About Strong Passwords | Entropy, Passphrases and Diceware

Entropy: counting the guesses

Password strength is measured in bits of entropy. A password chosen at random from N possibilities has log2(N) bits, and every extra bit doubles the work for an attacker. A random 12 character password from 94 printable characters has about 79 bits. The catch is the word random: a password that people choose, such as a name with a year and an exclamation mark, has far fewer bits than its length suggests, because attackers try those patterns first.

Diceware and passphrases

In 1995 Arnold Reinhold published diceware: roll five dice to pick a word from a list of 7776, and repeat. Each word adds about 12.9 bits, so six words give about 77 bits while staying easy to type. The Electronic Frontier Foundation published improved word lists in 2016, and this generator uses its large list. The idea became famous through the 2011 comic that compared correct horse battery staple with a hard to remember but weak Tr0ub4dor&3.

What the guidelines say

The NIST Digital Identity Guidelines (SP 800-63B) favor length over composition rules: allow long passwords and passphrases, check new passwords against lists of breached ones, and do not force periodic changes without a reason. Forced complexity rules mostly lead to predictable patterns. Length combined with real randomness, and a different password for every site, matter much more.

How fast attackers guess

When a site is breached, attackers try guesses offline against the stolen hashes. With fast hashes and modern graphics cards that can be billions of guesses per second, which is the assumption behind the crack time shown here. Slow hashes like bcrypt or Argon2 cut that rate a lot, but you cannot know what a site uses. Aim for at least 70 to 80 bits, keep passwords unique, use a password manager and turn on two factor authentication.

Frequently asked questions

How long should a password be?

For a random password with letters, digits and symbols, 16 characters or more gives over 100 bits. For a passphrase, use at least 5 or 6 random words. Length is the simplest way to add strength.

Are substitutions like P@ssw0rd strong?

No. Attackers know common substitutions and try them automatically, so they add very little. Real randomness is what makes a password strong.

Should I change passwords regularly?

Current guidance says no, unless there is a reason such as a breach. Frequent forced changes tend to produce weaker, predictable passwords. Use unique passwords and change one when it may have leaked.