Traditional password advice has spent decades forcing users to create combinations of uppercase, lowercase, numbers, and symbols. The result is often passwords like 'Tr0ub4dor&3'. These are difficult for humans to remember but relatively easy for computers to crack because humans use predictable substitution patterns.
A passphrase, famously popularized by the 'correct horse battery staple' comic, abandons character-level complexity in favor of word-level length. By stringing together multiple random dictionary words, you achieve massive length (and therefore high entropy) while remaining memorable to the human brain.
The math of Diceware passphrases
When generating a passphrase, the 'character pool' from the entropy formula is replaced by a 'word pool'. The EFF provides a standard Diceware list containing 7,776 words. If you randomly select a word from this list, that single word has log2(7776) ≈ 12.9 bits of entropy.
If you select 4 random words, the entropy is 4 × 12.9 = 51.6 bits. If you select 6 words, the entropy scales to 6 × 12.9 = 77.4 bits. Six random English words separated by spaces provide mathematical security equivalent to a 12-character string of completely random gibberish (symbols, numbers, cases), but the words are vastly easier to type and memorize.
Dictionary attacks and structure
Critics of passphrases often point out that attackers use dictionary attacks. However, a dictionary attack works by testing single dictionary words or common phrases. When a passphrase is constructed of truly random, unrelated dictionary words, the attacker must attempt a permutation attack across the entire dictionary space.
To crack a 6-word passphrase using a 7,776 word dictionary, the attacker must search a space of 7776^6 combinations. This is 2.2 × 10^23 possibilities. Even knowing exactly which dictionary the words came from, the search space is far too large for any modern computing cluster to brute-force.