PHP code example of guillaumetissier / galois-fields

    
        
<?php
require_once('vendor/autoload.php');

/* Start to develop here. Best regards https://php-download.com/ */

    

guillaumetissier / galois-fields example snippets

use Guillaumetissier\GaloisFields\GaloisField;

// Create GF(256) - used in QR codes
$gf256 = new GaloisField(256);

// Basic operations
$sum = $gf256->add(123, 45);        // Addition (XOR for binary fields)
$product = $gf256->multiply(53, 78); // Multiplication
$quotient = $gf256->divide(200, 17);  // Division
$inverse = $gf256->inverse(123);      // Multiplicative inverse

// Check field properties
echo $gf256->getOrder();              // 256
echo $gf256->getCharacteristic();     // 2
echo $gf256->getDegree();             // 8

// Create GF(7)
$gf7 = new GaloisField(7);

// All operations work modulo 7
echo $gf7->add(5, 3);        // 1  (8 mod 7)
echo $gf7->multiply(4, 2);   // 1  (8 mod 7)
echo $gf7->power(3, 2);      // 2  (9 mod 7)

// Every non-zero element has an inverse
echo $gf7->multiply(3, $gf7->inverse(3)); // 1

$gf = new GaloisField(256);

// Reed-Solomon error correction uses GF(256)
// Polynomial evaluation in GF(256)
function evaluatePolynomial(GaloisField $gf, array $coefficients, int $x): int {
    $result = 0;
    foreach ($coefficients as $coeff) {
        $result = $gf->add($gf->multiply($result, $x), $coeff);
    }
    return $result;
}

$polynomial = [1, 2, 3]; // 1*x^2 + 2*x + 3
$value = evaluatePolynomial($gf, $polynomial, 5);

// Small fields
$gf4 = new GaloisField(4);    // GF(2^2)
$gf8 = new GaloisField(8);    // GF(2^3)
$gf16 = new GaloisField(16);  // GF(2^4)

// Medium fields
$gf256 = new GaloisField(256);   // GF(2^8) - QR codes
$gf65536 = new GaloisField(65536); // GF(2^16) - 

$gf = new GaloisField(256);

// Get detailed information
$info = $gf->getInfo();
print_r($info);
// Output:
// [
//     'order' => 256,
//     'characteristic' => 2,
//     'degree' => 8,
//     'notation' => 'GF(2^8)'
// ]

// Validate elements
$gf->isValidElement(123);  // true
$gf->isValidElement(256);  // false (out of range)