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cipherModes.js
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			/**
			* 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];
			}