Encryption Key Length Security Estimator

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Encryption Key Length Security Estimator

Evaluate the security strength of encryption keys based on algorithm type, key length, and estimated attack resources. Compares symmetric and asymmetric key strengths using NIST-recommended equivalence tables.

Algorithm Type

Symmetric (AES, 3DES, etc.) Asymmetric RSA / DH / DSA Elliptic Curve (ECC / ECDSA)

Key Length (bits)

Attacker Capability

Nation-State (10¹² ops/sec) Well-Funded (10¹⁰ ops/sec) Moderate (10⁸ ops/sec) Limited (10⁶ ops/sec)

Target Security Year

Estimate Security

Results will appear here.

function encUpdateKeyOptions() { var algo = document.getElementById('enc-algo-type').value; var keyInput = document.getElementById('enc-key-length'); if (algo === 'symmetric') { keyInput.value = 256; keyInput.placeholder = 'e.g. 128, 192, 256'; } else if (algo === 'rsa') { keyInput.value = 2048; keyInput.placeholder = 'e.g. 1024, 2048, 4096'; } else if (algo === 'ecc') { keyInput.value = 256; keyInput.placeholder = 'e.g. 192, 256, 384, 521'; } }

function encCalc() { var algo = document.getElementById('enc-algo-type').value; var keyLen = parseFloat(document.getElementById('enc-key-length').value); var attackerOps = parseFloat(document.getElementById('enc-attacker').value); var targetYear = parseInt(document.getElementById('enc-year').value); var resultDiv = document.getElementById('enc-result');

// --- Input Validation --- if (isNaN(keyLen) || keyLen ⚠ Key length must be a positive integer.'; return; } if (isNaN(targetYear) || targetYear 2100) { resultDiv.innerHTML = '⚠ Target year must be between 2024 and 2100.'; return; }

// --- Compute Symmetric Security Bits --- // For symmetric: security bits = key length (brute force = 2^n operations) // For RSA/DH: NIST SP 800-57 approximation using sub-exponential complexity // Security bits ≈ 1.923 * (ln(n))^(1/3) * (ln(ln(n)))^(2/3) — General Number Field Sieve // Simplified NIST table mapping used with interpolation // For ECC: security bits ≈ key_length / 2 (Pollard's rho)

var symmetricBits; var algoLabel; var complexityNote;

if (algo === 'symmetric') { symmetricBits = keyLen; algoLabel = 'Symmetric'; complexityNote = 'Brute-force complexity: 2' + keyLen + ' operations'; if (keyLen > 512) { resultDiv.innerHTML = '⚠ Symmetric key lengths above 512 bits are not standard. Please check your input.'; return; } } else if (algo === 'rsa') { // GNFS complexity for RSA: exp((1.923 + o(1)) * (ln n)^(1/3) * (ln ln n)^(2/3)) // Security bits = log2 of GNFS complexity // Using NIST SP 800-57 Part 1 Rev 5 Table 2 values with interpolation if (keyLen ⚠ RSA key length must be at least 512 bits (though 512-bit RSA is broken).'; return; } if (keyLen > 32768) { resultDiv.innerHTML = '⚠ RSA key length above 32768 bits is impractical.'; return; } // GNFS security estimate: security_bits = log2(exp(1.923 * (nln2)^(1/3) * (ln(nln2))^(2/3))) // where n = key length in bits var lnN = keyLen * Math.log(2); // ln of the modulus value (approx n * ln2 for bit length) var gnfsExponent = 1.923 * Math.pow(lnN, 1/3) * Math.pow(Math.log(lnN), 2/3); symmetricBits = gnfsExponent / Math.log(2); // convert nats to bits algoLabel = 'RSA/DH/DSA'; complexityNote = 'GNFS complexity: exp(1.923 × (ln N)1/3 × (ln ln N)2/3) ≈ 2' + symmetricBits.toFixed(1) + ''; } else if (algo === 'ecc') { // Pollard's rho: security bits = key_length / 2 if (keyLen ⚠ ECC key length must be at least 112 bits.'; return; } if (keyLen > 8192) { resultDiv.innerHTML = '⚠ ECC key length above 8192 bits is impractical.'; return; } symmetricBits = keyLen / 2; algoLabel = 'ECC/ECDSA'; complexityNote = "Pollard's ρ complexity: 2" + symmetricBits.toFixed(1) + ' operations'; }

// --- Moore's Law Adjustment --- // Computing power doubles roughly every 2 years (Moore's Law) // Effective security degrades by ~0.5 bits/year var currentYear = 2024; var yearsAhead = targetYear - currentYear; var mooreAdjustment = yearsAhead * 0.5; // bits lost per year var adjustedBits = symmetricBits - mooreAdjustment;

// --- Time to Break Estimate --- // Operations needed = 2^symmetricBits // Time (seconds) = 2^symmetricBits / attackerOps var log2Ops = Math.log2(attackerOps); var timeLog2Seconds = symmetricBits - log2Ops;

// Convert to human-readable time function formatTime(log2Sec) { if (log2Sec 300) return '> 1090 years (effectively unbreakable)'; var minutes = seconds / 60; var hours = minutes / 60; var days = hours / 24; var years = days / 365.25; var universeAge = 1.38e10; // years if (years > universeAge * 1e10) return '> 1020 × age of universe'; if (years > universeAge) return (years / universeAge).toExponential(2) + ' × age of universe'; if (years > 1e9) return (years / 1e9).toExponential(2) + ' billion years'; if (years > 1e6) return (years / 1e6).toExponential(2) + ' million years'; if (years > 1000) return years.toFixed(0) + ' years'; if (days > 1) return days.toFixed(1) + ' days'; if (hours > 1) return hours.toFixed(1) + ' hours'; if (minutes > 1) return minutes.toFixed(1) + ' minutes'; return seconds.toFixed(2) + ' seconds'; }

var timeToBreak = formatTime(timeLog2Seconds);

// --- Security Rating --- var rating, ratingColor, ratingEmoji, nistRec; if (adjustedBits >= 256) { rating = 'Excellent'; ratingColor = '#1a7a1a'; ratingEmoji = '🟢'; nistRec = 'Exceeds NIST recommendations through 2100+'; } else if (adjustedBits >= 128) { rating = 'Strong'; ratingColor = '#2e7d32'; ratingEmoji = '🟢'; nistRec = 'Meets NIST recommendations (128-bit security)'; } else if (adjustedBits >= 112) { rating = 'Adequate'; ratingColor = '#f57f17'; ratingEmoji = '🟡'; nistRec = 'Meets legacy NIST minimum (112-bit); upgrade recommended'; } else if (adjustedBits >= 80) { rating = 'Weak'; ratingColor = '#e65100'; ratingEmoji = '🟠'; nistRec = 'Below NIST minimum; vulnerable to well-funded attackers'; } else { rating = 'Broken / Insecure'; ratingColor = '#b71c1c'; ratingEmoji = '🔴'; nistRec = 'Critically insecure; do not use for sensitive data'; }

// --- NIST Equivalent Key Comparison --- // NIST SP 800-57 symmetric equivalents var nistTable = [ {sym: 80, rsa: 1024, ecc: 160, label: '80-bit (Legacy)'}, {sym: 112, rsa: 2048, ecc: 224, label: '112-bit (Transitional)'}, {sym: 128, rsa: 3072, ecc: 256, label: '128-bit (Standard)'}, {sym: 192, rsa: 7680, ecc: 384, label: '192-bit (High Security)'}, {sym: 256, rsa: 15360, ecc: 521, label: '256-bit (Ultra High)'} ];

var closestNIST = nistTable[0]; for (var i = 0; i = nistTable[i].sym) closestNIST = nistTable[i]; }

// --- Build Result HTML --- var html = '### Security Analysis Results '; html += ''; html += 'Algorithm Type' + algoLabel + ' (' + keyLen + '-bit key)'; html += 'Equivalent Symmetric Strength' + symmetricBits.toFixed(1) + ' bits'; html += 'Complexity' + complexityNote + ''; html += 'Adjusted Strength (' + targetYear + ')' + adjustedBits.toFixed(1) + ' bits (−' + mooreAdjustment.toFixed(1) + ' bits Moore adjustment)'; html += 'Estimated Time to Break' + timeToBreak + ''; html += 'Security Rating' + ratingEmoji + ' ' + rating + ''; html += 'NIST Assessment' + nistRec + ''; html += '';

html += '#### NIST SP 800-57 Equivalent Key Sizes '; html += ''; html += 'Security LevelSymmetricRSA/DHECC'; for (var j = 0; j '; html += '' + nistTable[j].label + marker + ''; html += '' + nistTable[j].sym + ' bits'; html += '' + nistTable[j].rsa + ' bits'; html += '' + nistTable[j].ecc + ' bits'; html += ''; } html += '';

resultDiv.innerHTML = html; }

#### Formulas Used

Symmetric (AES, etc.): Security bits = Key length. Brute-force requires 2n operations.

RSA / DH / DSA (GNFS): Security bits = log2(exp(1.923 × (ln N)1/3 × (ln ln N)2/3)) where N is the modulus value (≈ 2key_length). Based on the General Number Field Sieve algorithm complexity.

ECC / ECDSA (Pollard's ρ): Security bits = key_length / 2. The best known attack (Pollard's rho) requires ~2n/2 operations for an n-bit curve.

Moore's Law Adjustment: Adjusted bits = Security bits − (0.5 × years ahead). Computing power doubles every ~2 years, reducing effective security by ~0.5 bits/year.

Time to Break: T = 2security_bits / attacker_ops_per_second

#### Assumptions & References

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