Michael Schiemer
95147ff23e
Remove WireGuard integration from production deployment to simplify infrastructure: - Remove docker-compose-direct-access.yml (VPN-bound services) - Remove VPN-only middlewares from Grafana, Prometheus, Portainer - Remove WireGuard middleware definitions from Traefik - Remove WireGuard IPs (10.8.0.0/24) from Traefik forwarded headers All monitoring services now publicly accessible via subdomains: - grafana.michaelschiemer.de (with Grafana native auth) - prometheus.michaelschiemer.de (with Basic Auth) - portainer.michaelschiemer.de (with Portainer native auth) All services use Let's Encrypt SSL certificates via Traefik.
113 lines
3.5 KiB
PHP
113 lines
3.5 KiB
PHP
<?php
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declare(strict_types=1);
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echo "=== Syndrome Formula Test ===\n\n";
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// For Reed-Solomon, syndromes are calculated as:
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// S[i] = c(α^i) where c(x) is the codeword polynomial
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// c(x) = c[0] + c[1]*x + c[2]*x^2 + ... + c[n-1]*x^(n-1)
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// S[i] = sum over j: c[j] * (α^i)^j
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// Initialize GF(256)
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$gfLog = array_fill(0, 256, 0);
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$gfExp = array_fill(0, 512, 0);
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$x = 1;
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for ($i = 0; $i < 255; $i++) {
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$gfExp[$i] = $x;
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$gfLog[$x] = $i;
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$x <<= 1;
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if ($x & 0x100) {
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$x ^= 0x11d;
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}
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}
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for ($i = 255; $i < 512; $i++) {
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$gfExp[$i] = $gfExp[$i - 255];
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}
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function gfMult(array $gfExp, array $gfLog, int $a, int $b): int
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{
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if ($a === 0 || $b === 0) return 0;
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return $gfExp[$gfLog[$a] + $gfLog[$b]];
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}
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// Test with a known valid codeword
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// For RS(7, 4), if data = [1, 2, 3, 4] and generator = [1, 7, 14, 8]
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// We need to calculate the correct EC codewords
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echo "Testing syndrome calculation:\n";
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echo "For a valid RS codeword, all syndromes should be 0.\n\n";
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// Try with a simple case: data = [1], ecCodewords = 2
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// Generator: g(x) = (x-1)(x-2) = x^2 + 3x + 2
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// But in GF(256), we need to use α^i values
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// Actually, let's use the correct generator polynomial from specification
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// For 10 EC codewords: [0, 251, 67, 46, 61, 118, 70, 64, 94, 32, 45]
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// This means: g(x) = x^10 + 251*x^9 + 67*x^8 + ... + 45
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// The key insight: For the codeword to be valid, when we evaluate it at
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// the roots of the generator (α^0, α^1, ..., α^9), we should get 0.
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// But wait - maybe the issue is that we're evaluating at the wrong powers?
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// In RS, we evaluate at α^0, α^1, ..., α^(t-1) where t is the number of EC codewords.
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echo "Note: Syndrome calculation evaluates c(x) at α^0, α^1, ..., α^(t-1)\n";
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echo "where c(x) = c[0] + c[1]*x + c[2]*x^2 + ... + c[n-1]*x^(n-1)\n";
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echo "and c[0] is the FIRST codeword (highest power)\n";
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echo "OR c[n-1] is the FIRST codeword (lowest power)?\n\n";
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echo "This is the key question - what is the polynomial representation?\n";
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echo "In QR codes, codewords are placed MSB-first, so:\n";
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echo " c[0] is the coefficient of x^(n-1) (highest power)\n";
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echo " c[n-1] is the coefficient of x^0 (lowest power)\n\n";
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echo "So the polynomial is: c(x) = c[0]*x^(n-1) + c[1]*x^(n-2) + ... + c[n-1]*1\n";
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echo "When evaluating at α^i, we need: c(α^i) = sum(c[j] * (α^i)^(n-1-j))\n\n";
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// Test with reversed order
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echo "=== Testing Reversed Evaluation ===\n";
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$codeword = [64, 180, 132, 84, 196, 196, 242, 5, 116, 245, 36, 196, 64, 236, 17, 236, 48, 24, 202, 227, 36, 252, 121, 15, 219, 141];
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$n = count($codeword);
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$t = 10;
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echo "Codeword length: {$n}\n";
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echo "EC codewords: {$t}\n\n";
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$syndromes = [];
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for ($i = 0; $i < $t; $i++) {
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$alphaPower = $gfExp[$i]; // α^i
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$syndrome = 0;
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// Evaluate: c(x) = c[0]*x^(n-1) + c[1]*x^(n-2) + ... + c[n-1]
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// At x = α^i: c(α^i) = sum(c[j] * (α^i)^(n-1-j))
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$power = $gfExp[$i * ($n - 1) % 255]; // (α^i)^(n-1)
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for ($j = 0; $j < $n; $j++) {
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$syndrome ^= gfMult($gfExp, $gfLog, $codeword[$j], $power);
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// Next power: (α^i)^(n-2-j) = current_power / α^i
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$power = gfMult($gfExp, $gfLog, $power, $gfExp[255 - $i]); // Divide by α^i
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}
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$syndromes[$i] = $syndrome;
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echo " S[{$i}] = {$syndrome}\n";
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}
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$allZero = true;
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foreach ($syndromes as $s) {
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if ($s !== 0) {
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$allZero = false;
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break;
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}
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}
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if ($allZero) {
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echo "\n✅ All syndromes are zero with reversed evaluation!\n";
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} else {
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echo "\n❌ Still not all zero\n";
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}
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