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mirror of https://github.com/danog/phpseclib.git synced 2024-12-03 10:08:04 +01:00

- fixed a few E_NOTICE errors

- sped up Math_BigInteger::_barrett()


git-svn-id: http://phpseclib.svn.sourceforge.net/svnroot/phpseclib/trunk@73 21d32557-59b3-4da0-833f-c5933fad653e
This commit is contained in:
Jim Wigginton 2009-12-31 06:11:07 +00:00
parent 8ea5e6883f
commit e16ba96789
4 changed files with 217 additions and 159 deletions

View File

@ -62,7 +62,7 @@
* @author Jim Wigginton <terrafrost@php.net>
* @copyright MMIX Jim Wigginton
* @license http://www.gnu.org/licenses/lgpl.txt
* @version $Id: RSA.php,v 1.6 2009-12-08 14:18:59 terrafrost Exp $
* @version $Id: RSA.php,v 1.7 2009-12-31 06:11:06 terrafrost Exp $
* @link http://phpseclib.sourceforge.net
*/
@ -966,7 +966,7 @@ class Crypt_RSA {
$bytes = $bits >> 3;
$min = str_repeat(chr(0), $bytes);
$max = str_repeat(chr(0xFF), $bytes);
$msb = $num_bits & 7;
$msb = $bits & 7;
if ($msb) {
$min = chr(1 << ($msb - 1)) . $min;
$max = chr((1 << $msb) - 1) . $max;

View File

@ -24,6 +24,9 @@
* allow bitwise operators, and will increase the maximum possible base to 2**31 (or 2**62 for addition /
* subtraction).
*
* Numbers are stored in {@link http://en.wikipedia.org/wiki/Endianness little endian}} format. ie.
* (new Math_BigInteger(pow(2, 26)))->value = array(0, 1)
*
* Useful resources are as follows:
*
* - {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf Handbook of Applied Cryptography (HAC)}
@ -69,7 +72,7 @@
* @author Jim Wigginton <terrafrost@php.net>
* @copyright MMVI Jim Wigginton
* @license http://www.gnu.org/licenses/lgpl.txt
* @version $Id: BigInteger.php,v 1.20 2009-12-14 23:47:15 terrafrost Exp $
* @version $Id: BigInteger.php,v 1.21 2009-12-31 06:11:07 terrafrost Exp $
* @link http://pear.php.net/package/Math_BigInteger
*/
@ -154,7 +157,7 @@ define('MATH_BIGINTEGER_MAX_DIGIT52', pow(2, 52));
*
* @access private
*/
define('MATH_BIGINTEGER_KARATSUBA_CUTOFF', 15);
define('MATH_BIGINTEGER_KARATSUBA_CUTOFF', 25);
/**
* Pure-PHP arbitrary precision integer arithmetic library. Supports base-2, base-10, base-16, and base-256
@ -945,72 +948,6 @@ class Math_BigInteger {
return $this->_normalize($product);
}
/**
* Performs long multiplication up to $stop digits
*
* If you're going to be doing array_slice($product->value, 0, $stop), some cycles can be saved.
*
* @see _barrett()
* @param Math_BigInteger $x
* @return Math_BigInteger
* @access private
*/
function _multiplyLower($x, $stop)
{
$this_length = count($this->value);
$x_length = count($x->value);
if ( !$this_length || !$x_length ) { // a 0 is being multiplied
return new Math_BigInteger();
}
if ( $this_length < $x_length ) {
return $x->_multiplyLower($this, $stop);
}
$product = new Math_BigInteger();
$product->value = $this->_array_repeat(0, $this_length + $x_length);
// the following for loop could be removed if the for loop following it
// (the one with nested for loops) initially set $i to 0, but
// doing so would also make the result in one set of unnecessary adds,
// since on the outermost loops first pass, $product->value[$k] is going
// to always be 0
$carry = 0;
for ($j = 0; $j < $this_length; $j++) { // ie. $i = 0, $k = $i
$temp = $this->value[$j] * $x->value[0] + $carry; // $product->value[$k] == 0
$carry = floor($temp / 0x4000000);
$product->value[$j] = $temp - 0x4000000 * $carry;
}
if ($j < $stop) {
$product->value[$j] = $carry;
}
// the above for loop is what the previous comment was talking about. the
// following for loop is the "one with nested for loops"
for ($i = 1; $i < $x_length; $i++) {
$carry = 0;
for ($j = 0, $k = $i; $j < $this_length && $k < $stop; $j++, $k++) {
$temp = $product->value[$k] + $this->value[$j] * $x->value[$i] + $carry;
$carry = floor($temp / 0x4000000);
$product->value[$k] = $temp - 0x4000000 * $carry;
}
if ($k < $stop) {
$product->value[$k] = $carry;
}
}
$product->is_negative = $this->is_negative != $x->is_negative;
return $product;
}
/**
* Performs long multiplication on two BigIntegers
*
@ -1334,9 +1271,9 @@ class Math_BigInteger {
for ($i = $x_max; $i >= $y_max + 1; $i--) {
$x_value = array(
$x->value[$i],
( $i > 0 ) ? $x->value[$i - 1] : 0,
( $i > 1 ) ? $x->value[$i - 2] : 0
isset($x->value[$i]) ? $x->value[$i] : 0,
isset($x->value[$i - 1]) ? $x->value[$i - 1] : 0,
isset($x->value[$i - 2]) ? $x->value[$i - 2] : 0
);
$y_value = array(
$y->value[$y_max],
@ -1605,54 +1542,26 @@ class Math_BigInteger {
// calculate the appropriate window size.
// $window_size == 3 if $window_ranges is between 25 and 81, for example.
for ($i = 0, $window_size = 1; $e_length > $window_ranges[$i] && $i < count($window_ranges); $window_size++, $i++);
switch ($mode) {
case MATH_BIGINTEGER_MONTGOMERY:
$reduce = '_montgomery';
$prep = '_prepMontgomery';
break;
case MATH_BIGINTEGER_BARRETT:
$reduce = '_barrett';
$prep = '_barrett';
break;
case MATH_BIGINTEGER_POWEROF2:
$reduce = '_mod2';
$prep = '_mod2';
break;
case MATH_BIGINTEGER_CLASSIC:
$reduce = '_remainder';
$prep = '_remainder';
break;
case MATH_BIGINTEGER_NONE:
// ie. do no modular reduction. useful if you want to just do pow as opposed to modPow.
$reduce = 'copy';
$prep = 'copy';
break;
default:
// an invalid $mode was provided
}
// precompute $this^0 through $this^$window_size
$powers = array();
$powers[1] = $this->$prep($n);
$powers[2] = $powers[1]->_square();
$powers[2] = $powers[2]->$reduce($n);
$powers[1] = $this->_prepareReduce($n, $mode);
$powers[2] = $powers[1]->_squareReduce($n, $mode);
// we do every other number since substr($e_bits, $i, $j+1) (see below) is supposed to end
// in a 1. ie. it's supposed to be odd.
$temp = 1 << ($window_size - 1);
for ($i = 1; $i < $temp; $i++) {
$powers[2 * $i + 1] = $powers[2 * $i - 1]->multiply($powers[2]);
$powers[2 * $i + 1] = $powers[2 * $i + 1]->$reduce($n);
$powers[2 * $i + 1] = $powers[2 * $i - 1]->_multiplyReduce($powers[2], $n, $mode);
}
$result = new Math_BigInteger();
$result->value = array(1);
$result = $result->$prep($n);
$result = $result->_prepareReduce($n, $mode);
for ($i = 0; $i < $e_length; ) {
if ( !$e_bits[$i] ) {
$result = $result->_square();
$result = $result->$reduce($n);
$result = $result->_squareReduce($n, $mode);
$i++;
} else {
for ($j = $window_size - 1; $j > 0; $j--) {
@ -1662,37 +1571,101 @@ class Math_BigInteger {
}
for ($k = 0; $k <= $j; $k++) {// eg. the length of substr($e_bits, $i, $j+1)
$result = $result->_square();
$result = $result->$reduce($n);
$result = $result->_squareReduce($n, $mode);
}
$result = $result->multiply($powers[bindec(substr($e_bits, $i, $j + 1))]);
$result = $result->$reduce($n);
$result = $result->_multiplyReduce($powers[bindec(substr($e_bits, $i, $j + 1))], $n, $mode);
$i+=$j + 1;
}
}
$result = $result->$reduce($n);
$result = $result->_reduce($n, $mode);
return $result;
}
/**
* Remainder
* Modular reduction
*
* A wrapper for the divide function.
* For most $modes this will return the remainder.
*
* @see divide()
* @see _slidingWindow()
* @access private
* @param Math_BigInteger
* @param Math_BigInteger $n
* @param Integer $n
* @return Math_BigInteger
*/
function _remainder($n)
function _reduce($n, $mode)
{
list(, $temp) = $this->divide($n);
return $temp;
switch ($mode) {
case MATH_BIGINTEGER_MONTGOMERY:
return $this->_montgomery($n);
case MATH_BIGINTEGER_BARRETT:
return $this->_barrett($n);
case MATH_BIGINTEGER_POWEROF2:
return $this->_mod2($n);
case MATH_BIGINTEGER_CLASSIC:
list(, $temp) = $this->divide($n);
return $temp;
case MATH_BIGINTEGER_NONE:
return $this->copy();
default:
// an invalid $mode was provided
}
}
/**
* Modular reduction preperation
*
* @see _slidingWindow()
* @access private
* @param Math_BigInteger $n
* @param Integer $n
* @return Math_BigInteger
*/
function _prepareReduce($n, $mode)
{
if ($mode == MATH_BIGINTEGER_MONTGOMERY) {
return $this->_prepMontgomery($n);
}
return $this->_reduce($n, $mode);
}
/**
* Modular multiply
*
* @see _slidingWindow()
* @access private
* @param Math_BigInteger $n
* @param Integer $n
* @return Math_BigInteger
*/
function _multiplyReduce($y, $n, $mode)
{
if ($mode == MATH_BIGINTEGER_MONTGOMERY) {
return $this->_montgomeryMultiply($y, $n);
}
$temp = $this->multiply($y);
return $temp->_reduce($n, $mode);
}
/**
* Modular square
*
* @see _slidingWindow()
* @access private
* @param Math_BigInteger $n
* @param Integer $n
* @return Math_BigInteger
*/
function _squareReduce($n, $mode)
{
if ($mode == MATH_BIGINTEGER_MONTGOMERY) {
return $this->_montgomeryMultiply($this, $n);
}
$temp = $this->_square();
return $temp->_reduce($n, $mode);
}
/**
@ -1720,54 +1693,75 @@ class Math_BigInteger {
* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=165 MPM 6.2.5} for more information. Modified slightly,
* so as not to require negative numbers (initially, this script didn't support negative numbers).
*
* Employs "folding", as described at
* {@link http://www.cosic.esat.kuleuven.be/publications/thesis-149.pdf#page=66 thesis-149.pdf#page=66}. To quote from
* it, "the idea [behind folding] is to find a value x' such that x (mod m) = x' (mod m), with x' being smaller than x."
*
* Unfortunately, the "Barrett Reduction with Folding" algorithm described in thesis-149.pdf is not, as written, all that
* usable on account of its not using reasonable radix points as discussed in
* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=162 MPM 6.2.2}.
*
* @see _slidingWindow()
* @access private
* @param Math_BigInteger
* @return Math_BigInteger
*/
function _barrett($n)
function _barrett($m)
{
static $cache = array(
MATH_BIGINTEGER_VARIABLE => array(),
MATH_BIGINTEGER_DATA => array()
);
$n_length = count($n->value);
// "given an n-bit modulus, M, ..."
$n_length = count($m->value);
if (count($this->value) > 2 * $n_length) {
list(, $temp) = $this->divide($n);
if (count($this->value) > 2 * $n_length) {// || count($this->value) < count($m->value)) {
list(, $temp) = $this->divide($m);
return $temp;
}
if ( ($key = array_search($n->value, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) {
$n = $this->copy();
$temp = new Math_BigInteger();
$temp2= new Math_BigInteger();
if ( ($key = array_search($m->value, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) {
$key = count($cache[MATH_BIGINTEGER_VARIABLE]);
$cache[MATH_BIGINTEGER_VARIABLE][] = $n->value;
$temp = new Math_BigInteger();
$temp->value = $this->_array_repeat(0, 2 * $n_length);
$cache[MATH_BIGINTEGER_VARIABLE][] = $m->value;
$temp->value = $this->_array_repeat(0, $n_length + ($n_length >> 1));
$temp->value[] = 1;
list($cache[MATH_BIGINTEGER_DATA][], ) = $temp->divide($n);
list($u, $m1) = $temp->divide($m);
$cache[MATH_BIGINTEGER_DATA][] = array(
'u' => $u,
'm1'=> $m1
);
}
extract($cache[MATH_BIGINTEGER_DATA][$key]);
$cutoff = $n_length + ($n_length >> 1);
$msd = new Math_BigInteger();
$lsd = new Math_BigInteger();
$lsd->value = array_slice($n->value, 0, $cutoff);
$msd->value = array_slice($n->value, $cutoff);
$lsd->_trim();
$n = $lsd->add($msd->multiply($m1));
/* at this point, given list($a, $b) = $n->divide($m) and list($c, $d) = $this->divide($m),
we can safely assume $b == $d (even though $a != $c). */
$temp = new Math_BigInteger();
$temp->value = array_slice($this->value, $n_length - 1);
$temp = $temp->multiply($cache[MATH_BIGINTEGER_DATA][$key]);
$temp->value = array_slice($temp->value, $n_length + 1);
$temp->value = array_slice($n->value, $n_length - 1);
$temp = $temp->multiply($u);
$temp->value = array_slice($temp->value, ($n_length >> 1) + 1);
$temp = $temp->multiply($m);
$result = new Math_BigInteger();
$result->value = array_slice($this->value, 0, $n_length + 1);
$temp = $temp->_multiplyLower($n, $n_length + 1);
// $temp->value == array_slice($temp->multiply($n)->value, 0, $n_length + 1)
if ($result->compare($temp) < 0) {
$corrector = new Math_BigInteger();
$corrector->value = $this->_array_repeat(0, $n_length + 1);
$corrector->value[] = 1;
$result = $result->add($corrector);
}
$result = $result->subtract($temp);
while ($result->compare($n) > 0) {
$result = $result->subtract($n);
$result = $n->subtract($temp);
while ($result->compare($m) >= 0) {
$result = $result->subtract($m);
}
return $result;
@ -1776,7 +1770,7 @@ class Math_BigInteger {
/**
* Montgomery Modular Reduction
*
* ($this->_prepMontgomery($n))->_montgomery($n) yields $x%$n.
* ($x->_prepMontgomery($n))->_montgomery($n) yields $x % $n.
* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=170 MPM 6.3} provides insights on how this can be
* improved upon (basically, by using the comba method). gcd($n, 2) must be equal to one for this function
* to work correctly.
@ -1824,6 +1818,52 @@ class Math_BigInteger {
return $result;
}
/**
* Montgomery Multiply
*
* Interleaves the montgomery reduction and long multiplication algorithms together as described in
* {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=13 HAC 14.36}
*
* @see _prepMontgomery()
* @see _montgomery()
* @access private
* @param Math_BigInteger
* @return Math_BigInteger
*/
function _montgomeryMultiply($y, $m)
{
static $cache = array(
MATH_BIGINTEGER_VARIABLE => array(),
MATH_BIGINTEGER_DATA => array()
);
if ( ($key = array_search($m->value, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) {
$key = count($cache[MATH_BIGINTEGER_VARIABLE]);
$cache[MATH_BIGINTEGER_VARIABLE][] = $m->value;
$cache[MATH_BIGINTEGER_DATA][] = $m->_modInverse67108864();
}
$x = $this->copy();
$n = max(count($x->value), count($y->value), count($m->value));
$x->value = array_pad($x->value, $n, 0);
$y->value = array_pad($y->value, $n, 0);
$m->value = array_pad($m->value, $n, 0);
$a = new Math_BigInteger();
$a->value = $this->_array_repeat(0, $n + 1);
for ($i = 0; $i < $n; $i++) {
$temp = ($a->value[0] + $x->value[$i] * $y->value[0]) & 0x3FFFFFF;
$temp = ($temp * $cache[MATH_BIGINTEGER_DATA][$key]) & 0x3FFFFFF;
$part1 = $y->multiply(new Math_BigInteger($x->value[$i]));
$part2 = $m->multiply(new Math_BigInteger($temp));
$a = $a->add($part1->add($part2));
$a->value = array_slice($a->value, 1);
}
if ($a->compare($m) >= 0) {
$a = $a->subtract($m);
}
return $a;
}
/**
* Prepare a number for use in Montgomery Modular Reductions
*
@ -1975,7 +2015,8 @@ class Math_BigInteger {
* {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=19 HAC 14.61}. As the text above 14.61 notes,
* the more traditional algorithim requires "relatively costly multiple-precision divisions".
*/
function extendedGCD($n) {
function extendedGCD($n)
{
switch ( MATH_BIGINTEGER_MODE ) {
case MATH_BIGINTEGER_MODE_GMP:
extract(gmp_gcdext($this->value, $n->value));
@ -2041,6 +2082,7 @@ class Math_BigInteger {
$d = new Math_BigInteger();
$a->value = $d->value = $g->value = array(1);
$b->value = $c->value = array();
while ( !empty($u->value) ) {
while ( !($u->value[0] & 1) ) {
@ -2697,7 +2739,7 @@ class Math_BigInteger {
/**
* Checks a numer to see if it's prime
*
* Assuming the $t parameter is not set, this functoin has an error rate of 2**-80. The main motivation for the
* Assuming the $t parameter is not set, this function has an error rate of 2**-80. The main motivation for the
* $t parameter is distributability. Math_BigInteger::randomPrime() can be distributed accross multiple pageloads
* on a website instead of just one.
*
@ -2904,9 +2946,11 @@ class Math_BigInteger {
/**
* Normalize
*
* Deletes leading zeros and truncates (if necessary) to maintain the appropriate precision
* Removes leading zeros and truncates (if necessary) to maintain the appropriate precision
*
* @param Math_BigInteger
* @return Math_BigInteger
* @see _trim()
* @access private
*/
function _normalize($result)
@ -2933,12 +2977,7 @@ class Math_BigInteger {
return $result;
}
for ($i = count($result->value) - 1; $i >= 0; $i--) {
if ( $result->value[$i] ) {
break;
}
unset($result->value[$i]);
}
$result->_trim();
if (!empty($result->bitmask->value)) {
$length = min(count($result->value), count($this->bitmask->value));
@ -2949,9 +2988,28 @@ class Math_BigInteger {
}
}
//return $result->copy();
return $result;
}
/**
* Trim
*
* Removes leading zeros
*
* @return Math_BigInteger
* @access private
*/
function _trim()
{
for ($i = count($this->value) - 1; $i >= 0; $i--) {
if ( $this->value[$i] ) {
break;
}
unset($this->value[$i]);
}
}
/**
* Array Repeat
*

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@ -48,7 +48,7 @@
* @author Jim Wigginton <terrafrost@php.net>
* @copyright MMIX Jim Wigginton
* @license http://www.gnu.org/licenses/lgpl.txt
* @version $Id: SFTP.php,v 1.13 2009-12-14 18:14:54 terrafrost Exp $
* @version $Id: SFTP.php,v 1.14 2009-12-31 06:11:07 terrafrost Exp $
* @link http://phpseclib.sourceforge.net
*/
@ -332,7 +332,7 @@ class Net_SFTP extends Net_SSH2 {
}
$packet = pack('CNNa*CNa*',
NET_SSH2_MSG_CHANNEL_REQUEST, $server_channel, strlen('subsystem'), 'subsystem', 1, strlen('sftp'), 'sftp');
NET_SSH2_MSG_CHANNEL_REQUEST, $this->server_channels[NET_SFTP_CHANNEL], strlen('subsystem'), 'subsystem', 1, strlen('sftp'), 'sftp');
if (!$this->_send_binary_packet($packet)) {
return false;
}

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@ -60,7 +60,7 @@
* @author Jim Wigginton <terrafrost@php.net>
* @copyright MMVII Jim Wigginton
* @license http://www.gnu.org/licenses/lgpl.txt
* @version $Id: SSH2.php,v 1.32 2009-12-14 18:17:36 terrafrost Exp $
* @version $Id: SSH2.php,v 1.33 2009-12-31 06:11:07 terrafrost Exp $
* @link http://phpseclib.sourceforge.net
*/
@ -990,7 +990,7 @@ class Net_SSH2 {
list(, $v) = $v->divide($q);
if (!$v->equals($r)) {
user_error('Invalid signature', E_USER_NOTICE);
user_error('Bad server signature', E_USER_NOTICE);
return $this->_disconnect(NET_SSH2_DISCONNECT_HOST_KEY_NOT_VERIFIABLE);
}