x The x coordinate.
 * @param {bigInt/string} y The y coordinate.
 * @param {bigInt/string} z The z coordinate.
 * @param {sjcl.ecc.curve} curve The curve that this point lies on.
 */
sjcl.ecc.pointJac = function(curve, x, y, z) {
  if (x === undefined) {
    this.isIdentity = true;
  } else {
    this.x = x;
    this.y = y;
    this.z = z;
    this.isIdentity = false;
  }
  this.curve = curve;
};

sjcl.ecc.pointJac.prototype = {
  /**
   * Adds S and T and returns the result in Jacobian coordinates. Note that S must be in Jacobian coordinates and T must be in affine coordinates.
   * @param {sjcl.ecc.pointJac} S One of the points to add, in Jacobian coordinates.
   * @param {sjcl.ecc.point} T The other point to add, in affine coordinates.
   * @return {sjcl.ecc.pointJac} The sum of the two points, in Jacobian coordinates. 
   */
  add: function(T) {
    var S = this, sz2, c, d, c2, x1, x2, x, y1, y2, y, z;
    if (S.curve !== T.curve) {
      throw("sjcl.ecc.add(): Points must be on the same curve to add them!");
    }

    if (S.isIdentity) {
      return T.toJac();
    } else if (T.isIdentity) {
      return S;
    }

    sz2 = S.z.square();
    c = T.x.mul(sz2).subM(S.x);

    if (c.equals(0)) {
      if (S.y.equals(T.y.mul(sz2.mul(S.z)))) {
        // same point
        return S.doubl();
      } else {
        // inverses
        return new sjcl.ecc.pointJac(S.curve);
      }
    }
    
    d = T.y.mul(sz2.mul(S.z)).subM(S.y);
    c2 = c.square();

    x1 = d.square();
    x2 = c.square().mul(c).addM( S.x.add(S.x).mul(c2) );
    x  = x1.subM(x2);

    y1 = S.x.mul(c2).subM(x).mul(d);
    y2 = S.y.mul(c.square().mul(c));
    y  = y1.subM(y2);

    z  = S.z.mul(c);

    return new sjcl.ecc.pointJac(this.curve,x,y,z);
  },
  
  /**
   * doubles this point.
   * @return {sjcl.ecc.pointJac} The doubled point.
   */
  doubl: function() {
    if (this.isIdentity) { return this; }

    var
      y2 = this.y.square(),
      a  = y2.mul(this.x.mul(4)),
      b  = y2.square().mul(8),
      z2 = this.z.square(),
      c  = this.x.sub(z2).mul(3).mul(this.x.add(z2)),
      x  = c.square().subM(a).subM(a),
      y  = a.sub(x).mul(c).subM(b),
      z  = this.y.add(this.y).mul(this.z);
    return new sjcl.ecc.pointJac(this.curve, x, y, z);
  },

  /**
   * Returns a copy of this point converted to affine coordinates.
   * @return {sjcl.ecc.point} The converted point.
   */  
  toAffine: function() {
    if (this.isIdentity || this.z.equals(0)) {
      return new sjcl.ecc.point(this.curve);
    }
    var zi = this.z.inverse(), zi2 = zi.square();
    return new sjcl.ecc.point(this.curve, this.x.mul(zi2).fullReduce(), this.y.mul(zi2.mul(zi)).fullReduce());
  },
  
  /**
   * Multiply this point by k and return the answer in Jacobian coordinates.
   * @param {bigInt} k The coefficient to multiply by.
   * @param {sjcl.ecc.point} affine This point in affine coordinates.
   * @return {sjcl.ecc.pointJac} The result of the multiplication, in Jacobian coordinates.
   */
  mult: function(k, affine) {
    if (typeof(k) === "number") {
      k = [k];
    } else if (k.limbs !== undefined) {
      k = k.normalize().limbs;
    }
    
    var i, j, out = new sjcl.ecc.point(this.curve).toJac(), multiples = affine.multiples();

    for (i=k.length-1; i>=0; i--) {
      for (j=sjcl.bn.prototype.radix-4; j>=0; j-=4) {
        out = out.doubl().doubl().doubl().doubl().add(multiples[k[i]>>j & 0xF]);
      }
    }
    
    return out;
  },
  
  /**
   * Multiply this point by k, added to affine2*k2, and return the answer in Jacobian coordinates.
   * @param {bigInt} k The coefficient to multiply this by.
   * @param {sjcl.ecc.point} affine This point in affine coordinates.
   * @param {bigInt} k2 The coefficient to multiply affine2 this by.
   * @param {sjcl.ecc.point} affine The other point in affine coordinates.
   * @return {sjcl.ecc.pointJac} The result of the multiplication and addition, in Jacobian coordinates.
   */
  mult2: function(k1, affine, k2, affine2) {
    if (typeof(k1) === "number") {
      k1 = [k1];
    } else if (k1.limbs !== undefined) {
      k1 = k1.normalize().limbs;
    }
    
    if (typeof(k2) === "number") {
      k2 = [k2];
    } else if (k2.limbs !== undefined) {
      k2 = k2.normalize().limbs;
    }
    
    var i, j, out = new sjcl.ecc.point(this.curve).toJac(), m1 = affine.multiples(),
        m2 = affine2.multiples(), l1, l2;

    for (i=Math.max(k1.length,k2.length)-1; i>=0; i--) {
      l1 = k1[i] | 0;
      l2 = k2[i] | 0;
      for (j=sjcl.bn.prototype.radix-4; j>=0; j-=4) {
        out = out.doubl().doubl().doubl().doubl().add(m1[l1>>j & 0xF]).add(m2[l2>>j & 0xF]);
      }
    }
    
    return out;
  },

  isValid: function() {
    var z2 = this.z.square(), z4 = z2.square(), z6 = z4.mul(z2);
    return this.y.square().equals(
             this.curve.b.mul(z6).add(this.x.mul(
               this.curve.a.mul(z4).add(this.x.square()))));
  }
};

/**
 * Construct an elliptic curve. Most users will not use this and instead start with one of the NIST curves defined below.
 *
 * @constructor
 * @param {bigInt} p The prime modulus.
 * @param {bigInt} r The prime order of the curve.
 * @param {bigInt} a The constant a in the equation of the curve y^2 = x^3 + ax + b (for NIST curves, a is always -3).
 * @param {bigInt} x The x coordinate of a base point of the curve.
 * @param {bigInt} y The y coordinate of a base point of the curve.
 */
sjcl.ecc.curve = function(Field, r, a, b, x, y) {
  this.field = Field;
  this.r = Field.prototype.modulus.sub(r);
  this.a = new Field(a);
  this.b = new Field(b);
  this.G = new sjcl.ecc.point(this, new Field(x), new Field(y));
};

sjcl.ecc.curve.prototype.fromBits = function (bits) {
  var w = sjcl.bitArray, l = this.field.prototype.exponent + 7 & -8,
      p = new sjcl.ecc.point(this, this.field.fromBits(w.bitSlice(bits, 0, l)),
                             this.field.fromBits(w.bitSlice(bits, l, 2*l)));
  if (!p.isValid()) {
    throw new sjcl.exception.corrupt("not on the curve!");
  }
  return p;
};

sjcl.ecc.curves = {
  c192: new sjcl.ecc.curve(
    sjcl.bn.prime.p192,
    "0x662107c8eb94364e4b2dd7ce",
    -3,
    "0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1",
    "0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012",
    "0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811"),

  c224: new sjcl.ecc.curve(
    sjcl.bn.prime.p224,
    "0xe95c1f470fc1ec22d6baa3a3d5c4",
    -3,
    "0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4",
    "0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
    "0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34"),

  c256: new sjcl.ecc.curve(
    sjcl.bn.prime.p256,
    "0x4319055358e8617b0c46353d039cdaae",
    -3,
    "0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
    "0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
    "0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"),

  c384: new sjcl.ecc.curve(
    sjcl.bn.prime.p384,
    "0x389cb27e0bc8d21fa7e5f24cb74f58851313e696333ad68c",
    -3,
    "0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef",
    "0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7",
    "0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f")
};


/* Diffie-Hellman-like public-key system */
sjcl.ecc._dh = function(cn) {
  sjcl.ecc[cn] = {
    /** @constructor */
    publicKey: function(curve, point) {
      this._curve = curve;
      this._curveBitLength = curve.r.bitLength();
      if (point instanceof Array) {
        this._point = curve.fromBits(point);
      } else {
        this._point = point;
      }

      this.get = function() {
        var pointbits = this._point.toBits();
        var len = sjcl.bitArray.bitLength(pointbits);
        var x = sjcl.bitArray.bitSlice(pointbits, 0, len/2);
        var y = sjcl.bitArray.bitSlice(pointbits, len/2);
        return { x: x, y: y };
      }
    },

    /** @constructor */
    secretKey: function(curve, exponent) {
      this._curve = curve;
      this._curveBitLength = curve.r.bitLength();
      this._exponent = exponent;

      this.get = function() {
        return this._exponent.toBits();
      }
    },

    /** @constructor */
    generateKeys: function(curve, paranoia, sec) {
      if (curve === undefined) {
        curve = 256;
      }
      if (typeof curve === "number") {
        curve = sjcl.ecc.curves['c'+curve];
        if (curve === undefined) {
          throw new sjcl.exception.invalid("no such curve");
        }
      }
      if (sec === undefined) {
        var sec = sjcl.bn.random(curve.r, paranoia);
      }
      var pub = curve.G.mult(sec);
      return { pub: new sjcl.ecc[cn].publicKey(curve, pub),
               sec: new sjcl.ecc[cn].secretKey(curve, sec) };
    }
  }; 
};

sjcl.ecc._dh("elGamal");

sjcl.ecc.elGamal.publicKey.prototype = {
  kem: function(paranoia) {
    var sec = sjcl.bn.random(this._curve.r, paranoia),
        tag = this._curve.G.mult(sec).toBits(),
        key = sjcl.hash.sha256.hash(this._point.mult(sec).toBits());
    return { key: key, tag: tag };
  }
};

sjcl.ecc.elGamal.secretKey.prototype = {
  unkem: function(tag) {
    return sjcl.hash.sha256.hash(this._curve.fromBits(tag).mult(this._exponent).toBits());
  },

  dh: function(pk) {
    return sjcl.hash.sha256.hash(pk._point.mult(this._exponent).toBits());
  }
};

sjcl.ecc._dh("ecdsa");

sjcl.ecc.ecdsa.secretKey.prototype = {
  sign: function(hash, paranoia, fakeLegacyVersion, fixedKForTesting) {
    if (sjcl.bitArray.bitLength(hash) > this._curveBitLength) {
      hash = sjcl.bitArray.clamp(hash, this._curveBitLength);
    }
    var R  = this._curve.r,
        l  = R.bitLength(),
        k  = fixedKForTesting || sjcl.bn.random(R.sub(1), paranoia).add(1),
        r  = this._curve.G.mult(k).x.mod(R),
        ss = sjcl.bn.fromBits(hash).add(r.mul(this._exponent)),
        s  = fakeLegacyVersion ? ss.inverseMod(R).mul(k).mod(R)
             : ss.mul(k.inverseMod(R)).mod(R);
    return sjcl.bitArray.concat(r.toBits(l), s.toBits(l));
  }
};

sjcl.ecc.ecdsa.publicKey.prototype = {
  verify: function(hash, rs, fakeLegacyVersion) {
    if (sjcl.bitArray.bitLength(hash) > this._curveBitLength) {
      hash = sjcl.bitArray.clamp(hash, this._curveBitLength);
    }
    var w = sjcl.bitArray,
        R = this._curve.r,
        l = this._curveBitLength,
        r = sjcl.bn.fromBits(w.bitSlice(rs,0,l)),
        ss = sjcl.bn.fromBits(w.bitSlice(rs,l,2*l)),
        s = fakeLegacyVersion ? ss : ss.inverseMod(R),
        hG = sjcl.bn.fromBits(hash).mul(s).mod(R),
        hA = r.mul(s).mod(R),
        r2 = this._curve.G.mult2(hG, hA, this._point).x;
    if (r.equals(0) || ss.equals(0) || r.greaterEquals(R) || ss.greaterEquals(R) || !r2.equals(r)) {
      if (fakeLegacyVersion === undefined) {
        return this.verify(hash, rs, true);
      } else {
        throw (new sjcl.exception.corrupt("signature didn't check out"));
      }
    }
    return true;
  }
};

/** @fileOverview Javascript SRP implementation.
 *
 * This file contains a partial implementation of the SRP (Secure Remote
 * Password) password-authenticated key exchange protocol. Given a user
 * identity, salt, and SRP group, it generates the SRP verifier that may
 * be sent to a remote server to establish and SRP account.
 *
 * For more information, see http://srp.stanford.edu/.
 *
 * @author Quinn Slack
 */

/**
 * Compute the SRP verifier from the username, password, salt, and group.
 * @class SRP
 */
sjcl.keyexchange.srp = {
  /**
   * Calculates SRP v, the verifier. 
   *   v = g^x mod N [RFC 5054]
   * @param {String} I The username.
   * @param {String} P The password.
   * @param {Object} s A bitArray of the salt.
   * @param {Object} group The SRP group. Use sjcl.keyexchange.srp.knownGroup
                           to obtain this object.
   * @return {Object} A bitArray of SRP v.
   */
  makeVerifier: function(I, P, s, group) {
    var x;
    x = sjcl.keyexchange.srp.makeX(I, P, s);
    x = sjcl.bn.fromBits(x);
    return group.g.powermod(x, group.N);
  },

  /**
   * Calculates SRP x.
   *   x = SHA1(<salt> | SHA(<username> | ":" | <raw password>)) [RFC 2945]
   * @param {String} I The username.
   * @param {String} P The password.
   * @param {Object} s A bitArray of the salt.
   * @return {Object} A bitArray of SRP x.
   */
  makeX: function(I, P, s) {
    var inner = sjcl.hash.sha1.hash(I + ':' + P);
    return sjcl.hash.sha1.hash(sjcl.bitArray.concat(s, inner));
  },

  /**
   * Returns the known SRP group with the given size (in bits).
   * @param {String} i The size of the known SRP group.
   * @return {Object} An object with "N" and "g" properties.
   */
  knownGroup:function(i) {
    if (typeof i !== "string") { i = i.toString(); }
    if (!sjcl.keyexchange.srp._didInitKnownGroups) { sjcl.keyexchange.srp._initKnownGroups(); }
    return sjcl.keyexchange.srp._knownGroups[i];
  },

  /**
   * Initializes bignum objects for known group parameters.
   * @private
   */
  _didInitKnownGroups: false,
  _initKnownGroups:function() {
    var i, size, group;
    for (i=0; i < sjcl.keyexchange.srp._knownGroupSizes.length; i++) {
      size = sjcl.keyexchange.srp._knownGroupSizes[i].toString();
      group = sjcl.keyexchange.srp._knownGroups[size];
      group.N = new sjcl.bn(group.N);
      group.g = new sjcl.bn(group.g);
    }
    sjcl.keyexchange.srp._didInitKnownGroups = true;
  },

  _knownGroupSizes: [1024, 1536, 2048],
  _knownGroups: {
    1024: {
      N: "EEAF0AB9ADB38DD69C33F80AFA8FC5E86072618775FF3C0B9EA2314C" +
         "9C256576D674DF7496EA81D3383B4813D692C6E0E0D5D8E250B98BE4" +
         "8E495C1D6089DAD15DC7D7B46154D6B6CE8EF4AD69B15D4982559B29" +
         "7BCF1885C529F566660E57EC68EDBC3C05726CC02FD4CBF4976EAA9A" +
         "FD5138FE8376435B9FC61D2FC0EB06E3",
      g:2
    },

    1536: {
      N: "9DEF3CAFB939277AB1F12A8617A47BBBDBA51DF499AC4C80BEEEA961" +
         "4B19CC4D5F4F5F556E27CBDE51C6A94BE4607A291558903BA0D0F843" +
         "80B655BB9A22E8DCDF028A7CEC67F0D08134B1C8B97989149B609E0B" +
         "E3BAB63D47548381DBC5B1FC764E3F4B53DD9DA1158BFD3E2B9C8CF5" +
         "6EDF019539349627DB2FD53D24B7C48665772E437D6C7F8CE442734A" +
         "F7CCB7AE837C264AE3A9BEB87F8A2FE9B8B5292E5A021FFF5E91479E" +
         "8CE7A28C2442C6F315180F93499A234DCF76E3FED135F9BB",
      g: 2
    },

    2048: {
      N: "AC6BDB41324A9A9BF166DE5E1389582FAF72B6651987EE07FC319294" +
         "3DB56050A37329CBB4A099ED8193E0757767A13DD52312AB4B03310D" +
         "CD7F48A9DA04FD50E8083969EDB767B0CF6095179A163AB3661A05FB" +
         "D5FAAAE82918A9962F0B93B855F97993EC975EEAA80D740ADBF4FF74" +
         "7359D041D5C33EA71D281E446B14773BCA97B43A23FB801676BD207A" +
         "436C6481F1D2B9078717461A5B9D32E688F87748544523B524B0D57D" +
         "5EA77A2775D2ECFA032CFBDBF52FB3786160279004E57AE6AF874E73" +
         "03CE53299CCC041C7BC308D82A5698F3A8D0C38271AE35F8E9DBFBB6" +
         "94B5C803D89F7AE435DE236D525F54759B65E372FCD68EF20FA7111F" +
         "9E4AFF73",
      g: 2
    }
  }

};


/**
 *  Check that the point is valid based on the method described in
 *  SEC 1: Elliptic Curve Cryptography, section 3.2.2.1: 
 *  Elliptic Curve Public Key Validation Primitive
 *  http://www.secg.org/download/aid-780/sec1-v2.pdf
 *
 *  @returns {Boolean}
 */
sjcl.ecc.point.prototype.isValidPoint = function() {

  var self = this;

  var field_modulus = self.curve.field.modulus;

  if (self.isIdentity) {
    return false;
  }

  // Check that coordinatres are in bounds
  // Return false if x < 1 or x > (field_modulus - 1)
  if (((new sjcl.bn(1).greaterEquals(self.x)) &&
    !self.x.equals(1)) ||
    (self.x.greaterEquals(field_modulus.sub(1))) &&
    !self.x.equals(1)) {

    return false;
  }

  // Return false if y < 1 or y > (field_modulus - 1)
  if (((new sjcl.bn(1).greaterEquals(self.y)) &&
    !self.y.equals(1)) ||
    (self.y.greaterEquals(field_modulus.sub(1))) &&
    !self.y.equals(1)) {

    return false;
  }

  if (!self.isOnCurve()) {
    return false;
  }

  // TODO check to make sure point is a scalar multiple of base_point

  return true;

};

/**
 *  Check that the point is on the curve
 *
 *  @returns {Boolean}
 */
sjcl.ecc.point.prototype.isOnCurve = function() {

  var self = this;

  var field_order = self.curve.r;
  var component_a = self.curve.a;
  var component_b = self.curve.b;
  var field_modulus = self.curve.field.modulus;

  var left_hand_side = self.y.mul(self.y).mod(field_modulus);
  var right_hand_side = self.x.mul(self.x).mul(self.x).add(component_a.mul(self.x)).add(component_b).mod(field_modulus);

  return left_hand_side.equals(right_hand_side);

};


sjcl.ecc.point.prototype.toString = function() {
  return '(' + 
    this.x.toString() + ', ' +
    this.y.toString() +
    ')';
};

sjcl.ecc.pointJac.prototype.toString = function() {
  return '(' + 
    this.x.toString() + ', ' +
    this.y.toString() + ', ' +
    this.z.toString() +
    ')';
};

// ----- for secp256k1 ------

// Overwrite NIST-P256 with secp256k1
sjcl.ecc.curves.c256 = new sjcl.ecc.curve(
    sjcl.bn.pseudoMersennePrime(256, [[0,-1],[4,-1],[6,-1],[7,-1],[8,-1],[9,-1],[32,-1]]),
    "0x14551231950b75fc4402da1722fc9baee",
    0,
    7,
    "0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798",
    "0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"
);

// Replace point addition and doubling algorithms
// NIST-P256 is a=-3, we need algorithms for a=0
sjcl.ecc.pointJac.prototype.add = function(T) {
  var S = this;
  if (S.curve !== T.curve) {
    throw("sjcl.ecc.add(): Points must be on the same curve to add them!");
  }

  if (S.isIdentity) {
    return T.toJac();
  } else if (T.isIdentity) {
    return S;
  }

  var z1z1 = S.z.square();
  var h = T.x.mul(z1z1).subM(S.x);
  var s2 = T.y.mul(S.z).mul(z1z1);

  if (h.equals(0)) {
    if (S.y.equals(T.y.mul(z1z1.mul(S.z)))) {
      // same point
      return S.doubl();
    } else {
      // inverses
      return new sjcl.ecc.pointJac(S.curve);
    }
  }

  var hh = h.square();
  var i = hh.copy().doubleM().doubleM();
  var j = h.mul(i);
  var r = s2.sub(S.y).doubleM();
  var v = S.x.mul(i);
  
  var x = r.square().subM(j).subM(v.copy().doubleM());
  var y = r.mul(v.sub(x)).subM(S.y.mul(j).doubleM());
  var z = S.z.add(h).square().subM(z1z1).subM(hh);

  return new sjcl.ecc.pointJac(this.curve,x,y,z);
};

sjcl.ecc.pointJac.prototype.doubl = function () {
  if (this.isIdentity) { return this; }

  var a = this.x.square();
  var b = this.y.square();
  var c = b.square();
  var d = this.x.add(b).square().subM(a).subM(c).doubleM();
  var e = a.mul(3);
  var f = e.square();
  var x = f.sub(d.copy().doubleM());
  var y = e.mul(d.sub(x)).subM(c.doubleM().doubleM().doubleM());
  var z = this.z.mul(this.y).doubleM();
  return new sjcl.ecc.pointJac(this.curve, x, y, z);
};

sjcl.ecc.point.prototype.toBytesCompressed = function () {
  var header = this.y.mod(2).toString() == "0x0" ? 0x02 : 0x03;
  return [header].concat(sjcl.codec.bytes.fromBits(this.x.toBits()))
};

/** @fileOverview Javascript RIPEMD-160 implementation.
 *
 * @author Artem S Vybornov <vybornov@gmail.com>
 */
(function() {

/**
 * Context for a RIPEMD-160 operation in progress.
 * @constructor
 * @class RIPEMD, 160 bits.
 */
sjcl.hash.ripemd160 = function (hash) {
    if (hash) {
        this._h = hash._h.slice(0);
        this._buffer = hash._buffer.slice(0);
        this._length = hash._length;
    } else {
        this.reset();
    }
};

/**
 * Hash a string or an array of words.
 * @static
 * @param {bitArray|String} data the data to hash.
 * @return {bitArray} The hash value, an array of 5 big-endian words.
 */
sjcl.hash.ripemd160.hash = function (data) {
  return (new sjcl.hash.ripemd160()).update(data).finalize();
};

sjcl.hash.ripemd160.prototype = {
    /**
     * Reset the hash state.
     * @return this
     */
    reset: function () {
        this._h = _h0.slice(0);
        this._buffer = [];
        this._length = 0;
        return this;
    },

    /**
     * Reset the hash state.
     * @param {bitArray|String} data the data to hash.
     * @return this
     */
    update: function (data) {
        if ( typeof data === "string" )
            data = sjcl.codec.utf8String.toBits(data);

        var i, b = this._buffer = sjcl.bitArray.concat(this._buffer, data),
            ol = this._length,
            nl = this._length = ol + sjcl.bitArray.bitLength(data);
        for (i = 512+ol & -512; i <= nl; i+= 512) {
            var words = b.splice(0,16);
            for ( var w = 0; w < 16; ++w )
                words[w] = _cvt(words[w]);

            _block.call( this, words );
        }

        return this;
    },

    /**
     * Complete hashing and output the hash value.
     * @return {bitArray} The hash value, an array of 5 big-endian words.
     */
    finalize: function () {
        var b = sjcl.bitArray.concat( this._buffer, [ sjcl.bitArray.partial(1,1) ] ),
            l = ( this._length + 1 ) % 512,
            z = ( l > 448 ? 512 : 448 ) - l % 448,
            zp = z % 32;

        if ( zp > 0 )
            b = sjcl.bitArray.concat( b, [ sjcl.bitArray.partial(zp,0) ] )
        for ( ; z >= 32; z -= 32 )
            b.push(0);

        b.push( _cvt( this._length | 0 ) );
        b.push( _cvt( Math.floor(this._length / 0x100000000) ) );

        while ( b.length ) {
            var words = b.splice(0,16);
            for ( var w = 0; w < 16; ++w )
                words[w] = _cvt(words[w]);

            _block.call( this, words );
        }

        var h = this._h;
        this.reset();

        for ( var w = 0; w < 5; ++w )
            h[w] = _cvt(h[w]);

        return h;
    }
};

var _h0 = [ 0x67452301, 0xefcdab89, 0x98badcfe, 0x10325476, 0xc3d2e1f0 ];

var _k1 = [ 0x00000000, 0x5a827999, 0x6ed9eba1, 0x8f1bbcdc, 0xa953fd4e ];
var _k2 = [ 0x50a28be6, 0x5c4dd124, 0x6d703ef3, 0x7a6d76e9, 0x00000000 ];
for ( var i = 4; i >= 0; --i ) {
    for ( var j = 1; j < 16; ++j ) {
        _k1.splice(i,0,_k1[i]);
        _k2.splice(i,0,_k2[i]);
    }
}

var _r1 = [  0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15,
             7,  4, 13,  1, 10,  6, 15,  3, 12,  0,  9,  5,  2, 14, 11,  8,
             3, 10, 14,  4,  9, 15,  8,  1,  2,  7,  0,  6, 13, 11,  5, 12,
             1,  9, 11, 10,  0,  8, 12,  4, 13,  3,  7, 15, 14,  5,  6,  2,
             4,  0,  5,  9,  7, 12,  2, 10, 14,  1,  3,  8, 11,  6, 15, 13 ];
var _r2 = [  5, 14,  7,  0,  9,  2, 11,  4, 13,  6, 15,  8,  1, 10,  3, 12,
             6, 11,  3,  7,  0, 13,  5, 10, 14, 15,  8, 12,  4,  9,  1,  2,
            15,  5,  1,  3,  7, 14,  6,  9, 11,  8, 12,  2, 10,  0,  4, 13,
             8,  6,  4,  1,  3, 11, 15,  0,  5, 12,  2, 13,  9,  7, 10, 14,
            12, 15, 10,  4,  1,  5,  8,  7,  6,  2, 13, 14,  0,  3,  9, 11 ];

var _s1 = [ 11, 14, 15, 12,  5,  8,  7,  9, 11, 13, 14, 15,  6,  7,  9,  8,
             7,  6,  8, 13, 11,  9,  7, 15,  7, 12, 15,  9, 11,  7, 13, 12,
            11, 13,  6,  7, 14,  9, 13, 15, 14,  8, 13,  6,  5, 12,  7,  5,
            11, 12, 14, 15, 14, 15,  9,  8,  9, 14,  5,  6,  8,  6,  5, 12,
             9, 15,  5, 11,  6,  8, 13, 12,  5, 12, 13, 14, 11,  8,  5,  6 ];
var _s2 = [  8,  9,  9, 11, 13, 15, 15,  5,  7,  7,  8, 11, 14, 14, 12,  6,
             9, 13, 15,  7, 12,  8,  9, 11,  7,  7, 12,  7,  6, 15, 13, 11,
             9,  7, 15, 11,  8,  6,  6, 14, 12, 13,  5, 14, 13, 13,  7,  5,
            15,  5,  8, 11, 14, 14,  6, 14,  6,  9, 12,  9, 12,  5, 15,  8,
             8,  5, 12,  9, 12,  5, 14,  6,  8, 13,  6,  5, 15, 13, 11, 11 ];

function _f0(x,y,z) {
    return x ^ y ^ z;
};

function _f1(x,y,z) {
    return (x & y) | (~x & z);
};

function _f2(x,y,z) {
    return (x | ~y) ^ z;
};

function _f3(x,y,z) {
    return (x & z) | (y & ~z);
};

function _f4(x,y,z) {
    return x ^ (y | ~z);
};

function _rol(n,l) {
    return (n << l) | (n >>> (32-l));
}

function _cvt(n) {
    return ( (n & 0xff <<  0) <<  24 )
         | ( (n & 0xff <<  8) <<   8 )
         | ( (n & 0xff << 16) >>>  8 )
         | ( (n & 0xff << 24) >>> 24 );
}

function _block(X) {
    var A1 = this._h[0], B1 = this._h[1], C1 = this._h[2], D1 = this._h[3], E1 = this._h[4],
        A2 = this._h[0], B2 = this._h[1], C2 = this._h[2], D2 = this._h[3], E2 = this._h[4];

    var j = 0, T;

    for ( ; j < 16; ++j ) {
        T = _rol( A1 + _f0(B1,C1,D1) + X[_r1[j]] + _k1[j], _s1[j] ) + E1;
        A1 = E1; E1 = D1; D1 = _rol(C1,10); C1 = B1; B1 = T;
        T = _rol( A2 + _f4(B2,C2,D2) + X[_r2[j]] + _k2[j], _s2[j] ) + E2;
        A2 = E2; E2 = D2; D2 = _rol(C2,10); C2 = B2; B2 = T; }
    for ( ; j < 32; ++j ) {
        T = _rol( A1 + _f1(B1,C1,D1) + X[_r1[j]] + _k1[j], _s1[j] ) + E1;
        A1 = E1; E1 = D1; D1 = _rol(C1,10); C1 = B1; B1 = T;
        T = _rol( A2 + _f3(B2,C2,D2) + X[_r2[j]] + _k2[j], _s2[j] ) + E2;
        A2 = E2; E2 = D2; D2 = _rol(C2,10); C2 = B2; B2 = T; }
    for ( ; j < 48; ++j ) {
        T = _rol( A1 + _f2(B1,C1,D1) + X[_r1[j]] + _k1[j], _s1[j] ) + E1;
        A1 = E1; E1 = D1; D1 = _rol(C1,10); C1 = B1; B1 = T;
        T = _rol( A2 + _f2(B2,C2,D2) + X[_r2[j]] + _k2[j], _s2[j] ) + E2;
        A2 = E2; E2 = D2; D2 = _rol(C2,10); C2 = B2; B2 = T; }
    for ( ; j < 64; ++j ) {
        T = _rol( A1 + _f3(B1,C1,D1) + X[_r1[j]] + _k1[j], _s1[j] ) + E1;
        A1 = E1; E1 = D1; D1 = _rol(C1,10); C1 = B1; B1 = T;
        T = _rol( A2 + _f1(B2,C2,D2) + X[_r2[j]] + _k2[j], _s2[j] ) + E2;
        A2 = E2; E2 = D2; D2 = _rol(C2,10); C2 = B2; B2 = T; }
    for ( ; j < 80; ++j ) {
        T = _rol( A1 + _f4(B1,C1,D1) + X[_r1[j]] + _k1[j], _s1[j] ) + E1;
        A1 = E1; E1 = D1; D1 = _rol(C1,10); C1 = B1; B1 = T;
        T = _rol( A2 + _f0(B2,C2,D2) + X[_r2[j]] + _k2[j], _s2[j] ) + E2;
        A2 = E2; E2 = D2; D2 = _rol(C2,10); C2 = B2; B2 = T; }

    T = this._h[1] + C1 + D2;
    this._h[1] = this._h[2] + D1 + E2;
    this._h[2] = this._h[3] + E1 + A2;
    this._h[3] = this._h[4] + A1 + B2;
    this._h[4] = this._h[0] + B1 + C2;
    this._h[0] = T;
}

})();

sjcl.bn.ZERO = new sjcl.bn(0);

/** [ this / that , this % that ] */
sjcl.bn.prototype.divRem = function (that) {
  if (typeof(that) !== "object") { that = new this._class(that); }
  var thisa = this.abs(), thata = that.abs(), quot = new this._class(0),
      ci = 0;
  if (!thisa.greaterEquals(thata)) {
    return [new sjcl.bn(0), this.copy()];
  } else if (thisa.equals(thata)) {
    return [new sjcl.bn(1), new sjcl.bn(0)];
  }

  for (; thisa.greaterEquals(thata); ci++) {
    thata.doubleM();
  }
  for (; ci > 0; ci--) {
    quot.doubleM();
    thata.halveM();
    if (thisa.greaterEquals(thata)) {
      quot.addM(1);
      thisa.subM(that).normalize();
    }
  }
  return [quot, thisa];
};

/** this /= that (rounded to nearest int) */
sjcl.bn.prototype.divRound = function (that) {
  var dr = this.divRem(that), quot = dr[0], rem = dr[1];

  if (rem.doubleM().greaterEquals(that)) {
    quot.addM(1);
  }

  return quot;
};

/** this /= that (rounded down) */
sjcl.bn.prototype.div = function (that) {
  var dr = this.divRem(that);
  return dr[0];
};

sjcl.bn.prototype.sign = function () {
  return this.greaterEquals(sjcl.bn.ZERO) ? 1 : -1;
};

/** -this */
sjcl.bn.prototype.neg = function () {
  return sjcl.bn.ZERO.sub(this);
};

/** |this| */
sjcl.bn.prototype.abs = function () {
  if (this.sign() === -1) {
    return this.neg();
  } else return this;
};

/** this >> that */
sjcl.bn.prototype.shiftRight = function (that) {
  if ("number" !== typeof that) {
    throw new Error("shiftRight expects a number");
  }

  that = +that;

  if (that < 0) {
    return this.shiftLeft(that);
  }

  var a = new sjcl.bn(this);

  while (that >= this.radix) {
    a.limbs.shift();
    that -= this.radix;
  }

  while (that--) {
    a.halveM();
  }

  return a;
};

/** this >> that */
sjcl.bn.prototype.shiftLeft = function (that) {
  if ("number" !== typeof that) {
    throw new Error("shiftLeft expects a number");
  }

  that = +that;

  if (that < 0) {
    return this.shiftRight(that);
  }

  var a = new sjcl.bn(this);

  while (that >= this.radix) {
    a.limbs.unshift(0);
    that -= this.radix;
  }

  while (that--) {
    a.doubleM();
  }

  return a;
};

/** (int)this */
// NOTE Truncates to 32-bit integer
sjcl.bn.prototype.toNumber = function () {
  return this.limbs[0] | 0;
};

/** find n-th bit, 0 = LSB */
sjcl.bn.prototype.testBit = function (bitIndex) {
  var limbIndex = Math.floor(bitIndex / this.radix);
  var bitIndexInLimb = bitIndex % this.radix;

  if (limbIndex >= this.limbs.length) return 0;

  return (this.limbs[limbIndex] >>> bitIndexInLimb) & 1;
};

/** set n-th bit, 0 = LSB */
sjcl.bn.prototype.setBitM = function (bitIndex) {
  var limbIndex = Math.floor(bitIndex / this.radix);
  var bitIndexInLimb = bitIndex % this.radix;

  while (limbIndex >= this.limbs.length) this.limbs.push(0);

  this.limbs[limbIndex] |= 1 << bitIndexInLimb;

  this.cnormalize();

  return this;
};

sjcl.bn.prototype.modInt = function (n) {
  return this.toNumber() % n;
};

sjcl.bn.prototype.invDigit = function ()
{
  var radixMod = 1 + this.radixMask;

  if (this.limbs.length < 1) return 0;
  var x = this.limbs[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 < radixMod <= 32 and assumes ability to handle 48-bit ints
  y = (y*(2-x*y%radixMod))%radixMod;		// y == 1/x mod 2^dbits
  // we really want the negative inverse, and -DV < y < DV
  return (y>0)?radixMod-y:-y;
};

// 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;
}

// JSBN-style add and multiply for SJCL w/ 24 bit radix
sjcl.bn.prototype.am = function (i,x,w,j,c,n) {
  var xl = x&0xfff, xh = x>>12;
  while (--n >= 0) {
    var l = this.limbs[i]&0xfff;
    var h = this.limbs[i++]>>12;
    var m = xh*l+h*xl;
    l = xl*l+((m&0xfff)<<12)+w.limbs[j]+c;
    c = (l>>24)+(m>>12)+xh*h;
    w.limbs[j++] = l&0xffffff;
  }
  return c;
}

var Montgomery = function (m)
{
  this.m = m;
  this.mt = m.limbs.length;
  this.mt2 = this.mt * 2;
  this.mp = m.invDigit();
  this.mpl = this.mp&0x7fff;
  this.mph = this.mp>>15;
  this.um = (1<<(m.radix-15))-1;
};

Montgomery.prototype.reduce = function (x)
{
  var radixMod = x.radixMask + 1;
  while (x.limbs.length <= this.mt2)	// pad x so am has enough room later
    x.limbs[x.limbs.length] = 0;
  for (var i = 0; i < this.mt; ++i) {
    // faster way of calculating u0 = x[i]*mp mod 2^radix
    var j = x.limbs[i]&0x7fff;
    var u0 = (j*this.mpl+(((j*this.mph+(x.limbs[i]>>15)*this.mpl)&this.um)<<15))&x.radixMask;
    // use am to combine the multiply-shift-add into one call
    j = i+this.mt;
    x.limbs[j] += this.m.am(0,u0,x,i,0,this.mt);
    // propagate carry
    while (x.limbs[j] >= radixMod) { x.limbs[j] -= radixMod; x.limbs[++j]++; }
  }
  x.trim();
  x = x.shiftRight(this.mt * this.m.radix);
  if (x.greaterEquals(this.m)) x = x.sub(this.m);
  return x.trim().normalize().reduce();
};

Montgomery.prototype.square = function (x)
{
  return this.reduce(x.square());
};

Montgomery.prototype.multiply = function (x, y)
{
  return this.reduce(x.mul(y));
};

Montgomery.prototype.convert = function (x)
{
  return x.abs().shiftLeft(this.mt * this.m.radix).mod(this.m);
};

Montgomery.prototype.revert = function (x)
{
  return this.reduce(x.copy());
};

sjcl.bn.prototype.powermodMontgomery = function (e, m)
{
  var i = e.bitLength(), k, r = new this._class(1);

  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 || !m.testBit(0)) {
    // For small exponents and even moduli, use a simple square-and-multiply
    // algorithm.
    return this.powermod(e, m);
  }

  var z = new Montgomery(m);

  e.trim().normalize();

  // precomputation
  var g = new Array(), n = 3, k1 = k-1, km = (1<<k)-1;
  g[1] = z.convert(this);
  if (k > 1) {
    var g2 = z.square(g[1]);

    while (n <= km) {
      g[n] = z.multiply(g2, g[n-2]);
      n += 2;
    }
  }

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

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

    while (j >= 0 && (e.limbs[j]&(1<<i)) == 0) {
      r2 = z.square(r); t = r; r = r2; r2 = t;
      if (--i < 0) { i = this.radix-1; --j; }
    }
  }
  return z.revert(r);
}

sjcl.ecc.ecdsa.secretKey.prototype.sign = function(hash, paranoia, k_for_testing) {
  var R = this._curve.r,
      l = R.bitLength();

  // k_for_testing should ONLY BE SPECIFIED FOR TESTING
  // specifying it will make the signature INSECURE
  var k;
  if (typeof k_for_testing === 'object' && k_for_testing.length > 0 && typeof k_for_testing[0] === 'number') {
    k = k_for_testing;
  } else if (typeof k_for_testing === 'string' && /^[0-9a-fA-F]+$/.test(k_for_testing)) {
    k = sjcl.bn.fromBits(sjcl.codec.hex.toBits(k_for_testing));        
  } else {
    // This is the only option that should be used in production
    k = sjcl.bn.random(R.sub(1), paranoia).add(1);
  }

  var r = this._curve.G.mult(k).x.mod(R);
  var s = sjcl.bn.fromBits(hash).add(r.mul(this._exponent)).mul(k.inverseMod(R)).mod(R);

  return sjcl.bitArray.concat(r.toBits(l), s.toBits(l));
};

sjcl.ecc.ecdsa.publicKey.prototype.verify = function(hash, rs) {
  var w = sjcl.bitArray,
      R = this._curve.r,
      l = R.bitLength(),
      r = sjcl.bn.fromBits(w.bitSlice(rs,0,l)),
      s = sjcl.bn.fromBits(w.bitSlice(rs,l,2*l)),
      sInv = s.inverseMod(R),
      hG = sjcl.bn.fromBits(hash).mul(sInv).mod(R),
      hA = r.mul(sInv).mod(R),
      r2 = this._curve.G.mult2(hG, hA, this._point).x;

  if (r.equals(0) || s.equals(0) || r.greaterEquals(R) || s.greaterEquals(R) || !r2.equals(r)) {
    throw (new sjcl.exception.corrupt("signature didn't check out"));
  }
  return true;
};

sjcl.ecc.ecdsa.secretKey.prototype.canonicalizeSignature = function(rs) {
  var w = sjcl.bitArray,
      R = this._curve.r,
      l = R.bitLength();

  var r = sjcl.bn.fromBits(w.bitSlice(rs,0,l)),
      s = sjcl.bn.fromBits(w.bitSlice(rs,l,2*l));

  // For a canonical signature we want the lower of two possible values for s
  // 0 < s <= n/2
  if (!R.copy().halveM().greaterEquals(s)) {
    s = R.sub(s);
  }

  return w.concat(r.toBits(l), s.toBits(l));
};


sjcl.ecc.ecdsa.secretKey.prototype.signDER = function(hash, paranoia) {
  return this.encodeDER(this.sign(hash, paranoia));
};

sjcl.ecc.ecdsa.secretKey.prototype.encodeDER = function(rs) {
  var w = sjcl.bitArray,
      R = this._curve.r,
      l = R.bitLength();

  var rb = sjcl.codec.bytes.fromBits(w.bitSlice(rs,0,l)),
      sb = sjcl.codec.bytes.fromBits(w.bitSlice(rs,l,2*l));

  // Drop empty leading bytes
  while (!rb[0] && rb.length) rb.shift();
  while (!sb[0] && sb.length) sb.shift();

  // If high bit is set, prepend an extra zero byte (DER signed integer)
  if (rb[0] & 0x80) rb.unshift(0);
  if (sb[0] & 0x80) sb.unshift(0);

  var buffer = [].concat(
    0x30,
    4 + rb.length + sb.length,
    0x02,
    rb.length,
    rb,
    0x02,
    sb.length,
    sb
  );

  return sjcl.codec.bytes.toBits(buffer);
};


/**
 *  This module uses the public key recovery method
 *  described in SEC 1: Elliptic Curve Cryptography,
 *  section 4.1.6, "Public Key Recovery Operation".
 *  http://www.secg.org/download/aid-780/sec1-v2.pdf
 *
 *  Implementation based on:
 *  https://github.com/bitcoinjs/bitcoinjs-lib/blob/89cf731ac7309b4f98994e3b4b67b7226020181f/src/ecdsa.js
 */

// Defined here so that this value only needs to be calculated once
var FIELD_MODULUS_PLUS_ONE_DIVIDED_BY_FOUR;

/**
 *  Sign the given hash such that the public key, prepending an extra byte 
 *  so that the public key will be recoverable from the signature
 *
 *  @param {bitArray} hash
 *  @param {Number} paranoia
 *  @returns {bitArray} Signature formatted as bitArray
 */
sjcl.ecc.ecdsa.secretKey.prototype.signWithRecoverablePublicKey = function(hash, paranoia, k_for_testing) {

  var self = this;

  // Convert hash to bits and determine encoding for output
  var hash_bits;
  if (typeof hash === 'object' && hash.length > 0 && typeof hash[0] === 'number') {
    hash_bits = hash;
  } else {
    throw new sjcl.exception.invalid('hash. Must be a bitArray');
  }

  // Sign hash with standard, canonicalized method
  var standard_signature = self.sign(hash_bits, paranoia, k_for_testing);
  var canonical_signature = self.canonicalizeSignature(standard_signature);

  // Extract r and s signature components from canonical signature
  var r_and_s = getRandSFromSignature(self._curve, canonical_signature);

  // Rederive public key
  var public_key = self._curve.G.mult(sjcl.bn.fromBits(self.get()));

  // Determine recovery factor based on which possible value
  // returns the correct public key
  var recovery_factor = calculateRecoveryFactor(self._curve, r_and_s.r, r_and_s.s, hash_bits, public_key);

  // Prepend recovery_factor to signature and encode in DER
  // The value_to_prepend should be 4 bytes total
  var value_to_prepend = recovery_factor + 27;

  var final_signature_bits = sjcl.bitArray.concat([value_to_prepend], canonical_signature);

  // Return value in bits
  return final_signature_bits;

};


/**
 *  Recover the public key from a signature created with the
 *  signWithRecoverablePublicKey method in this module
 *
 *  @static
 *
 *  @param {bitArray} hash
 *  @param {bitArray} signature
 *  @param {sjcl.ecc.curve} [sjcl.ecc.curves['c256']] curve
 *  @returns {sjcl.ecc.ecdsa.publicKey} Public key
 */
sjcl.ecc.ecdsa.publicKey.recoverFromSignature = function(hash, signature, curve) {

  if (!signature || signature instanceof sjcl.ecc.curve) {
    throw new sjcl.exception.invalid('must supply hash and signature to recover public key');
  }

  if (!curve) {
    curve = sjcl.ecc.curves['c256'];
  }

  // Convert hash to bits and determine encoding for output
  var hash_bits;
  if (typeof hash === 'object' && hash.length > 0 && typeof hash[0] === 'number') {
    hash_bits = hash;
  } else {
    throw new sjcl.exception.invalid('hash. Must be a bitArray');
  }

  var signature_bits;
  if (typeof signature === 'object' && signature.length > 0 && typeof signature[0] === 'number') {
    signature_bits = signature;
  } else {
    throw new sjcl.exception.invalid('signature. Must be a bitArray');
  }

  // Extract recovery_factor from first 4 bytes
  var recovery_factor = signature_bits[0] - 27;

  if (recovery_factor < 0 || recovery_factor > 3) {
    throw new sjcl.exception.invalid('signature. Signature must be generated with algorithm ' +
      'that prepends the recovery factor in order to recover the public key');
  }

  // Separate r and s values
  var r_and_s = getRandSFromSignature(curve, signature_bits.slice(1));
  var signature_r = r_and_s.r;
  var signature_s = r_and_s.s;

  // Recover public key using recovery_factor
  var recovered_public_key_point = recoverPublicKeyPointFromSignature(curve, signature_r, signature_s, hash_bits, recovery_factor);
  var recovered_public_key = new sjcl.ecc.ecdsa.publicKey(curve, recovered_public_key_point);

  return recovered_public_key;

};


/**
 *  Retrieve the r and s components of a signature  
 *
 *  @param {sjcl.ecc.curve} curve
 *  @param {bitArray} signature
 *  @returns {Object} Object with 'r' and 's' fields each as an sjcl.bn
 */
function getRandSFromSignature(curve, signature) {

  var r_length = curve.r.bitLength();

  return {
    r: sjcl.bn.fromBits(sjcl.bitArray.bitSlice(signature, 0, r_length)),
    s: sjcl.bn.fromBits(sjcl.bitArray.bitSlice(signature, r_length, sjcl.bitArray.bitLength(signature)))
  };
};


/**
 *  Determine the recovery factor by trying all four
 *  possibilities and figuring out which results in the
 *  correct public key
 *
 *  @param {sjcl.ecc.curve} curve
 *  @param {sjcl.bn} r
 *  @param {sjcl.bn} s
 *  @param {bitArray} hash_bits
 *  @param {sjcl.ecc.point} original_public_key_point
 *  @returns {Number, 0-3} Recovery factor
 */
function calculateRecoveryFactor(curve, r, s, hash_bits, original_public_key_point) {

  var original_public_key_point_bits = original_public_key_point.toBits();

  // TODO: verify that it is possible for the recovery_factor to be 2 or 3,
  // we may only need 1 bit because the canonical signature might remove the
  // possibility of us needing to "use the second candidate key"
  for (var possible_factor = 0; possible_factor < 4; possible_factor++) {

    var resulting_public_key_point;
    try {
      resulting_public_key_point = recoverPublicKeyPointFromSignature(curve, r, s, hash_bits, possible_factor);
    } catch (err) {
      // console.log(err, err.stack);
      continue;
    }

    if (sjcl.bitArray.equal(resulting_public_key_point.toBits(), original_public_key_point_bits)) {
      return possible_factor;
    }

  }

  throw new sjcl.exception.bug('unable to calculate recovery factor from signature');

};


/**
 *  Recover the public key from the signature.
 *
 *  @param {sjcl.ecc.curve} curve
 *  @param {sjcl.bn} r
 *  @param {sjcl.bn} s
 *  @param {bitArray} hash_bits
 *  @param {Number, 0-3} recovery_factor
 *  @returns {sjcl.point} Public key corresponding to signature
 */
function recoverPublicKeyPointFromSignature(curve, signature_r, signature_s, hash_bits, recovery_factor) {

  var field_order = curve.r;
  var field_modulus = curve.field.modulus;

  // Reduce the recovery_factor to the two bits used
  recovery_factor = recovery_factor & 3;

  // The less significant bit specifies whether the y coordinate
  // of the compressed point is even or not.
  var compressed_point_y_coord_is_even = recovery_factor & 1;

  // The more significant bit specifies whether we should use the
  // first or second candidate key.
  var use_second_candidate_key = recovery_factor >> 1;

  // Calculate (field_order + 1) / 4
  if (!FIELD_MODULUS_PLUS_ONE_DIVIDED_BY_FOUR) {
    FIELD_MODULUS_PLUS_ONE_DIVIDED_BY_FOUR = field_modulus.add(1).div(4);
  }

  // In the paper they write "1. For j from 0 to h do the following..."
  // That is not necessary here because we are given the recovery_factor
  // step 1.1 Let x = r + jn
  // Here "j" is either 0 or 1
  var x;
  if (use_second_candidate_key) {
    x = signature_r.add(field_order);
  } else {
    x = signature_r;
  }

  // step 1.2 and 1.3  convert x to an elliptic curve point
  // Following formula in section 2.3.4 Octet-String-to-Elliptic-Curve-Point Conversion
  var alpha = x.mul(x).mul(x).add(curve.a.mul(x)).add(curve.b).mod(field_modulus);
  var beta = alpha.powermodMontgomery(FIELD_MODULUS_PLUS_ONE_DIVIDED_BY_FOUR, field_modulus);

  // If beta is even but y isn't or
  // if beta is odd and y is even
  // then subtract beta from the field_modulus
  var y;
  var beta_is_even = beta.mod(2).equals(0);
  if (beta_is_even && !compressed_point_y_coord_is_even ||
    !beta_is_even && compressed_point_y_coord_is_even) {
    y = beta;
  } else {
    y = field_modulus.sub(beta);
  }

  // generated_point_R is the point generated from x and y
  var generated_point_R = new sjcl.ecc.point(curve, x, y);

  // step 1.4  check that R is valid and R x field_order !== infinity
  // TODO: add check for R x field_order === infinity
  if (!generated_point_R.isValidPoint()) {
    throw new sjcl.exception.corrupt('point R. Not a valid point on the curve. Cannot recover public key');
  }

  // step 1.5  Compute e from M
  var message_e = sjcl.bn.fromBits(hash_bits);
  var message_e_neg = new sjcl.bn(0).sub(message_e).mod(field_order);

  // step 1.6  Compute Q = r^-1 (sR - eG)
  // console.log('r: ', signature_r);
  var signature_r_inv = signature_r.inverseMod(field_order);
  var public_key_point = generated_point_R.mult2(signature_s, message_e_neg, curve.G).mult(signature_r_inv);

  // Validate public key point
  if (!public_key_point.isValidPoint()) {
    throw new sjcl.exception.corrupt('public_key_point. Not a valid point on the curve. Cannot recover public key');
  }

  // Verify that this public key matches the signature
  if (!verify_raw(curve, message_e, signature_r, signature_s, public_key_point)) {
    throw new sjcl.exception.corrupt('cannot recover public key');
  }

  return public_key_point;

};


/**
 *  Verify a signature given the raw components
 *  using method defined in section 4.1.5:
 *  "Alternative Verifying Operation"
 *
 *  @param {sjcl.ecc.curve} curve
 *  @param {sjcl.bn} e
 *  @param {sjcl.bn} r
 *  @param {sjcl.bn} s
 *  @param {sjcl.ecc.point} public_key_point
 *  @returns {Boolean} 
 */
function verify_raw(curve, e, r, s, public_key_point) {

  var field_order = curve.r;

  // Return false if r is out of bounds
  if ((new sjcl.bn(1)).greaterEquals(r) || r.greaterEquals(new sjcl.bn(field_order))) {
    return false;
  }

  // Return false if s is out of bounds
  if ((new sjcl.bn(1)).greaterEquals(s) || s.greaterEquals(new sjcl.bn(field_order))) {
    return false;
  }

  // Check that r = (u1 + u2)G
  // u1 = e x s^-1 (mod field_order)
  // u2 = r x s^-1 (mod field_order)
  var s_mod_inverse_field_order = s.inverseMod(field_order);
  var u1 = e.mul(s_mod_inverse_field_order).mod(field_order);
  var u2 = r.mul(s_mod_inverse_field_order).mod(field_order);

  var point_computed = curve.G.mult2(u1, u2, public_key_point);

  return r.equals(point_computed.x.mod(field_order));

};


sjcl.bn.prototype.jacobi = function (that) {
  var a = this;
  that = new sjcl.bn(that);

  if (that.sign() === -1) return;

  // 1. If a = 0 then return(0).
  if (a.equals(0)) { return 0; }

  // 2. If a = 1 then return(1).
  if (a.equals(1)) { return 1; }

  var s = 0;

  // 3. Write a = 2^e * a1, where a1 is odd.
  var e = 0;
  while (!a.testBit(e)) e++;
  var a1 = a.shiftRight(e);

  // 4. If e is even then set s ← 1.
  if ((e & 1) === 0) {
    s = 1;
  } else {
    var residue = that.modInt(8);

    if (residue === 1 || residue === 7) {
      // Otherwise set s ← 1 if n ≡ 1 or 7 (mod 8)
      s = 1;
    } else if (residue === 3 || residue === 5) {
      // Or set s ← −1 if n ≡ 3 or 5 (mod 8).
      s = -1;
    }
  }

  // 5. If n ≡ 3 (mod 4) and a1 ≡ 3 (mod 4) then set s ← −s.
  if (that.modInt(4) === 3 && a1.modInt(4) === 3) {
    s = -s;
  }

  if (a1.equals(1)) {
    return s;
  } else {
    return s * that.mod(a1).jacobi(a1);
  }
};