This class contains utility methods for performing mathematical operations over * the Galois Fields. Operations use a given primitive polynomial in calculations.

* *

Throughout this package, elements of the GF are represented as an {@code int} * for convenience and speed (but at the cost of memory). *

* * @author Sean Owen * @author David Olivier */ final class GenericGF { public static $AZTEC_DATA_12; public static $AZTEC_DATA_10; public static $AZTEC_DATA_6; public static $AZTEC_PARAM; public static $QR_CODE_FIELD_256; public static $DATA_MATRIX_FIELD_256; public static $AZTEC_DATA_8; public static $MAXICODE_FIELD_64; private $expTable; private $logTable; private $zero; private $one; private $size; private $primitive; private $generatorBase; /** * Create a representation of GF(size) using the given primitive polynomial. * * @param primitive irreducible polynomial whose coefficients are represented by * the bits of an int, where the least-significant bit represents the constant * coefficient * @param size the size of the field * @param b the factor b in the generator polynomial can be 0- or 1-based * (g(x) = (x+a^b)(x+a^(b+1))...(x+a^(b+2t-1))). * In most cases it should be 1, but for QR code it is 0. */ public function __construct($primitive, $size, $b) { $this->primitive = $primitive; $this->size = $size; $this->generatorBase = $b; $this->expTable = []; $this->logTable = []; $x = 1; for ($i = 0; $i < $size; $i++) { $this->expTable[$i] = $x; $x *= 2; // we're assuming the generator alpha is 2 if ($x >= $size) { $x ^= $primitive; $x &= $size - 1; } } for ($i = 0; $i < $size - 1; $i++) { $this->logTable[$this->expTable[$i]] = $i; } // logTable[0] == 0 but this should never be used $this->zero = new GenericGFPoly($this, [0]); $this->one = new GenericGFPoly($this, [1]); } public static function Init() { self::$AZTEC_DATA_12 = new GenericGF(0x1069, 4096, 1); // x^12 + x^6 + x^5 + x^3 + 1 self::$AZTEC_DATA_10 = new GenericGF(0x409, 1024, 1); // x^10 + x^3 + 1 self::$AZTEC_DATA_6 = new GenericGF(0x43, 64, 1); // x^6 + x + 1 self::$AZTEC_PARAM = new GenericGF(0x13, 16, 1); // x^4 + x + 1 self::$QR_CODE_FIELD_256 = new GenericGF(0x011D, 256, 0); // x^8 + x^4 + x^3 + x^2 + 1 self::$DATA_MATRIX_FIELD_256 = new GenericGF(0x012D, 256, 1); // x^8 + x^5 + x^3 + x^2 + 1 self::$AZTEC_DATA_8 = self::$DATA_MATRIX_FIELD_256; self::$MAXICODE_FIELD_64 = self::$AZTEC_DATA_6; } /** * Implements both addition and subtraction -- they are the same in GF(size). * * @return sum/difference of a and b */ public static function addOrSubtract($a, $b) { return $a ^ $b; } public function getZero() { return $this->zero; } public function getOne() { return $this->one; } /** * @return the monomial representing coefficient * x^degree */ public function buildMonomial($degree, $coefficient) { if ($degree < 0) { throw new \InvalidArgumentException(); } if ($coefficient == 0) { return $this->zero; } $coefficients = fill_array(0, $degree + 1, 0);//new int[degree + 1]; $coefficients[0] = $coefficient; return new GenericGFPoly($this, $coefficients); } /** * @return 2 to the power of a in GF(size) */ public function exp($a) { return $this->expTable[$a]; } /** * @return base 2 log of a in GF(size) */ public function log($a) { if ($a == 0) { throw new \InvalidArgumentException(); } return $this->logTable[$a]; } /** * @return multiplicative inverse of a */ public function inverse($a) { if ($a == 0) { throw new \Exception(); } return $this->expTable[$this->size - $this->logTable[$a] - 1]; } /** * @return int product of a and b in GF(size) */ public function multiply($a, $b) { if ($a == 0 || $b == 0) { return 0; } return $this->expTable[($this->logTable[$a] + $this->logTable[$b]) % ($this->size - 1)]; } public function getSize() { return $this->size; } public function getGeneratorBase() { return $this->generatorBase; } // @Override public function toString() { return "GF(0x" . dechex((int)($this->primitive)) . ',' . $this->size . ')'; } } GenericGF::Init();