/** @fileOverview Arrays of bits, encoded as arrays of Numbers.
*
* @author Emily Stark
* @author Mike Hamburg
* @author Dan Boneh
*/
/**
* Arrays of bits, encoded as arrays of Numbers.
* @namespace
* @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} blength 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 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} [_end=0] 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]];
},
/** byteswap a word array inplace.
* (does not handle partial words)
* @param {sjcl.bitArray} a word array
* @return {sjcl.bitArray} byteswapped array
*/
byteswapM: function(a) {
var i, v, m = 0xff00;
for (i = 0; i < a.length; ++i) {
v = a[i];
a[i] = (v >>> 24) | ((v >>> 8) & m) | ((v & m) << 8) | (v << 24);
}
return a;
}
};