Learn-Coding/rsa.html at main · mithleshprasad/Learn-Coding · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>RSA Encryption Visualizer</title>
    <style>
        body {
            font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
            margin: 0;
            padding: 20px;
            background-color: #f5f5f5;
            color: #333;
            line-height: 1.6;
        }

        .container {
            max-width: 1000px;
            margin: 0 auto;
        }

        h1, h2, h3 {
            color: #2c3e50;
        }

        .panel {
            background-color: white;
            padding: 20px;
            border-radius: 8px;
            box-shadow: 0 2px 10px rgba(0,0,0,0.1);
            margin-bottom: 20px;
        }

        .control-group {
            margin-bottom: 15px;
        }

        label {
            display: block;
            margin-bottom: 5px;
            font-weight: bold;
        }

        input, select, button {
            padding: 8px 12px;
            border: 1px solid #ddd;
            border-radius: 4px;
            font-size: 16px;
        }

        button {
            background-color: #3498db;
            color: white;
            border: none;
            cursor: pointer;
            transition: background-color 0.3s;
            margin-right: 10px;
        }

        button:hover {
            background-color: #2980b9;
        }

        button:disabled {
            background-color: #95a5a6;
            cursor: not-allowed;
        }

        .step {
            margin: 20px 0;
            padding: 15px;
            background-color: #f8f9fa;
            border-radius: 4px;
            border-left: 4px solid #3498db;
        }

        .math {
            font-family: 'Courier New', monospace;
            background-color: #f0f0f0;
            padding: 2px 5px;
            border-radius: 3px;
        }

        .key-display {
            font-family: monospace;
            background-color: #f0f0f0;
            padding: 10px;
            border-radius: 4px;
            overflow-x: auto;
        }

        .visualization {
            display: flex;
            gap: 20px;
            margin: 20px 0;
        }

        .visual-box {
            flex: 1;
            padding: 15px;
            background-color: #e8f4fc;
            border-radius: 4px;
            text-align: center;
        }

        table {
            width: 100%;
            border-collapse: collapse;
            margin: 15px 0;
        }

        th, td {
            border: 1px solid #ddd;
            padding: 8px;
            text-align: left;
        }

        th {
            background-color: #f2f2f2;
        }

        .prime-candidate {
            display: inline-block;
            padding: 5px;
            margin: 2px;
            border: 1px solid #ddd;
            border-radius: 3px;
        }

        .prime-candidate.prime {
            background-color: #d4edda;
            border-color: #c3e6cb;
        }

        .prime-candidate.not-prime {
            background-color: #f8d7da;
            border-color: #f5c6cb;
        }
    </style>
</head>
<body>
    <div class="container">
        <h1>RSA Encryption Visualizer</h1>

        <div class="panel">
            <h2>Key Generation</h2>

            <div class="control-group">
                <label for="primeRange">Prime Number Range:</label>
                <select id="primeRange">
                    <option value="10">Very Small (3-19)</option>
                    <option value="50" selected>Small (3-53)</option>
                    <option value="100">Medium (3-101)</option>
                </select>
            </div>

            <button id="generatePrimesBtn">Generate Primes</button>
            <button id="generateKeysBtn" disabled>Generate Keys</button>
            <button id="resetBtn">Reset</button>

            <div id="primeGenerationSteps">
                <div class="step" id="primeStep1">
                    <h3>Step 1: Select Two Prime Numbers</h3>
                    <p>First, we need to select two distinct prime numbers (p and q).</p>
                    <div id="primeCandidates"></div>
                </div>

                <div class="step" id="primeStep2" style="display: none;">
                    <h3>Step 2: Calculate n and φ(n)</h3>
                    <p>Compute <span class="math">n = p × q</span> and <span class="math">φ(n) = (p-1) × (q-1)</span></p>
                    <div id="nAndPhiCalculation"></div>
                </div>

                <div class="step" id="primeStep3" style="display: none;">
                    <h3>Step 3: Choose Public Exponent e</h3>
                    <p>Select <span class="math">e</span> such that <span class="math">1 < e < φ(n)</span> and <span class="math">gcd(e, φ(n)) = 1</span></p>
                    <div id="eSelection"></div>
                </div>

                <div class="step" id="primeStep4" style="display: none;">
                    <h3>Step 4: Calculate Private Exponent d</h3>
                    <p>Find <span class="math">d</span> such that <span class="math">d × e ≡ 1 mod φ(n)</span></p>
                    <div id="dCalculation"></div>
                </div>
            </div>
        </div>

        <div class="panel" id="keyPanel" style="display: none;">
            <h2>Generated Keys</h2>
            <div class="visualization">
                <div class="visual-box">
                    <h3>Public Key</h3>
                    <p>(e, n)</p>
                    <div class="key-display" id="publicKey"></div>
                </div>
                <div class="visual-box">
                    <h3>Private Key</h3>
                    <p>(d, n)</p>
                    <div class="key-display" id="privateKey"></div>
                </div>
            </div>
        </div>

        <div class="panel" id="encryptionPanel" style="display: none;">
            <h2>Encryption & Decryption</h2>

            <div class="control-group">
                <label for="messageInput">Message (Number):</label>
                <input type="number" id="messageInput" min="1" value="42">
                <p class="hint">Note: In real RSA, messages are converted to numbers first.</p>
            </div>

            <button id="encryptBtn">Encrypt</button>
            <button id="decryptBtn">Decrypt</button>

            <div id="encryptionSteps">
                <div class="step" id="encryptStep" style="display: none;">
                    <h3>Encryption Process</h3>
                    <p>To encrypt message <span class="math">m</span>, compute:</p>
                    <p><span class="math">c ≡ m<sup>e</sup> mod n</span></p>
                    <div id="encryptionCalculation"></div>
                </div>

                <div class="step" id="decryptStep" style="display: none;">
                    <h3>Decryption Process</h3>
                    <p>To decrypt ciphertext <span class="math">c</span>, compute:</p>
                    <p><span class="math">m ≡ c<sup>d</sup> mod n</span></p>
                    <div id="decryptionCalculation"></div>
                </div>
            </div>
        </div>

        <div class="panel">
            <h2>How RSA Works</h2>
            <h3>Key Generation</h3>
            <ol>
                <li>Choose two distinct prime numbers <span class="math">p</span> and <span class="math">q</span></li>
                <li>Compute <span class="math">n = p × q</span></li>
                <li>Compute <span class="math">φ(n) = (p-1)(q-1)</span></li>
                <li>Choose integer <span class="math">e</span> such that <span class="math">1 < e < φ(n)</span> and <span class="math">gcd(e, φ(n)) = 1</span></li>
                <li>Determine <span class="math">d</span> as modular inverse of <span class="math">e</span> modulo <span class="math">φ(n)</span></li>
            </ol>

            <h3>Encryption</h3>
            <p><span class="math">c ≡ m<sup>e</sup> mod n</span></p>

            <h3>Decryption</h3>
            <p><span class="math">m ≡ c<sup>d</sup> mod n</span></p>

            <h3>Why It Works</h3>
            <p>Euler's theorem guarantees that for any message <span class="math">m</span>:</p>
            <p><span class="math">m<sup>φ(n)</sup> ≡ 1 mod n</span></p>
            <p>Since <span class="math">e × d ≡ 1 mod φ(n)</span>, we have:</p>
            <p><span class="math">(m<sup>e</sup>)<sup>d</sup> ≡ m<sup>e×d</sup> ≡ m<sup>kφ(n)+1</sup> ≡ (m<sup>φ(n)</sup>)<sup>k</sup> × m ≡ m mod n</span></p>
        </div>
    </div>

    <script>
        // DOM Elements
        const primeRange = document.getElementById('primeRange');
        const generatePrimesBtn = document.getElementById('generatePrimesBtn');
        const generateKeysBtn = document.getElementById('generateKeysBtn');
        const resetBtn = document.getElementById('resetBtn');
        const encryptBtn = document.getElementById('encryptBtn');
        const decryptBtn = document.getElementById('decryptBtn');
        const messageInput = document.getElementById('messageInput');

        // RSA State
        let primes = [];
        let p = 0, q = 0;
        let n = 0, phi = 0;
        let e = 0, d = 0;

        // Initialize
        reset();

        // Event Listeners
        generatePrimesBtn.addEventListener('click', generatePrimes);
        generateKeysBtn.addEventListener('click', generateKeys);
        resetBtn.addEventListener('click', reset);
        encryptBtn.addEventListener('click', encrypt);
        decryptBtn.addEventListener('click', decrypt);

        // Reset everything
        function reset() {
            primes = [];
            p = q = n = phi = e = d = 0;

            document.getElementById('primeStep1').style.display = 'block';
            document.getElementById('primeStep2').style.display = 'none';
            document.getElementById('primeStep3').style.display = 'none';
            document.getElementById('primeStep4').style.display = 'none';
            document.getElementById('keyPanel').style.display = 'none';
            document.getElementById('encryptionPanel').style.display = 'none';
            document.getElementById('encryptStep').style.display = 'none';
            document.getElementById('decryptStep').style.display = 'none';

            generatePrimesBtn.disabled = false;
            generateKeysBtn.disabled = true;
        }

        // Generate prime candidates
        function generatePrimes() {
            const range = parseInt(primeRange.value);
            primes = getPrimesUpTo(range);

            const container = document.getElementById('primeCandidates');
            container.innerHTML = '';

            primes.forEach(prime => {
                const elem = document.createElement('div');
                elem.className = 'prime-candidate';
                elem.textContent = prime;
                elem.onclick = function() {
                    if (!p) {
                        p = prime;
                        elem.style.backgroundColor = '#d4edda';
                        document.getElementById('primeStep1').innerHTML +=
                            `<p>Selected p = ${p}</p>`;
                    } else if (!q && prime !== p) {
                        q = prime;
                        elem.style.backgroundColor = '#d4edda';
                        document.getElementById('primeStep1').innerHTML +=
                            `<p>Selected q = ${q}</p>`;
                        generateKeysBtn.disabled = false;
                    }
                };
                container.appendChild(elem);
            });
        }

        // Generate RSA keys
        function generateKeys() {
            // Step 2: Calculate n and φ(n)
            n = p * q;
            phi = (p - 1) * (q - 1);

            document.getElementById('primeStep2').style.display = 'block';
            document.getElementById('nAndPhiCalculation').innerHTML = `
                <p>n = p × q = ${p} × ${q} = <span class="math">${n}</span></p>
                <p>φ(n) = (p-1) × (q-1) = ${p-1} × ${q-1} = <span class="math">${phi}</span></p>
            `;

            // Step 3: Choose e (public exponent)
            e = findCoprime(phi);

            document.getElementById('primeStep3').style.display = 'block';
            document.getElementById('eSelection').innerHTML = `
                <p>Selected e = <span class="math">${e}</span> (coprime with φ(n))</p>
            `;

            // Step 4: Calculate d (private exponent)
            d = modInverse(e, phi);

            document.getElementById('primeStep4').style.display = 'block';
            document.getElementById('dCalculation').innerHTML = `
                <p>Calculated d = <span class="math">${d}</span> (${e} × ${d} ≡ 1 mod ${phi})</p>
            `;

            // Show keys
            document.getElementById('keyPanel').style.display = 'block';
            document.getElementById('publicKey').textContent = `(${e}, ${n})`;
            document.getElementById('privateKey').textContent = `(${d}, ${n})`;

            // Enable encryption panel
            document.getElementById('encryptionPanel').style.display = 'block';
        }

        // Encrypt message
        function encrypt() {
            const m = parseInt(messageInput.value);
            if (m >= n) {
                alert(`Message must be less than n (${n})`);
                return;
            }

            const c = modExp(m, e, n);

            document.getElementById('encryptStep').style.display = 'block';
            document.getElementById('encryptionCalculation').innerHTML = `
                <p>c ≡ m<sup>e</sup> mod n ≡ ${m}<sup>${e}</sup> mod ${n}</p>
                <p>c ≡ ${c} mod ${n}</p>
                <p>Ciphertext: <span class="math">${c}</span></p>
            `;
        }

        // Decrypt message
        function decrypt() {
            const c = parseInt(messageInput.value);

            const m = modExp(c, d, n);

            document.getElementById('decryptStep').style.display = 'block';
            document.getElementById('decryptionCalculation').innerHTML = `
                <p>m ≡ c<sup>d</sup> mod n ≡ ${c}<sup>${d}</sup> mod ${n}</p>
                <p>m ≡ ${m} mod ${n}</p>
                <p>Decrypted message: <span class="math">${m}</span></p>
            `;
        }

        // Helper functions

        // Sieve of Eratosthenes to find primes up to max
        function getPrimesUpTo(max) {
            const sieve = new Array(max + 1).fill(true);
            sieve[0] = sieve[1] = false;

            for (let i = 2; i <= Math.sqrt(max); i++) {
                if (sieve[i]) {
                    for (let j = i * i; j <= max; j += i) {
                        sieve[j] = false;
                    }
                }
            }

            return sieve.map((isPrime, num) => isPrime ? num : 0).filter(num => num > 1);
        }

        // Find a number coprime with phi (usually 65537 is used in practice)
        function findCoprime(phi) {
            // Try common values first
            const commonEs = [3, 5, 17, 257, 65537];
            for (let candidate of commonEs) {
                if (candidate < phi && gcd(candidate, phi) === 1) {
                    return candidate;
                }
            }

            // If no common values work, find the smallest possible
            for (let i = 2; i < phi; i++) {
                if (gcd(i, phi) === 1) {
                    return i;
                }
            }

            return 0;
        }

        // Greatest Common Divisor (Euclidean algorithm)
        function gcd(a, b) {
            while (b !== 0) {
                [a, b] = [b, a % b];
            }
            return a;
        }

        // Modular inverse (extended Euclidean algorithm)
        function modInverse(a, m) {
            let [oldR, r] = [a, m];
            let [oldS, s] = [1, 0];
            let [oldT, t] = [0, 1];

            while (r !== 0) {
                const quotient = Math.floor(oldR / r);
                [oldR, r] = [r, oldR - quotient * r];
                [oldS, s] = [s, oldS - quotient * s];
                [oldT, t] = [t, oldT - quotient * t];
            }

            return oldS < 0 ? oldS + m : oldS;
        }

        // Modular exponentiation (for large numbers)
        function modExp(base, exp, mod) {
            let result = 1;
            base = base % mod;

            while (exp > 0) {
                if (exp % 2 === 1) {
                    result = (result * base) % mod;
                }
                exp = Math.floor(exp / 2);
                base = (base * base) % mod;
            }

            return result;
        }
    </script>
</body>
</html>