Glossary · Definition
Password entropy
Password entropy measures randomness in bits. Formula: <code>log2(pool_size) × length</code>. 80 bits is the modern minimum for unfeasible brute-forcing; 128+ bits is best practice. Length wins over complexity: 20 lowercase letters (94 bits) beats 10-char symbol soup (66 bits).
Definition
Password entropy measures randomness in bits. Formula: <code>log2(pool_size) × length</code>. 80 bits is the modern minimum for unfeasible brute-forcing; 128+ bits is best practice. Length wins over complexity: 20 lowercase letters (94 bits) beats 10-char symbol soup (66 bits).
What it means
Brute-forcing tries every possible password. With N possibilities, average effort is N/2 attempts. Modern GPUs do ~50-100 billion guesses/second on common hashes (MD5, SHA-1, fast hashes). Slow hashes (bcrypt, Argon2id with strong work factors) are 100,000x slower — still vulnerable to weak passwords. <strong>Entropy thresholds</strong>: 40-50 bits: cracked in seconds. 60-70 bits: cracked in hours-days. 80 bits: infeasible for individual attackers (years). 100+ bits: infeasible for state actors. 128+ bits: infeasible for any imaginable attacker. Length matters more than complexity because length adds bits multiplicatively. <strong>Entropy by length</strong> (assuming all 4 character classes, ~94 chars): 8 chars = 52 bits, 12 = 79, 16 = 105, 20 = 131, 24 = 157.
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Formula
entropy_bits = log2(pool_size) × length
Why it matters
Password strength meters (zxcvbn, owasp) estimate entropy and crack time. Real-world attacks: credential stuffing (using leaked password lists) defeats short passwords. Targeted attacks (state actors, dedicated cracking rigs) can break 60-70 bit passwords. For master passwords on password managers, 100+ bits is essential — that’s the only password between an attacker and ALL your accounts. Length-based entropy + truly random characters from a CSPRNG (Web Crypto getRandomValues) is the gold standard.
Example
16-char all-lowercase: log2(26) × 16 = 75 bits (borderline). 16-char mixed-case + digits: log2(62) × 16 = 95 bits (strong). 20-char with all symbols: log2(94) × 20 = 131 bits (extremely strong). Adding more length is always more efficient than adding character classes.
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Frequently asked questions
Is 12-char password enough?
12 chars with all 4 classes = 79 bits. Borderline acceptable for low-stakes accounts; not enough for master passwords or banking. Use 16+ chars for sensitive accounts.
Why is length better than complexity?
Each added character multiplies pool^length. Adding character classes only multiplies pool size additively. 20 lowercase chars (94 bits) > 10 random chars from all classes (66 bits).
What about diceware passphrases?
Each random word from a 7,776-word list adds ~13 bits. 6-word passphrase: 78 bits (passable). 7-word: 91 bits (strong). Easier to memorize than random characters.