How to Generate Strong Random Passwords
Password generation requires cryptographic randomness and careful character selection. This guide covers the principles behind strong password generation, entropy calculation, and common generation mistakes to avoid.
Key Takeaways
- Password strength is measured in entropy — the number of bits of randomness.
- Entropy = log2(character_set_size ^ password_length)
- Never use `Math.random()` or similar pseudo-random functions for password generation.
- Random word passphrases (like "correct horse battery staple") offer high entropy while being memorizable.
- Using common substitutions (p@ssw0rd) — these are in every cracking dictionary.
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What Makes a Password Strong?
Password strength is measured in entropy — the number of bits of randomness. Higher entropy means more possible combinations, making brute-force attacks impractical.
Entropy Calculation
Entropy = log2(character_set_size ^ password_length)
| Character Set | Pool Size | 12-char Entropy | 16-char Entropy |
|---|---|---|---|
| Lowercase only | 26 | 56 bits | 75 bits |
| Mixed case | 52 | 68 bits | 91 bits |
| Mixed + digits | 62 | 71 bits | 95 bits |
| Mixed + digits + symbols | 95 | 79 bits | 105 bits |
A password with 80+ bits of entropy is considered strong for most purposes.
Cryptographic Randomness
Never use Math.random() or similar pseudo-random functions for password generation. These are predictable. Use cryptographically secure random number generators (CSPRNG):
- JavaScript:
crypto.getRandomValues() - Python:
secretsmodule - Node.js:
crypto.randomBytes()
Passphrase Alternative
Random word passphrases (like "correct horse battery staple") offer high entropy while being memorizable. A 4-word passphrase from a 7776-word list (Diceware) provides 51 bits of entropy; 6 words provides 77 bits.
Common Mistakes
- Using common substitutions (p@ssw0rd) — these are in every cracking dictionary.
- Truncating generated passwords to meet site limits (reduces entropy).
- Generating passwords that don't meet the site's character requirements.
- Using non-cryptographic random sources.
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