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- 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
parent
8ea5e6883f
commit
e16ba96789
@ -62,7 +62,7 @@
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* @author Jim Wigginton <terrafrost@php.net>
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* @copyright MMIX Jim Wigginton
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* @license http://www.gnu.org/licenses/lgpl.txt
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* @version $Id: RSA.php,v 1.6 2009-12-08 14:18:59 terrafrost Exp $
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* @version $Id: RSA.php,v 1.7 2009-12-31 06:11:06 terrafrost Exp $
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* @link http://phpseclib.sourceforge.net
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*/
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@ -966,7 +966,7 @@ class Crypt_RSA {
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$bytes = $bits >> 3;
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$min = str_repeat(chr(0), $bytes);
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$max = str_repeat(chr(0xFF), $bytes);
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$msb = $num_bits & 7;
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$msb = $bits & 7;
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if ($msb) {
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$min = chr(1 << ($msb - 1)) . $min;
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$max = chr((1 << $msb) - 1) . $max;
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@ -24,6 +24,9 @@
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* allow bitwise operators, and will increase the maximum possible base to 2**31 (or 2**62 for addition /
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* subtraction).
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*
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* Numbers are stored in {@link http://en.wikipedia.org/wiki/Endianness little endian}} format. ie.
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* (new Math_BigInteger(pow(2, 26)))->value = array(0, 1)
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*
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* Useful resources are as follows:
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*
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* - {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf Handbook of Applied Cryptography (HAC)}
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@ -69,7 +72,7 @@
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* @author Jim Wigginton <terrafrost@php.net>
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* @copyright MMVI Jim Wigginton
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* @license http://www.gnu.org/licenses/lgpl.txt
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* @version $Id: BigInteger.php,v 1.20 2009-12-14 23:47:15 terrafrost Exp $
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* @version $Id: BigInteger.php,v 1.21 2009-12-31 06:11:07 terrafrost Exp $
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* @link http://pear.php.net/package/Math_BigInteger
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*/
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@ -154,7 +157,7 @@ define('MATH_BIGINTEGER_MAX_DIGIT52', pow(2, 52));
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*
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* @access private
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*/
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define('MATH_BIGINTEGER_KARATSUBA_CUTOFF', 15);
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define('MATH_BIGINTEGER_KARATSUBA_CUTOFF', 25);
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/**
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* Pure-PHP arbitrary precision integer arithmetic library. Supports base-2, base-10, base-16, and base-256
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@ -945,72 +948,6 @@ class Math_BigInteger {
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return $this->_normalize($product);
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}
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/**
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* Performs long multiplication up to $stop digits
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*
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* If you're going to be doing array_slice($product->value, 0, $stop), some cycles can be saved.
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*
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* @see _barrett()
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* @param Math_BigInteger $x
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* @return Math_BigInteger
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* @access private
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*/
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function _multiplyLower($x, $stop)
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{
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$this_length = count($this->value);
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$x_length = count($x->value);
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if ( !$this_length || !$x_length ) { // a 0 is being multiplied
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return new Math_BigInteger();
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}
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if ( $this_length < $x_length ) {
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return $x->_multiplyLower($this, $stop);
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}
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$product = new Math_BigInteger();
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$product->value = $this->_array_repeat(0, $this_length + $x_length);
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// the following for loop could be removed if the for loop following it
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// (the one with nested for loops) initially set $i to 0, but
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// doing so would also make the result in one set of unnecessary adds,
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// since on the outermost loops first pass, $product->value[$k] is going
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// to always be 0
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$carry = 0;
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for ($j = 0; $j < $this_length; $j++) { // ie. $i = 0, $k = $i
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$temp = $this->value[$j] * $x->value[0] + $carry; // $product->value[$k] == 0
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$carry = floor($temp / 0x4000000);
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$product->value[$j] = $temp - 0x4000000 * $carry;
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}
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if ($j < $stop) {
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$product->value[$j] = $carry;
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}
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// the above for loop is what the previous comment was talking about. the
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// following for loop is the "one with nested for loops"
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for ($i = 1; $i < $x_length; $i++) {
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$carry = 0;
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for ($j = 0, $k = $i; $j < $this_length && $k < $stop; $j++, $k++) {
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$temp = $product->value[$k] + $this->value[$j] * $x->value[$i] + $carry;
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$carry = floor($temp / 0x4000000);
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$product->value[$k] = $temp - 0x4000000 * $carry;
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}
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if ($k < $stop) {
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$product->value[$k] = $carry;
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}
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}
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$product->is_negative = $this->is_negative != $x->is_negative;
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return $product;
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}
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/**
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* Performs long multiplication on two BigIntegers
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*
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@ -1334,9 +1271,9 @@ class Math_BigInteger {
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for ($i = $x_max; $i >= $y_max + 1; $i--) {
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$x_value = array(
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$x->value[$i],
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( $i > 0 ) ? $x->value[$i - 1] : 0,
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( $i > 1 ) ? $x->value[$i - 2] : 0
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isset($x->value[$i]) ? $x->value[$i] : 0,
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isset($x->value[$i - 1]) ? $x->value[$i - 1] : 0,
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isset($x->value[$i - 2]) ? $x->value[$i - 2] : 0
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);
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$y_value = array(
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$y->value[$y_max],
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@ -1605,54 +1542,26 @@ class Math_BigInteger {
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// calculate the appropriate window size.
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// $window_size == 3 if $window_ranges is between 25 and 81, for example.
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for ($i = 0, $window_size = 1; $e_length > $window_ranges[$i] && $i < count($window_ranges); $window_size++, $i++);
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switch ($mode) {
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case MATH_BIGINTEGER_MONTGOMERY:
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$reduce = '_montgomery';
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$prep = '_prepMontgomery';
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break;
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case MATH_BIGINTEGER_BARRETT:
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$reduce = '_barrett';
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$prep = '_barrett';
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break;
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case MATH_BIGINTEGER_POWEROF2:
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$reduce = '_mod2';
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$prep = '_mod2';
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break;
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case MATH_BIGINTEGER_CLASSIC:
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$reduce = '_remainder';
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$prep = '_remainder';
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break;
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case MATH_BIGINTEGER_NONE:
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// ie. do no modular reduction. useful if you want to just do pow as opposed to modPow.
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$reduce = 'copy';
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$prep = 'copy';
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break;
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default:
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// an invalid $mode was provided
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}
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// precompute $this^0 through $this^$window_size
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$powers = array();
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$powers[1] = $this->$prep($n);
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$powers[2] = $powers[1]->_square();
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$powers[2] = $powers[2]->$reduce($n);
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$powers[1] = $this->_prepareReduce($n, $mode);
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$powers[2] = $powers[1]->_squareReduce($n, $mode);
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// we do every other number since substr($e_bits, $i, $j+1) (see below) is supposed to end
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// in a 1. ie. it's supposed to be odd.
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$temp = 1 << ($window_size - 1);
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for ($i = 1; $i < $temp; $i++) {
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$powers[2 * $i + 1] = $powers[2 * $i - 1]->multiply($powers[2]);
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$powers[2 * $i + 1] = $powers[2 * $i + 1]->$reduce($n);
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$powers[2 * $i + 1] = $powers[2 * $i - 1]->_multiplyReduce($powers[2], $n, $mode);
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}
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$result = new Math_BigInteger();
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$result->value = array(1);
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$result = $result->$prep($n);
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$result = $result->_prepareReduce($n, $mode);
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for ($i = 0; $i < $e_length; ) {
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if ( !$e_bits[$i] ) {
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$result = $result->_square();
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$result = $result->$reduce($n);
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$result = $result->_squareReduce($n, $mode);
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$i++;
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} else {
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for ($j = $window_size - 1; $j > 0; $j--) {
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@ -1662,37 +1571,101 @@ class Math_BigInteger {
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}
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for ($k = 0; $k <= $j; $k++) {// eg. the length of substr($e_bits, $i, $j+1)
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$result = $result->_square();
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$result = $result->$reduce($n);
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$result = $result->_squareReduce($n, $mode);
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}
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$result = $result->multiply($powers[bindec(substr($e_bits, $i, $j + 1))]);
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$result = $result->$reduce($n);
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$result = $result->_multiplyReduce($powers[bindec(substr($e_bits, $i, $j + 1))], $n, $mode);
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$i+=$j + 1;
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}
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}
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$result = $result->$reduce($n);
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$result = $result->_reduce($n, $mode);
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return $result;
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}
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/**
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* Remainder
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* Modular reduction
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*
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* A wrapper for the divide function.
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* For most $modes this will return the remainder.
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*
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* @see divide()
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* @see _slidingWindow()
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* @access private
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* @param Math_BigInteger
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* @param Math_BigInteger $n
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* @param Integer $n
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* @return Math_BigInteger
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*/
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function _remainder($n)
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function _reduce($n, $mode)
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{
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list(, $temp) = $this->divide($n);
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return $temp;
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switch ($mode) {
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case MATH_BIGINTEGER_MONTGOMERY:
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return $this->_montgomery($n);
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case MATH_BIGINTEGER_BARRETT:
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return $this->_barrett($n);
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case MATH_BIGINTEGER_POWEROF2:
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return $this->_mod2($n);
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case MATH_BIGINTEGER_CLASSIC:
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list(, $temp) = $this->divide($n);
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return $temp;
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case MATH_BIGINTEGER_NONE:
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return $this->copy();
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default:
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// an invalid $mode was provided
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}
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}
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/**
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* Modular reduction preperation
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*
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* @see _slidingWindow()
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* @access private
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* @param Math_BigInteger $n
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* @param Integer $n
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* @return Math_BigInteger
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*/
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function _prepareReduce($n, $mode)
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{
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if ($mode == MATH_BIGINTEGER_MONTGOMERY) {
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return $this->_prepMontgomery($n);
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}
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return $this->_reduce($n, $mode);
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}
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/**
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* Modular multiply
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*
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* @see _slidingWindow()
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* @access private
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* @param Math_BigInteger $n
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* @param Integer $n
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* @return Math_BigInteger
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*/
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function _multiplyReduce($y, $n, $mode)
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{
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if ($mode == MATH_BIGINTEGER_MONTGOMERY) {
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return $this->_montgomeryMultiply($y, $n);
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}
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$temp = $this->multiply($y);
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return $temp->_reduce($n, $mode);
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}
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/**
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* Modular square
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*
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* @see _slidingWindow()
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* @access private
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* @param Math_BigInteger $n
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* @param Integer $n
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* @return Math_BigInteger
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*/
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function _squareReduce($n, $mode)
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{
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if ($mode == MATH_BIGINTEGER_MONTGOMERY) {
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return $this->_montgomeryMultiply($this, $n);
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}
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$temp = $this->_square();
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return $temp->_reduce($n, $mode);
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}
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/**
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@ -1720,54 +1693,75 @@ class Math_BigInteger {
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* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=165 MPM 6.2.5} for more information. Modified slightly,
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* so as not to require negative numbers (initially, this script didn't support negative numbers).
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*
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* Employs "folding", as described at
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* {@link http://www.cosic.esat.kuleuven.be/publications/thesis-149.pdf#page=66 thesis-149.pdf#page=66}. To quote from
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* 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."
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*
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* Unfortunately, the "Barrett Reduction with Folding" algorithm described in thesis-149.pdf is not, as written, all that
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* usable on account of its not using reasonable radix points as discussed in
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* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=162 MPM 6.2.2}.
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*
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* @see _slidingWindow()
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* @access private
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* @param Math_BigInteger
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* @return Math_BigInteger
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*/
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function _barrett($n)
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function _barrett($m)
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{
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static $cache = array(
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MATH_BIGINTEGER_VARIABLE => array(),
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MATH_BIGINTEGER_DATA => array()
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);
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$n_length = count($n->value);
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// "given an n-bit modulus, M, ..."
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$n_length = count($m->value);
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if (count($this->value) > 2 * $n_length) {
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list(, $temp) = $this->divide($n);
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if (count($this->value) > 2 * $n_length) {// || count($this->value) < count($m->value)) {
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list(, $temp) = $this->divide($m);
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return $temp;
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}
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if ( ($key = array_search($n->value, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) {
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$n = $this->copy();
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$temp = new Math_BigInteger();
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$temp2= new Math_BigInteger();
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if ( ($key = array_search($m->value, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) {
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$key = count($cache[MATH_BIGINTEGER_VARIABLE]);
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$cache[MATH_BIGINTEGER_VARIABLE][] = $n->value;
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$temp = new Math_BigInteger();
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$temp->value = $this->_array_repeat(0, 2 * $n_length);
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$cache[MATH_BIGINTEGER_VARIABLE][] = $m->value;
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$temp->value = $this->_array_repeat(0, $n_length + ($n_length >> 1));
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$temp->value[] = 1;
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list($cache[MATH_BIGINTEGER_DATA][], ) = $temp->divide($n);
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list($u, $m1) = $temp->divide($m);
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$cache[MATH_BIGINTEGER_DATA][] = array(
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'u' => $u,
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'm1'=> $m1
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);
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}
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extract($cache[MATH_BIGINTEGER_DATA][$key]);
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$cutoff = $n_length + ($n_length >> 1);
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$msd = new Math_BigInteger();
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$lsd = new Math_BigInteger();
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$lsd->value = array_slice($n->value, 0, $cutoff);
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$msd->value = array_slice($n->value, $cutoff);
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$lsd->_trim();
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$n = $lsd->add($msd->multiply($m1));
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/* at this point, given list($a, $b) = $n->divide($m) and list($c, $d) = $this->divide($m),
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we can safely assume $b == $d (even though $a != $c). */
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$temp = new Math_BigInteger();
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$temp->value = array_slice($this->value, $n_length - 1);
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$temp = $temp->multiply($cache[MATH_BIGINTEGER_DATA][$key]);
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$temp->value = array_slice($temp->value, $n_length + 1);
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$temp->value = array_slice($n->value, $n_length - 1);
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$temp = $temp->multiply($u);
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$temp->value = array_slice($temp->value, ($n_length >> 1) + 1);
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$temp = $temp->multiply($m);
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$result = new Math_BigInteger();
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$result->value = array_slice($this->value, 0, $n_length + 1);
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$temp = $temp->_multiplyLower($n, $n_length + 1);
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// $temp->value == array_slice($temp->multiply($n)->value, 0, $n_length + 1)
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if ($result->compare($temp) < 0) {
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$corrector = new Math_BigInteger();
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$corrector->value = $this->_array_repeat(0, $n_length + 1);
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$corrector->value[] = 1;
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$result = $result->add($corrector);
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}
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$result = $result->subtract($temp);
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while ($result->compare($n) > 0) {
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$result = $result->subtract($n);
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$result = $n->subtract($temp);
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while ($result->compare($m) >= 0) {
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$result = $result->subtract($m);
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}
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return $result;
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@ -1776,7 +1770,7 @@ class Math_BigInteger {
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/**
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* Montgomery Modular Reduction
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*
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* ($this->_prepMontgomery($n))->_montgomery($n) yields $x%$n.
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* ($x->_prepMontgomery($n))->_montgomery($n) yields $x % $n.
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* {@link http://math.libtomcrypt.com/files/tommath.pdf#page=170 MPM 6.3} provides insights on how this can be
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* improved upon (basically, by using the comba method). gcd($n, 2) must be equal to one for this function
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* to work correctly.
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@ -1824,6 +1818,52 @@ class Math_BigInteger {
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return $result;
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}
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/**
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* Montgomery Multiply
|
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*
|
||||
* Interleaves the montgomery reduction and long multiplication algorithms together as described in
|
||||
* {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=13 HAC 14.36}
|
||||
*
|
||||
* @see _prepMontgomery()
|
||||
* @see _montgomery()
|
||||
* @access private
|
||||
* @param Math_BigInteger
|
||||
* @return Math_BigInteger
|
||||
*/
|
||||
function _montgomeryMultiply($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
|
||||
*
|
||||
|
||||
@ -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;
|
||||
}
|
||||
|
||||
@ -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);
|
||||
}
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user