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<?php
/**
* Binary Finite Fields
*
* Utilizes the factory design pattern
*
* PHP version 5 and 7
*
* @author Jim Wigginton <[email protected]>
* @copyright 2017 Jim Wigginton
* @license http://www.opensource.org/licenses/mit-license.html MIT License
*/
namespace phpseclib3\Math;
use phpseclib3\Common\Functions\Strings;
use phpseclib3\Math\BinaryField\Integer;
use phpseclib3\Math\Common\FiniteField;
/**
* Binary Finite Fields
*
* @author Jim Wigginton <[email protected]>
*/
class BinaryField extends FiniteField
{
/**
* Instance Counter
*
* @var int
*/
private static $instanceCounter = 0;
/**
* Keeps track of current instance
*
* @var int
*/
protected $instanceID;
/** @var BigInteger */
private $randomMax;
/**
* Default constructor
*/
public function __construct(...$indices)
{
$m = array_shift($indices);
if ($m > 571) {
/* sect571r1 and sect571k1 are the largest binary curves that https://www.secg.org/sec2-v2.pdf defines
altho theoretically there may be legit reasons to use binary finite fields with larger degrees
imposing a limit on the maximum size is both reasonable and precedented. in particular,
http://tools.ietf.org/html/rfc4253#section-6.1 (The Secure Shell (SSH) Transport Layer Protocol) says
"implementations SHOULD check that the packet length is reasonable in order for the implementation to
avoid denial of service and/or buffer overflow attacks" */
throw new \OutOfBoundsException('Degrees larger than 571 are not supported');
}
$val = str_repeat('0', $m) . '1';
foreach ($indices as $index) {
$val[$index] = '1';
}
$modulo = static::base2ToBase256(strrev($val));
$mStart = 2 * $m - 2;
$t = ceil($m / 8);
$finalMask = chr((1 << ($m % 8)) - 1);
if ($finalMask == "\0") {
$finalMask = "\xFF";
}
$bitLen = $mStart + 1;
$pad = ceil($bitLen / 8);
$h = $bitLen & 7;
$h = $h ? 8 - $h : 0;
$r = rtrim(substr($val, 0, -1), '0');
$u = [static::base2ToBase256(strrev($r))];
for ($i = 1; $i < 8; $i++) {
$u[] = static::base2ToBase256(strrev(str_repeat('0', $i) . $r));
}
// implements algorithm 2.40 (in section 2.3.5) in "Guide to Elliptic Curve Cryptography"
// with W = 8
$reduce = function ($c) use ($u, $mStart, $m, $t, $finalMask, $pad, $h) {
$c = str_pad($c, $pad, "\0", STR_PAD_LEFT);
for ($i = $mStart; $i >= $m;) {
$g = $h >> 3;
$mask = $h & 7;
$mask = $mask ? 1 << (7 - $mask) : 0x80;
for (; $mask > 0; $mask >>= 1, $i--, $h++) {
if (ord($c[$g]) & $mask) {
$temp = $i - $m;
$j = $temp >> 3;
$k = $temp & 7;
$t1 = $j ? substr($c, 0, -$j) : $c;
$length = strlen($t1);
if ($length) {
$t2 = str_pad($u[$k], $length, "\0", STR_PAD_LEFT);
$temp = $t1 ^ $t2;
$c = $j ? substr_replace($c, $temp, 0, $length) : $temp;
}
}
}
}
$c = substr($c, -$t);
if (strlen($c) == $t) {
$c[0] = $c[0] & $finalMask;
}
return ltrim($c, "\0");
};
$this->instanceID = self::$instanceCounter++;
Integer::setModulo($this->instanceID, $modulo);
Integer::setRecurringModuloFunction($this->instanceID, $reduce);
$this->randomMax = new BigInteger($modulo, 2);
}
/**
* Returns an instance of a dynamically generated PrimeFieldInteger class
*
* @param string $num
* @return Integer
*/
public function newInteger($num)
{
return new Integer($this->instanceID, $num instanceof BigInteger ? $num->toBytes() : $num);
}
/**
* Returns an integer on the finite field between one and the prime modulo
*
* @return Integer
*/
public function randomInteger()
{
static $one;
if (!isset($one)) {
$one = new BigInteger(1);
}
return new Integer($this->instanceID, BigInteger::randomRange($one, $this->randomMax)->toBytes());
}
/**
* Returns the length of the modulo in bytes
*
* @return int
*/
public function getLengthInBytes()
{
return strlen(Integer::getModulo($this->instanceID));
}
/**
* Returns the length of the modulo in bits
*
* @return int
*/
public function getLength()
{
return strlen(Integer::getModulo($this->instanceID)) << 3;
}
/**
* Converts a base-2 string to a base-256 string
*
* @param string $x
* @param int|null $size
* @return string
*/
public static function base2ToBase256($x, $size = null)
{
$str = Strings::bits2bin($x);
$pad = strlen($x) >> 3;
if (strlen($x) & 3) {
$pad++;
}
$str = str_pad($str, $pad, "\0", STR_PAD_LEFT);
if (isset($size)) {
$str = str_pad($str, $size, "\0", STR_PAD_LEFT);
}
return $str;
}
/**
* Converts a base-256 string to a base-2 string
*
* @param string $x
* @return string
*/
public static function base256ToBase2($x)
{
if (function_exists('gmp_import')) {
return gmp_strval(gmp_import($x), 2);
}
return Strings::bin2bits($x);
}
}
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