Encryption Key Strength Calculator

ANA›Life Services Authority›National Calculator Authority›Encryption Key Strength Calculator

.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }

Encryption Key Strength Calculator

Evaluate the strength of encryption keys based on algorithm type, key length, and attacker capability. Estimates security bits and time-to-crack using standard cryptographic models.

Algorithm Type

Symmetric (AES, ChaCha20) Asymmetric RSA / DH Elliptic Curve (ECC) Hash / HMAC Key

Key Length (bits)

Attacker Capability

Script Kiddie — 10⁹ ops/sec (consumer GPU) Organized — 10¹² ops/sec (botnet / ASIC) Nation-State — 10¹⁵ ops/sec (dedicated hardware) Quantum Adversary — 10¹⁸ ops/sec (theoretical)

Quantum Threat Model

Classical computers only Include Grover / Shor quantum attacks

Calculate Strength

Results will appear here.

function encUpdateFields() { // Could show/hide hints per algorithm — kept simple for now }

function encCalc() { const algorithm = document.getElementById('enc-algorithm').value; const keyLength = parseFloat(document.getElementById('enc-keylength').value); const attackerOps = parseFloat(document.getElementById('enc-attacker').value); const quantum = document.getElementById('enc-quantum').value; const resultDiv = document.getElementById('enc-result');

// ── Input validation ────────────────────────────────────────────────────── if (isNaN(keyLength) || keyLength ⚠ Key length must be a positive integer (e.g. 128, 256, 4096).'; return; } if (keyLength > 65536) { resultDiv.innerHTML = '⚠ Key length exceeds practical maximum of 65 536 bits.'; return; }

// ── Security-bit model ──────────────────────────────────────────────────── // References: // NIST SP 800-57 Part 1 Rev 5 (2020) — Table 2 & 4 // Lenstra–Verheul (2001) RSA/DH security-bit formula // ECRYPT-CSA D5.4 (2018) — ECC security bits = key_bits / 2 // Grover's algorithm halves symmetric security bits // Shor's algorithm breaks RSA/ECC in polynomial time

let securityBits = 0; let algorithmLabel = ''; let quantumNote = ''; let classicalOps = 0; // operations needed for brute-force

if (algorithm === 'symmetric') { // Exhaustive key search: 2^n operations (birthday bound not applicable here) securityBits = keyLength; algorithmLabel = 'Symmetric'; classicalOps = Math.pow(2, securityBits);

if (quantum === 'yes') { // Grover's algorithm: O(2^(n/2)) quantum operations securityBits = keyLength / 2; quantumNote = 'Grover's algorithm reduces effective security to n/2 bits. AES-256 → 128-bit quantum security (still safe). AES-128 → 64-bit (marginal).'; classicalOps = Math.pow(2, securityBits); }

} else if (algorithm === 'rsa') { // NIST SP 800-57 Table 2 / Lenstra-Verheul approximation: // Security bits ≈ 1.923 * (ln(n))^(1/3) * (ln(ln(n)))^(2/3) — GNFS complexity // Simplified NIST mapping used for practical display: // 1024-bit RSA ≈ 80 bits, 2048 ≈ 112, 3072 ≈ 128, 7680 ≈ 192, 15360 ≈ 256 // Formula: secBits ≈ 1.923 * cbrt(ln(n)) * (ln(ln(n)))^(2/3) [in nats, scaled] const ln_n = Math.log(keyLength); const ln_ln_n = Math.log(ln_n); // GNFS sub-exponential: L[n, 1/3, 1.923] — result in bits // Full formula: exp(1.923 * (ln n)^(1/3) * (ln ln n)^(2/3)) operations // Security bits = log2 of that operation count const log2e = Math.LOG2E; securityBits = Math.round(log2e * 1.923 * Math.pow(ln_n, 1/3) * Math.pow(ln_ln_n, 2/3)); algorithmLabel = 'RSA / DH'; classicalOps = Math.pow(2, securityBits);

if (quantum === 'yes') { // Shor's algorithm breaks RSA in polynomial time — effectively 0 classical security securityBits = 0; quantumNote = 'Shor's algorithm solves integer factorization in polynomial time. RSA/DH provides NO security against a cryptographically relevant quantum computer. Migrate to post-quantum algorithms (CRYSTALS-Kyber, CRYSTALS-Dilithium).'; classicalOps = 1; }

} else if (algorithm === 'ecc') { // NIST SP 800-57 Table 2: ECC security bits = key_bits / 2 // (Pollard's rho attack on ECDLP: O(2^(n/2)) operations) securityBits = keyLength / 2; algorithmLabel = 'Elliptic Curve (ECC)'; classicalOps = Math.pow(2, securityBits);

if (quantum === 'yes') { // Shor's algorithm also solves ECDLP in polynomial time securityBits = 0; quantumNote = 'Shor's algorithm solves the Elliptic Curve Discrete Logarithm Problem (ECDLP) in polynomial time. ECC provides NO security against a cryptographically relevant quantum computer. Migrate to CRYSTALS-Kyber / CRYSTALS-Dilithium (NIST PQC standards).'; classicalOps = 1; }

} else if (algorithm === 'hash') { // HMAC / hash key: collision resistance = n/2 bits (birthday), preimage = n bits // For key strength (preimage resistance): securityBits = keyLength securityBits = keyLength; algorithmLabel = 'Hash / HMAC Key'; classicalOps = Math.pow(2, securityBits);

if (quantum === 'yes') { // Grover halves preimage resistance securityBits = keyLength / 2; quantumNote = 'Grover's algorithm reduces preimage resistance to n/2 bits. SHA-256 HMAC → 128-bit quantum security (acceptable). SHA-1 HMAC → 80-bit (deprecated).'; classicalOps = Math.pow(2, securityBits); } }

// ── Time-to-crack ───────────────────────────────────────────────────────── // seconds = operations / ops_per_second // Use log10 arithmetic to avoid Infinity for large exponents const log10_ops = securityBits * Math.log10(2); // log10(classicalOps) const log10_attacker = Math.log10(attackerOps); const log10_seconds = log10_ops - log10_attacker;

// Convert seconds to human-readable
function formatTime(log10_sec) {
if (log10_sec ⚛ Quantum Impact${quantumNote}`
'';

resultDiv.innerHTML = ` ### ${ratingIcon} Key Strength: ${rating}

Algorithm ${algorithmLabel} — ${keyLength}-bit key Effective Security Bits ${securityBits} bits Operations to Crack 2${securityBits} ≈ 10${(securityBits * Math.log10(2)).toFixed(1)} Estimated Crack Time ${crackTime} Attacker Speed ${attackerOps.toExponential(0)} operations/second ${quantumSection} NIST Guidance ${nistRec} `; }

#### Formulas Used

Symmetric (AES / ChaCha20): Security bits = n (key length). Brute-force requires 2n operations. With Grover's quantum algorithm: Security bits = n / 2.

RSA / Diffie-Hellman: Security bits ≈ log₂(exp(1.923 · (ln n)1/3 · (ln ln n)2/3)) Based on General Number Field Sieve (GNFS) sub-exponential complexity L[n, 1/3, 1.923]. With Shor's quantum algorithm: Security bits = 0 (broken in polynomial time).

Elliptic Curve (ECC): Security bits = n / 2 (Pollard's rho attack on ECDLP: O(2n/2) operations). With Shor's quantum algorithm: Security bits = 0 (broken in polynomial time).

Hash / HMAC Key: Security bits = n (preimage resistance). With Grover: Security bits = n / 2.

Time to Crack: T = 2security_bits / attacker_ops_per_second (seconds)

#### Assumptions & References

More Calculators

Read Next

Study Time Planner Authority Network America › Life Services Authority › National Calculator Authority .calc-container { max-width: 640px;...

References

Related Authorities

Life Services Authority › Professional Services Authority › Trade Services Authority › United States Authority ›