7.2 Strong Passphrases and Password Managers
Entropy Is a Number, Not a Feeling
Strength is measured in bits of entropy: the base-2 logarithm of the effective guess space. Eight characters drawn uniformly from 95 printable ASCII characters gives 8 x log2(95) ≈ 52.5 bits. But humans do not draw uniformly; studies of millions of leaked passwords show an 8-character human pick carries roughly 30 bits of real entropy, because everyone picks names, seasons, and 1! suffixes. The EFF wordlist has 7,776 words, so each randomly chosen word contributes log2(7,776) ≈ 12.9 bits: four words ≈ 52 bits, five words ≈ 65 bits. A dice-generated five-word passphrase therefore matches or beats a “complex” 8-character pick while remaining typeable from memory.
Threat Model Changes the Threshold
Bits only mean something against a guessing rate. Against a login endpoint throttled to ten guesses per second, 2^52 guesses is around 14 million years — a four-word passphrase is effectively unbreakable online. Offline against a fast unsalted hash at 10^11 guesses per second, the same 52 bits falls in hours. The practical reading: passphrases defeat online guessing and lockout-dodging spray attacks, while the server’s memory-hard hashing (Argon2id) is what keeps offline cracking slow. You control one half; pick a long memorable phrase.
The Vault Handles the Other Half: Uniqueness
Memorability caps at one or two high-entropy secrets, so the remaining N accounts need machine-generated 20-to-30-character random strings — 130+ bits each — stored in a client-side-encrypted vault. You memorize a single master passphrase; the vault derives its encryption key locally with a memory-hard KDF and never transmits it. Autocomplete fills credentials only on an exact domain match, so the vault silently refuses to type your banking secret into bank-secure-login.example.net — a side benefit that defeats large classes of phishing, and it stops keyloggers from ever seeing the site password typed.
Build the Master Passphrase Right
Choose random words, not clever mangling: rule engines crack Tr0ub4dor&3 faster than four random words because mangling patterns are exactly what rules model. Separators and capitalization add only a handful of bits — word count does the work. Set the vault itself to require a hardware key or app-based factor on new devices, keep encrypted emergency exports offline, and treat any password you ever type into a website as potentially public.
Architecture Diagram
Key Takeaways
- Entropy is measurable: 4 random dictionary words ≈ 52 bits, five words ≈ 65, a 20-char random string ≈ 131.
- Human picks lose about half their theoretical bits to predictable patterns — randomness must come from dice or a generator.
- Long passphrases defeat online guessing and spray attempts; server-side Argon2id is what slows offline cracking.
- A vault lets you hold one master secret while every site gets a unique 20+ character credential.
- Exact-domain autofill means the vault will not type your password into a look-alike phishing host.