node-forge/lib/cipherModes.js

/**
 * Supported cipher modes.
 *
 * @author Dave Longley
 *
 * Copyright (c) 2010-2014 Digital Bazaar, Inc.
 */
var forge = require('./forge');
require('./util');

forge.cipher = forge.cipher || {};

// supported cipher modes
var modes = module.exports = forge.cipher.modes = forge.cipher.modes || {};

/** Electronic codebook (ECB) (Don't use this; it's not secure) **/

modes.ecb = function(options) {
  options = options || {};
  this.name = 'ECB';
  this.cipher = options.cipher;
  this.blockSize = options.blockSize || 16;
  this._ints = this.blockSize / 4;
  this._inBlock = new Array(this._ints);
  this._outBlock = new Array(this._ints);
};

modes.ecb.prototype.start = function(options) {};

modes.ecb.prototype.encrypt = function(input, output, finish) {
  // not enough input to encrypt
  if(input.length() < this.blockSize && !(finish && input.length() > 0)) {
    return true;
  }

  // get next block
  for(var i = 0; i < this._ints; ++i) {
    this._inBlock[i] = input.getInt32();
  }

  // encrypt block
  this.cipher.encrypt(this._inBlock, this._outBlock);

  // write output
  for(var i = 0; i < this._ints; ++i) {
    output.putInt32(this._outBlock[i]);
  }
};

modes.ecb.prototype.decrypt = function(input, output, finish) {
  // not enough input to decrypt
  if(input.length() < this.blockSize && !(finish && input.length() > 0)) {
    return true;
  }

  // get next block
  for(var i = 0; i < this._ints; ++i) {
    this._inBlock[i] = input.getInt32();
  }

  // decrypt block
  this.cipher.decrypt(this._inBlock, this._outBlock);

  // write output
  for(var i = 0; i < this._ints; ++i) {
    output.putInt32(this._outBlock[i]);
  }
};

modes.ecb.prototype.pad = function(input, options) {
  // add PKCS#7 padding to block (each pad byte is the
  // value of the number of pad bytes)
  var padding = (input.length() === this.blockSize ?
    this.blockSize : (this.blockSize - input.length()));
  input.fillWithByte(padding, padding);
  return true;
};

modes.ecb.prototype.unpad = function(output, options) {
  // check for error: input data not a multiple of blockSize
  if(options.overflow > 0) {
    return false;
  }

  // ensure padding byte count is valid
  var len = output.length();
  var count = output.at(len - 1);
  if(count > (this.blockSize << 2)) {
    return false;
  }

  // trim off padding bytes
  output.truncate(count);
  return true;
};

/** Cipher-block Chaining (CBC) **/

modes.cbc = function(options) {
  options = options || {};
  this.name = 'CBC';
  this.cipher = options.cipher;
  this.blockSize = options.blockSize || 16;
  this._ints = this.blockSize / 4;
  this._inBlock = new Array(this._ints);
  this._outBlock = new Array(this._ints);
};

modes.cbc.prototype.start = function(options) {
  // Note: legacy support for using IV residue (has security flaws)
  // if IV is null, reuse block from previous processing
  if(options.iv === null) {
    // must have a previous block
    if(!this._prev) {
      throw new Error('Invalid IV parameter.');
    }
    this._iv = this._prev.slice(0);
  } else if(!('iv' in options)) {
    throw new Error('Invalid IV parameter.');
  } else {
    // save IV as "previous" block
    this._iv = transformIV(options.iv, this.blockSize);
    this._prev = this._iv.slice(0);
  }
};

modes.cbc.prototype.encrypt = function(input, output, finish) {
  // not enough input to encrypt
  if(input.length() < this.blockSize && !(finish && input.length() > 0)) {
    return true;
  }

  // get next block
  // CBC XOR's IV (or previous block) with plaintext
  for(var i = 0; i < this._ints; ++i) {
    this._inBlock[i] = this._prev[i] ^ input.getInt32();
  }

  // encrypt block
  this.cipher.encrypt(this._inBlock, this._outBlock);

  // write output, save previous block
  for(var i = 0; i < this._ints; ++i) {
    output.putInt32(this._outBlock[i]);
  }
  this._prev = this._outBlock;
};

modes.cbc.prototype.decrypt = function(input, output, finish) {
  // not enough input to decrypt
  if(input.length() < this.blockSize && !(finish && input.length() > 0)) {
    return true;
  }

  // get next block
  for(var i = 0; i < this._ints; ++i) {
    this._inBlock[i] = input.getInt32();
  }

  // decrypt block
  this.cipher.decrypt(this._inBlock, this._outBlock);

  // write output, save previous ciphered block
  // CBC XOR's IV (or previous block) with ciphertext
  for(var i = 0; i < this._ints; ++i) {
    output.putInt32(this._prev[i] ^ this._outBlock[i]);
  }
  this._prev = this._inBlock.slice(0);
};

modes.cbc.prototype.pad = function(input, options) {
  // add PKCS#7 padding to block (each pad byte is the
  // value of the number of pad bytes)
  var padding = (input.length() === this.blockSize ?
    this.blockSize : (this.blockSize - input.length()));
  input.fillWithByte(padding, padding);
  return true;
};

modes.cbc.prototype.unpad = function(output, options) {
  // check for error: input data not a multiple of blockSize
  if(options.overflow > 0) {
    return false;
  }

  // ensure padding byte count is valid
  var len = output.length();
  var count = output.at(len - 1);
  if(count > (this.blockSize << 2)) {
    return false;
  }

  // trim off padding bytes
  output.truncate(count);
  return true;
};

/** Cipher feedback (CFB) **/

modes.cfb = function(options) {
  options = options || {};
  this.name = 'CFB';
  this.cipher = options.cipher;
  this.blockSize = options.blockSize || 16;
  this._ints = this.blockSize / 4;
  this._inBlock = null;
  this._outBlock = new Array(this._ints);
  this._partialBlock = new Array(this._ints);
  this._partialOutput = forge.util.createBuffer();
  this._partialBytes = 0;
};

modes.cfb.prototype.start = function(options) {
  if(!('iv' in options)) {
    throw new Error('Invalid IV parameter.');
  }
  // use IV as first input
  this._iv = transformIV(options.iv, this.blockSize);
  this._inBlock = this._iv.slice(0);
  this._partialBytes = 0;
};

modes.cfb.prototype.encrypt = function(input, output, finish) {
  // not enough input to encrypt
  var inputLength = input.length();
  if(inputLength === 0) {
    return true;
  }

  // encrypt block
  this.cipher.encrypt(this._inBlock, this._outBlock);

  // handle full block
  if(this._partialBytes === 0 && inputLength >= this.blockSize) {
    // XOR input with output, write input as output
    for(var i = 0; i < this._ints; ++i) {
      this._inBlock[i] = input.getInt32() ^ this._outBlock[i];
      output.putInt32(this._inBlock[i]);
    }
    return;
  }

  // handle partial block
  var partialBytes = (this.blockSize - inputLength) % this.blockSize;
  if(partialBytes > 0) {
    partialBytes = this.blockSize - partialBytes;
  }

  // XOR input with output, write input as partial output
  this._partialOutput.clear();
  for(var i = 0; i < this._ints; ++i) {
    this._partialBlock[i] = input.getInt32() ^ this._outBlock[i];
    this._partialOutput.putInt32(this._partialBlock[i]);
  }

  if(partialBytes > 0) {
    // block still incomplete, restore input buffer
    input.read -= this.blockSize;
  } else {
    // block complete, update input block
    for(var i = 0; i < this._ints; ++i) {
      this._inBlock[i] = this._partialBlock[i];
    }
  }

  // skip any previous partial bytes
  if(this._partialBytes > 0) {
    this._partialOutput.getBytes(this._partialBytes);
  }

  if(partialBytes > 0 && !finish) {
    output.putBytes(this._partialOutput.getBytes(
      partialBytes - this._partialBytes));
    this._partialBytes = partialBytes;
    return true;
  }

  output.putBytes(this._partialOutput.getBytes(
    inputLength - this._partialBytes));
  this._partialBytes = 0;
};

modes.cfb.prototype.decrypt = function(input, output, finish) {
  // not enough input to decrypt
  var inputLength = input.length();
  if(inputLength === 0) {
    return true;
  }

  // encrypt block (CFB always uses encryption mode)
  this.cipher.encrypt(this._inBlock, this._outBlock);

  // handle full block
  if(this._partialBytes === 0 && inputLength >= this.blockSize) {
    // XOR input with output, write input as output
    for(var i = 0; i < this._ints; ++i) {
      this._inBlock[i] = input.getInt32();
      output.putInt32(this._inBlock[i] ^ this._outBlock[i]);
    }
    return;
  }

  // handle partial block
  var partialBytes = (this.blockSize - inputLength) % this.blockSize;
  if(partialBytes > 0) {
    partialBytes = this.blockSize - partialBytes;
  }

  // XOR input with output, write input as partial output
  this._partialOutput.clear();
  for(var i = 0; i < this._ints; ++i) {
    this._partialBlock[i] = input.getInt32();
    this._partialOutput.putInt32(this._partialBlock[i] ^ this._outBlock[i]);
  }

  if(partialBytes > 0) {
    // block still incomplete, restore input buffer
    input.read -= this.blockSize;
  } else {
    // block complete, update input block
    for(var i = 0; i < this._ints; ++i) {
      this._inBlock[i] = this._partialBlock[i];
    }
  }

  // skip any previous partial bytes
  if(this._partialBytes > 0) {
    this._partialOutput.getBytes(this._partialBytes);
  }

  if(partialBytes > 0 && !finish) {
    output.putBytes(this._partialOutput.getBytes(
      partialBytes - this._partialBytes));
    this._partialBytes = partialBytes;
    return true;
  }

  output.putBytes(this._partialOutput.getBytes(
    inputLength - this._partialBytes));
  this._partialBytes = 0;
};

/** Output feedback (OFB) **/

modes.ofb = function(options) {
  options = options || {};
  this.name = 'OFB';
  this.cipher = options.cipher;
  this.blockSize = options.blockSize || 16;
  this._ints = this.blockSize / 4;
  this._inBlock = null;
  this._outBlock = new Array(this._ints);
  this._partialOutput = forge.util.createBuffer();
  this._partialBytes = 0;
};

modes.ofb.prototype.start = function(options) {
  if(!('iv' in options)) {
    throw new Error('Invalid IV parameter.');
  }
  // use IV as first input
  this._iv = transformIV(options.iv, this.blockSize);
  this._inBlock = this._iv.slice(0);
  this._partialBytes = 0;
};

modes.ofb.prototype.encrypt = function(input, output, finish) {
  // not enough input to encrypt
  var inputLength = input.length();
  if(input.length() === 0) {
    return true;
  }

  // encrypt block (OFB always uses encryption mode)
  this.cipher.encrypt(this._inBlock, this._outBlock);

  // handle full block
  if(this._partialBytes === 0 && inputLength >= this.blockSize) {
    // XOR input with output and update next input
    for(var i = 0; i < this._ints; ++i) {
      output.putInt32(input.getInt32() ^ this._outBlock[i]);
      this._inBlock[i] = this._outBlock[i];
    }
    return;
  }

  // handle partial block
  var partialBytes = (this.blockSize - inputLength) % this.blockSize;
  if(partialBytes > 0) {
    partialBytes = this.blockSize - partialBytes;
  }

  // XOR input with output
  this._partialOutput.clear();
  for(var i = 0; i < this._ints; ++i) {
    this._partialOutput.putInt32(input.getInt32() ^ this._outBlock[i]);
  }

  if(partialBytes > 0) {
    // block still incomplete, restore input buffer
    input.read -= this.blockSize;
  } else {
    // block complete, update input block
    for(var i = 0; i < this._ints; ++i) {
      this._inBlock[i] = this._outBlock[i];
    }
  }

  // skip any previous partial bytes
  if(this._partialBytes > 0) {
    this._partialOutput.getBytes(this._partialBytes);
  }

  if(partialBytes > 0 && !finish) {
    output.putBytes(this._partialOutput.getBytes(
      partialBytes - this._partialBytes));
    this._partialBytes = partialBytes;
    return true;
  }

  output.putBytes(this._partialOutput.getBytes(
    inputLength - this._partialBytes));
  this._partialBytes = 0;
};

modes.ofb.prototype.decrypt = modes.ofb.prototype.encrypt;

/** Counter (CTR) **/

modes.ctr = function(options) {
  options = options || {};
  this.name = 'CTR';
  this.cipher = options.cipher;
  this.blockSize = options.blockSize || 16;
  this._ints = this.blockSize / 4;
  this._inBlock = null;
  this._outBlock = new Array(this._ints);
  this._partialOutput = forge.util.createBuffer();
  this._partialBytes = 0;
};

modes.ctr.prototype.start = function(options) {
  if(!('iv' in options)) {
    throw new Error('Invalid IV parameter.');
  }
  // use IV as first input
  this._iv = transformIV(options.iv, this.blockSize);
  this._inBlock = this._iv.slice(0);
  this._partialBytes = 0;
};

modes.ctr.prototype.encrypt = function(input, output, finish) {
  // not enough input to encrypt
  var inputLength = input.length();
  if(inputLength === 0) {
    return true;
  }

  // encrypt block (CTR always uses encryption mode)
  this.cipher.encrypt(this._inBlock, this._outBlock);

  // handle full block
  if(this._partialBytes === 0 && inputLength >= this.blockSize) {
    // XOR input with output
    for(var i = 0; i < this._ints; ++i) {
      output.putInt32(input.getInt32() ^ this._outBlock[i]);
    }
  } else {
    // handle partial block
    var partialBytes = (this.blockSize - inputLength) % this.blockSize;
    if(partialBytes > 0) {
      partialBytes = this.blockSize - partialBytes;
    }

    // XOR input with output
    this._partialOutput.clear();
    for(var i = 0; i < this._ints; ++i) {
      this._partialOutput.putInt32(input.getInt32() ^ this._outBlock[i]);
    }

    if(partialBytes > 0) {
      // block still incomplete, restore input buffer
      input.read -= this.blockSize;
    }

    // skip any previous partial bytes
    if(this._partialBytes > 0) {
      this._partialOutput.getBytes(this._partialBytes);
    }

    if(partialBytes > 0 && !finish) {
      output.putBytes(this._partialOutput.getBytes(
        partialBytes - this._partialBytes));
      this._partialBytes = partialBytes;
      return true;
    }

    output.putBytes(this._partialOutput.getBytes(
      inputLength - this._partialBytes));
    this._partialBytes = 0;
  }

  // block complete, increment counter (input block)
  inc32(this._inBlock);
};

modes.ctr.prototype.decrypt = modes.ctr.prototype.encrypt;

/** Galois/Counter Mode (GCM) **/

modes.gcm = function(options) {
  options = options || {};
  this.name = 'GCM';
  this.cipher = options.cipher;
  this.blockSize = options.blockSize || 16;
  this._ints = this.blockSize / 4;
  this._inBlock = new Array(this._ints);
  this._outBlock = new Array(this._ints);
  this._partialOutput = forge.util.createBuffer();
  this._partialBytes = 0;

  // R is actually this value concatenated with 120 more zero bits, but
  // we only XOR against R so the other zeros have no effect -- we just
  // apply this value to the first integer in a block
  this._R = 0xE1000000;
};

modes.gcm.prototype.start = function(options) {
  if(!('iv' in options)) {
    throw new Error('Invalid IV parameter.');
  }
  // ensure IV is a byte buffer
  var iv = forge.util.createBuffer(options.iv);

  // no ciphered data processed yet
  this._cipherLength = 0;

  // default additional data is none
  var additionalData;
  if('additionalData' in options) {
    additionalData = forge.util.createBuffer(options.additionalData);
  } else {
    additionalData = forge.util.createBuffer();
  }

  // default tag length is 128 bits
  if('tagLength' in options) {
    this._tagLength = options.tagLength;
  } else {
    this._tagLength = 128;
  }

  // if tag is given, ensure tag matches tag length
  this._tag = null;
  if(options.decrypt) {
    // save tag to check later
    this._tag = forge.util.createBuffer(options.tag).getBytes();
    if(this._tag.length !== (this._tagLength / 8)) {
      throw new Error('Authentication tag does not match tag length.');
    }
  }

  // create tmp storage for hash calculation
  this._hashBlock = new Array(this._ints);

  // no tag generated yet
  this.tag = null;

  // generate hash subkey
  // (apply block cipher to "zero" block)
  this._hashSubkey = new Array(this._ints);
  this.cipher.encrypt([0, 0, 0, 0], this._hashSubkey);

  // generate table M
  // use 4-bit tables (32 component decomposition of a 16 byte value)
  // 8-bit tables take more space and are known to have security
  // vulnerabilities (in native implementations)
  this.componentBits = 4;
  this._m = this.generateHashTable(this._hashSubkey, this.componentBits);

  // Note: support IV length different from 96 bits? (only supporting
  // 96 bits is recommended by NIST SP-800-38D)
  // generate J_0
  var ivLength = iv.length();
  if(ivLength === 12) {
    // 96-bit IV
    this._j0 = [iv.getInt32(), iv.getInt32(), iv.getInt32(), 1];
  } else {
    // IV is NOT 96-bits
    this._j0 = [0, 0, 0, 0];
    while(iv.length() > 0) {
      this._j0 = this.ghash(
        this._hashSubkey, this._j0,
        [iv.getInt32(), iv.getInt32(), iv.getInt32(), iv.getInt32()]);
    }
    this._j0 = this.ghash(
      this._hashSubkey, this._j0, [0, 0].concat(from64To32(ivLength * 8)));
  }

  // generate ICB (initial counter block)
  this._inBlock = this._j0.slice(0);
  inc32(this._inBlock);
  this._partialBytes = 0;

  // consume authentication data
  additionalData = forge.util.createBuffer(additionalData);
  // save additional data length as a BE 64-bit number
  this._aDataLength = from64To32(additionalData.length() * 8);
  // pad additional data to 128 bit (16 byte) block size
  var overflow = additionalData.length() % this.blockSize;
  if(overflow) {
    additionalData.fillWithByte(0, this.blockSize - overflow);
  }
  this._s = [0, 0, 0, 0];
  while(additionalData.length() > 0) {
    this._s = this.ghash(this._hashSubkey, this._s, [
      additionalData.getInt32(),
      additionalData.getInt32(),
      additionalData.getInt32(),
      additionalData.getInt32()
    ]);
  }
};

modes.gcm.prototype.encrypt = function(input, output, finish) {
  // not enough input to encrypt
  var inputLength = input.length();
  if(inputLength === 0) {
    return true;
  }

  // encrypt block
  this.cipher.encrypt(this._inBlock, this._outBlock);

  // handle full block
  if(this._partialBytes === 0 && inputLength >= this.blockSize) {
    // XOR input with output
    for(var i = 0; i < this._ints; ++i) {
      output.putInt32(this._outBlock[i] ^= input.getInt32());
    }
    this._cipherLength += this.blockSize;
  } else {
    // handle partial block
    var partialBytes = (this.blockSize - inputLength) % this.blockSize;
    if(partialBytes > 0) {
      partialBytes = this.blockSize - partialBytes;
    }

    // XOR input with output
    this._partialOutput.clear();
    for(var i = 0; i < this._ints; ++i) {
      this._partialOutput.putInt32(input.getInt32() ^ this._outBlock[i]);
    }

    if(partialBytes <= 0 || finish) {
      // handle overflow prior to hashing
      if(finish) {
        // get block overflow
        var overflow = inputLength % this.blockSize;
        this._cipherLength += overflow;
        // truncate for hash function
        this._partialOutput.truncate(this.blockSize - overflow);
      } else {
        this._cipherLength += this.blockSize;
      }

      // get output block for hashing
      for(var i = 0; i < this._ints; ++i) {
        this._outBlock[i] = this._partialOutput.getInt32();
      }
      this._partialOutput.read -= this.blockSize;
    }

    // skip any previous partial bytes
    if(this._partialBytes > 0) {
      this._partialOutput.getBytes(this._partialBytes);
    }

    if(partialBytes > 0 && !finish) {
      // block still incomplete, restore input buffer, get partial output,
      // and return early
      input.read -= this.blockSize;
      output.putBytes(this._partialOutput.getBytes(
        partialBytes - this._partialBytes));
      this._partialBytes = partialBytes;
      return true;
    }

    output.putBytes(this._partialOutput.getBytes(
      inputLength - this._partialBytes));
    this._partialBytes = 0;
  }

  // update hash block S
  this._s = this.ghash(this._hashSubkey, this._s, this._outBlock);

  // increment counter (input block)
  inc32(this._inBlock);
};

modes.gcm.prototype.decrypt = function(input, output, finish) {
  // not enough input to decrypt
  var inputLength = input.length();
  if(inputLength < this.blockSize && !(finish && inputLength > 0)) {
    return true;
  }

  // encrypt block (GCM always uses encryption mode)
  this.cipher.encrypt(this._inBlock, this._outBlock);

  // increment counter (input block)
  inc32(this._inBlock);

  // update hash block S
  this._hashBlock[0] = input.getInt32();
  this._hashBlock[1] = input.getInt32();
  this._hashBlock[2] = input.getInt32();
  this._hashBlock[3] = input.getInt32();
  this._s = this.ghash(this._hashSubkey, this._s, this._hashBlock);

  // XOR hash input with output
  for(var i = 0; i < this._ints; ++i) {
    output.putInt32(this._outBlock[i] ^ this._hashBlock[i]);
  }

  // increment cipher data length
  if(inputLength < this.blockSize) {
    this._cipherLength += inputLength % this.blockSize;
  } else {
    this._cipherLength += this.blockSize;
  }
};

modes.gcm.prototype.afterFinish = function(output, options) {
  var rval = true;

  // handle overflow
  if(options.decrypt && options.overflow) {
    output.truncate(this.blockSize - options.overflow);
  }

  // handle authentication tag
  this.tag = forge.util.createBuffer();

  // concatenate additional data length with cipher length
  var lengths = this._aDataLength.concat(from64To32(this._cipherLength * 8));

  // include lengths in hash
  this._s = this.ghash(this._hashSubkey, this._s, lengths);

  // do GCTR(J_0, S)
  var tag = [];
  this.cipher.encrypt(this._j0, tag);
  for(var i = 0; i < this._ints; ++i) {
    this.tag.putInt32(this._s[i] ^ tag[i]);
  }

  // trim tag to length
  this.tag.truncate(this.tag.length() % (this._tagLength / 8));

  // check authentication tag
  if(options.decrypt && this.tag.bytes() !== this._tag) {
    rval = false;
  }

  return rval;
};

/**
 * See NIST SP-800-38D 6.3 (Algorithm 1). This function performs Galois
 * field multiplication. The field, GF(2^128), is defined by the polynomial:
 *
 * x^128 + x^7 + x^2 + x + 1
 *
 * Which is represented in little-endian binary form as: 11100001 (0xe1). When
 * the value of a coefficient is 1, a bit is set. The value R, is the
 * concatenation of this value and 120 zero bits, yielding a 128-bit value
 * which matches the block size.
 *
 * This function will multiply two elements (vectors of bytes), X and Y, in
 * the field GF(2^128). The result is initialized to zero. For each bit of
 * X (out of 128), x_i, if x_i is set, then the result is multiplied (XOR'd)
 * by the current value of Y. For each bit, the value of Y will be raised by
 * a power of x (multiplied by the polynomial x). This can be achieved by
 * shifting Y once to the right. If the current value of Y, prior to being
 * multiplied by x, has 0 as its LSB, then it is a 127th degree polynomial.
 * Otherwise, we must divide by R after shifting to find the remainder.
 *
 * @param x the first block to multiply by the second.
 * @param y the second block to multiply by the first.
 *
 * @return the block result of the multiplication.
 */
modes.gcm.prototype.multiply = function(x, y) {
  var z_i = [0, 0, 0, 0];
  var v_i = y.slice(0);

  // calculate Z_128 (block has 128 bits)
  for(var i = 0; i < 128; ++i) {
    // if x_i is 0, Z_{i+1} = Z_i (unchanged)
    // else Z_{i+1} = Z_i ^ V_i
    // get x_i by finding 32-bit int position, then left shift 1 by remainder
    var x_i = x[(i / 32) | 0] & (1 << (31 - i % 32));
    if(x_i) {
      z_i[0] ^= v_i[0];
      z_i[1] ^= v_i[1];
      z_i[2] ^= v_i[2];
      z_i[3] ^= v_i[3];
    }

    // if LSB(V_i) is 1, V_i = V_i >> 1
    // else V_i = (V_i >> 1) ^ R
    this.pow(v_i, v_i);
  }

  return z_i;
};

modes.gcm.prototype.pow = function(x, out) {
  // if LSB(x) is 1, x = x >>> 1
  // else x = (x >>> 1) ^ R
  var lsb = x[3] & 1;

  // always do x >>> 1:
  // starting with the rightmost integer, shift each integer to the right
  // one bit, pulling in the bit from the integer to the left as its top
  // most bit (do this for the last 3 integers)
  for(var i = 3; i > 0; --i) {
    out[i] = (x[i] >>> 1) | ((x[i - 1] & 1) << 31);
  }
  // shift the first integer normally
  out[0] = x[0] >>> 1;

  // if lsb was not set, then polynomial had a degree of 127 and doesn't
  // need to divided; otherwise, XOR with R to find the remainder; we only
  // need to XOR the first integer since R technically ends w/120 zero bits
  if(lsb) {
    out[0] ^= this._R;
  }
};

modes.gcm.prototype.tableMultiply = function(x) {
  // assumes 4-bit tables are used
  var z = [0, 0, 0, 0];
  for(var i = 0; i < 32; ++i) {
    var idx = (i / 8) | 0;
    var x_i = (x[idx] >>> ((7 - (i % 8)) * 4)) & 0xF;
    var ah = this._m[i][x_i];
    z[0] ^= ah[0];
    z[1] ^= ah[1];
    z[2] ^= ah[2];
    z[3] ^= ah[3];
  }
  return z;
};

/**
 * A continuing version of the GHASH algorithm that operates on a single
 * block. The hash block, last hash value (Ym) and the new block to hash
 * are given.
 *
 * @param h the hash block.
 * @param y the previous value for Ym, use [0, 0, 0, 0] for a new hash.
 * @param x the block to hash.
 *
 * @return the hashed value (Ym).
 */
modes.gcm.prototype.ghash = function(h, y, x) {
  y[0] ^= x[0];
  y[1] ^= x[1];
  y[2] ^= x[2];
  y[3] ^= x[3];
  return this.tableMultiply(y);
  //return this.multiply(y, h);
};

/**
 * Precomputes a table for multiplying against the hash subkey. This
 * mechanism provides a substantial speed increase over multiplication
 * performed without a table. The table-based multiplication this table is
 * for solves X * H by multiplying each component of X by H and then
 * composing the results together using XOR.
 *
 * This function can be used to generate tables with different bit sizes
 * for the components, however, this implementation assumes there are
 * 32 components of X (which is a 16 byte vector), therefore each component
 * takes 4-bits (so the table is constructed with bits=4).
 *
 * @param h the hash subkey.
 * @param bits the bit size for a component.
 */
modes.gcm.prototype.generateHashTable = function(h, bits) {
  // TODO: There are further optimizations that would use only the
  // first table M_0 (or some variant) along with a remainder table;
  // this can be explored in the future
  var multiplier = 8 / bits;
  var perInt = 4 * multiplier;
  var size = 16 * multiplier;
  var m = new Array(size);
  for(var i = 0; i < size; ++i) {
    var tmp = [0, 0, 0, 0];
    var idx = (i / perInt) | 0;
    var shft = ((perInt - 1 - (i % perInt)) * bits);
    tmp[idx] = (1 << (bits - 1)) << shft;
    m[i] = this.generateSubHashTable(this.multiply(tmp, h), bits);
  }
  return m;
};

/**
 * Generates a table for multiplying against the hash subkey for one
 * particular component (out of all possible component values).
 *
 * @param mid the pre-multiplied value for the middle key of the table.
 * @param bits the bit size for a component.
 */
modes.gcm.prototype.generateSubHashTable = function(mid, bits) {
  // compute the table quickly by minimizing the number of
  // POW operations -- they only need to be performed for powers of 2,
  // all other entries can be composed from those powers using XOR
  var size = 1 << bits;
  var half = size >>> 1;
  var m = new Array(size);
  m[half] = mid.slice(0);
  var i = half >>> 1;
  while(i > 0) {
    // raise m0[2 * i] and store in m0[i]
    this.pow(m[2 * i], m[i] = []);
    i >>= 1;
  }
  i = 2;
  while(i < half) {
    for(var j = 1; j < i; ++j) {
      var m_i = m[i];
      var m_j = m[j];
      m[i + j] = [
        m_i[0] ^ m_j[0],
        m_i[1] ^ m_j[1],
        m_i[2] ^ m_j[2],
        m_i[3] ^ m_j[3]
      ];
    }
    i *= 2;
  }
  m[0] = [0, 0, 0, 0];
  /* Note: We could avoid storing these by doing composition during multiply
  calculate top half using composition by speed is preferred. */
  for(i = half + 1; i < size; ++i) {
    var c = m[i ^ half];
    m[i] = [mid[0] ^ c[0], mid[1] ^ c[1], mid[2] ^ c[2], mid[3] ^ c[3]];
  }
  return m;
};

/** Utility functions */

function transformIV(iv, blockSize) {
  if(typeof iv === 'string') {
    // convert iv string into byte buffer
    iv = forge.util.createBuffer(iv);
  }

  if(forge.util.isArray(iv) && iv.length > 4) {
    // convert iv byte array into byte buffer
    var tmp = iv;
    iv = forge.util.createBuffer();
    for(var i = 0; i < tmp.length; ++i) {
      iv.putByte(tmp[i]);
    }
  }

  if(iv.length() < blockSize) {
    throw new Error(
      'Invalid IV length; got ' + iv.length() +
      ' bytes and expected ' + blockSize + ' bytes.');
  }

  if(!forge.util.isArray(iv)) {
    // convert iv byte buffer into 32-bit integer array
    var ints = [];
    var blocks = blockSize / 4;
    for(var i = 0; i < blocks; ++i) {
      ints.push(iv.getInt32());
    }
    iv = ints;
  }

  return iv;
}

function inc32(block) {
  // increment last 32 bits of block only
  block[block.length - 1] = (block[block.length - 1] + 1) & 0xFFFFFFFF;
}

function from64To32(num) {
  // convert 64-bit number to two BE Int32s
  return [(num / 0x100000000) | 0, num & 0xFFFFFFFF];
}