Passphrases vs passwords

The old advice to use a short password with uppercase, a digit, and a symbol produces something like P@ssw0rd! that is hard for a human to remember and easy for a computer to guess. A passphrase of a few random words, like correct horse battery staple, inverts both: easy to remember, hard to crack. The reason comes down to how guessing attacks actually work and where strength really comes from.

Strength is entropy, not decoration

The security of a password against guessing is measured in entropy, the number of bits of genuine uncertainty an attacker faces. Entropy depends on how the password was chosen, not how complicated it looks. The formula for a randomly chosen secret is:

bits = length * log2(size of the pool each element is drawn from)

Crucially, this only holds when each element is chosen at random. P@ssw0rd! looks complex but it is a dictionary word with predictable substitutions, so a cracking tool that knows the common tricks treats it as little better than password. The symbols buy you almost nothing because they are not random.

Length beats complexity

Compare two random secrets. A random 8 character string from the 94 printable ASCII characters:

8 * log2(94)  ≈  52 bits

A passphrase of 5 words chosen randomly from a 7,776 word list, the standard Diceware list:

5 * log2(7776)  ≈  64 bits

The passphrase is stronger, and every extra word adds about 13 bits, which more than doubles the guessing effort. Adding one character to the random string adds only about 6.5 bits. Length is the cheapest lever you have, because entropy grows linearly with it while an attacker's work grows exponentially. This is why modern guidance, including from NIST, drops forced complexity rules and emphasizes length, allowing long passphrases up to at least 64 characters.

The correct horse principle

The idea popularized by the webcomic is that four random common words carry more entropy than a mangled single word, while being far easier to recall. The two conditions that make it true are easy to get wrong:

• The words must be chosen at random, ideally by dice or a secure generator, not picked by you. A phrase you compose from a favorite song is predictable and weak.
• More words is more strength. Four words is a reasonable floor; five or six is better for anything valuable.

A passphrase you can picture is a passphrase you will not write on a sticky note, and memorability is a real security property, not a convenience.

In practice

Use a random passphrase for the handful of secrets you must memorize, such as your device login and the master password for a password manager. For everything else, let the manager generate long random strings per site, since you never type those by hand.

To see how length and composition move the needle, paste a candidate into the password strength checker and watch the estimate change as you add words. It runs entirely in your browser, so the password you test is never transmitted anywhere. The rule to carry: pick randomly, favor length over symbols, and a memorable multi word passphrase will beat a short cryptic one on both strength and usability. For the math behind the estimate, see password entropy explained.