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| Rev | Author | Line No. | Line |
|---|---|---|---|
| 827 | daniel-mar | 1 | <?php |
| 2 | |||
| 3 | /** |
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| 4 | * Binary Finite Fields |
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| 5 | * |
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| 6 | * Utilizes the factory design pattern |
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| 7 | * |
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| 8 | * PHP version 5 and 7 |
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| 9 | * |
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| 874 | daniel-mar | 10 | * @category Math |
| 11 | * @package BigInteger |
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| 827 | daniel-mar | 12 | * @author Jim Wigginton <terrafrost@php.net> |
| 13 | * @copyright 2017 Jim Wigginton |
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| 14 | * @license http://www.opensource.org/licenses/mit-license.html MIT License |
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| 15 | */ |
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| 16 | |||
| 17 | namespace phpseclib3\Math; |
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| 18 | |||
| 19 | use phpseclib3\Common\Functions\Strings; |
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| 20 | use phpseclib3\Math\BinaryField\Integer; |
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| 21 | use phpseclib3\Math\Common\FiniteField; |
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| 22 | |||
| 23 | /** |
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| 24 | * Binary Finite Fields |
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| 25 | * |
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| 874 | daniel-mar | 26 | * @package Math |
| 827 | daniel-mar | 27 | * @author Jim Wigginton <terrafrost@php.net> |
| 874 | daniel-mar | 28 | * @access public |
| 827 | daniel-mar | 29 | */ |
| 30 | class BinaryField extends FiniteField |
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| 31 | { |
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| 32 | /** |
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| 33 | * Instance Counter |
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| 34 | * |
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| 35 | * @var int |
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| 36 | */ |
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| 37 | private static $instanceCounter = 0; |
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| 38 | |||
| 39 | /** |
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| 40 | * Keeps track of current instance |
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| 41 | * |
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| 42 | * @var int |
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| 43 | */ |
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| 44 | protected $instanceID; |
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| 45 | |||
| 46 | /** @var BigInteger */ |
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| 47 | private $randomMax; |
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| 48 | |||
| 49 | /** |
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| 50 | * Default constructor |
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| 51 | */ |
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| 52 | public function __construct(...$indices) |
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| 53 | { |
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| 54 | $m = array_shift($indices); |
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| 55 | $val = str_repeat('0', $m) . '1'; |
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| 56 | foreach ($indices as $index) { |
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| 57 | $val[$index] = '1'; |
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| 58 | } |
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| 59 | $modulo = static::base2ToBase256(strrev($val)); |
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| 60 | |||
| 61 | $mStart = 2 * $m - 2; |
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| 62 | $t = ceil($m / 8); |
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| 63 | $finalMask = chr((1 << ($m % 8)) - 1); |
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| 64 | if ($finalMask == "\0") { |
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| 65 | $finalMask = "\xFF"; |
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| 66 | } |
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| 67 | $bitLen = $mStart + 1; |
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| 68 | $pad = ceil($bitLen / 8); |
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| 69 | $h = $bitLen & 7; |
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| 70 | $h = $h ? 8 - $h : 0; |
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| 71 | |||
| 72 | $r = rtrim(substr($val, 0, -1), '0'); |
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| 73 | $u = [static::base2ToBase256(strrev($r))]; |
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| 74 | for ($i = 1; $i < 8; $i++) { |
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| 75 | $u[] = static::base2ToBase256(strrev(str_repeat('0', $i) . $r)); |
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| 76 | } |
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| 77 | |||
| 78 | // implements algorithm 2.40 (in section 2.3.5) in "Guide to Elliptic Curve Cryptography" |
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| 79 | // with W = 8 |
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| 80 | $reduce = function ($c) use ($u, $mStart, $m, $t, $finalMask, $pad, $h) { |
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| 81 | $c = str_pad($c, $pad, "\0", STR_PAD_LEFT); |
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| 82 | for ($i = $mStart; $i >= $m;) { |
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| 83 | $g = $h >> 3; |
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| 84 | $mask = $h & 7; |
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| 85 | $mask = $mask ? 1 << (7 - $mask) : 0x80; |
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| 86 | for (; $mask > 0; $mask >>= 1, $i--, $h++) { |
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| 87 | if (ord($c[$g]) & $mask) { |
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| 88 | $temp = $i - $m; |
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| 89 | $j = $temp >> 3; |
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| 90 | $k = $temp & 7; |
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| 91 | $t1 = $j ? substr($c, 0, -$j) : $c; |
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| 92 | $length = strlen($t1); |
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| 93 | if ($length) { |
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| 94 | $t2 = str_pad($u[$k], $length, "\0", STR_PAD_LEFT); |
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| 95 | $temp = $t1 ^ $t2; |
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| 96 | $c = $j ? substr_replace($c, $temp, 0, $length) : $temp; |
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| 97 | } |
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| 98 | } |
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| 99 | } |
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| 100 | } |
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| 101 | $c = substr($c, -$t); |
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| 102 | if (strlen($c) == $t) { |
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| 103 | $c[0] = $c[0] & $finalMask; |
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| 104 | } |
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| 105 | return ltrim($c, "\0"); |
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| 106 | }; |
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| 107 | |||
| 108 | $this->instanceID = self::$instanceCounter++; |
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| 109 | Integer::setModulo($this->instanceID, $modulo); |
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| 110 | Integer::setRecurringModuloFunction($this->instanceID, $reduce); |
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| 111 | |||
| 112 | $this->randomMax = new BigInteger($modulo, 2); |
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| 113 | } |
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| 114 | |||
| 115 | /** |
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| 116 | * Returns an instance of a dynamically generated PrimeFieldInteger class |
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| 117 | * |
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| 118 | * @param string $num |
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| 119 | * @return Integer |
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| 120 | */ |
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| 121 | public function newInteger($num) |
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| 122 | { |
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| 123 | return new Integer($this->instanceID, $num instanceof BigInteger ? $num->toBytes() : $num); |
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| 124 | } |
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| 125 | |||
| 126 | /** |
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| 127 | * Returns an integer on the finite field between one and the prime modulo |
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| 128 | * |
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| 129 | * @return Integer |
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| 130 | */ |
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| 131 | public function randomInteger() |
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| 132 | { |
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| 133 | static $one; |
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| 134 | if (!isset($one)) { |
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| 135 | $one = new BigInteger(1); |
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| 136 | } |
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| 137 | |||
| 138 | return new Integer($this->instanceID, BigInteger::randomRange($one, $this->randomMax)->toBytes()); |
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| 139 | } |
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| 140 | |||
| 141 | /** |
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| 142 | * Returns the length of the modulo in bytes |
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| 143 | * |
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| 144 | * @return int |
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| 145 | */ |
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| 146 | public function getLengthInBytes() |
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| 147 | { |
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| 148 | return strlen(Integer::getModulo($this->instanceID)); |
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| 149 | } |
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| 150 | |||
| 151 | /** |
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| 152 | * Returns the length of the modulo in bits |
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| 153 | * |
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| 154 | * @return int |
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| 155 | */ |
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| 156 | public function getLength() |
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| 157 | { |
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| 158 | return strlen(Integer::getModulo($this->instanceID)) << 3; |
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| 159 | } |
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| 160 | |||
| 161 | /** |
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| 162 | * Converts a base-2 string to a base-256 string |
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| 163 | * |
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| 164 | * @param string $x |
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| 165 | * @param int|null $size |
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| 166 | * @return string |
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| 167 | */ |
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| 168 | public static function base2ToBase256($x, $size = null) |
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| 169 | { |
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| 170 | $str = Strings::bits2bin($x); |
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| 171 | |||
| 172 | $pad = strlen($x) >> 3; |
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| 173 | if (strlen($x) & 3) { |
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| 174 | $pad++; |
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| 175 | } |
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| 176 | $str = str_pad($str, $pad, "\0", STR_PAD_LEFT); |
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| 177 | if (isset($size)) { |
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| 178 | $str = str_pad($str, $size, "\0", STR_PAD_LEFT); |
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| 179 | } |
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| 180 | |||
| 181 | return $str; |
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| 182 | } |
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| 183 | |||
| 184 | /** |
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| 185 | * Converts a base-256 string to a base-2 string |
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| 186 | * |
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| 187 | * @param string $x |
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| 188 | * @return string |
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| 189 | */ |
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| 190 | public static function base256ToBase2($x) |
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| 191 | { |
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| 192 | if (function_exists('gmp_import')) { |
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| 193 | return gmp_strval(gmp_import($x), 2); |
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| 194 | } |
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| 195 | |||
| 196 | return Strings::bin2bits($x); |
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| 197 | } |
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| 198 | } |