Passphrase vs Password: Which Is Actually More Secure? (With the Math)

Which of these is harder to crack: Tr0ub4dor&3 or correct horse battery staple? The first one looks stronger. It has capitals, a number and a symbol. The second is four plain words. But the second one is the better design, and the reason says a lot about what "strong" really means.

Entropy: how unpredictable is it?

Password strength is measured in bits of entropy, a way of counting how many guesses an attacker would need. It depends on two things: how big the pool is that you choose from, and how many independent choices you make. A real attacker does not guess blindly. They try the likeliest passwords first, so what matters is how predictable your pattern is.

Why Tr0ub4dor&3 is weaker than it looks

It is a dictionary word (troubadour) with the usual swaps (o to 0, a to 4), a symbol and a number added. Cracking tools run exactly those transformations on every word in their lists. Its real pool is "common words times common rules", which is far smaller than "any combination of characters".

Why random words work

If each word is picked truly at random from a list of 7,776 words (the Diceware list), every word adds about 12.9 bits. That gives:

Words	Entropy	Possible passphrases
4	about 51.7 bits	3.7 × 1015
5	about 64.6 bits	2.8 × 1019
6	about 77.5 bits	2.2 × 1023

How long would it take? It depends on how the site stores your password

Here is the whole space searched, assuming the attacker already knows you used this word list (a worst case). The speed depends on the hash a service uses. For a fast hash such as MD5, a good GPU can test on the order of 100 billion guesses per second. For a slow hash such as bcrypt, a rough figure is 100,000 per second.

Words	Fast hash (1011/s)	Slow hash (105/s)
4	about 10 hours	about 1,200 years
5	about 9 years	about 9 million years
6	about 70,000 years	far beyond any time frame

So four words is fine when a site uses a good slow hash, but it is not safe against a fast hash if the database leaks. You cannot know which one a site uses, which is why six words is the sensible length for anything important, like the master password of a password manager.

The word that matters is "random"

A phrase you chose because it sounded good is not random. A famous lyric, an idiom or a themed phrase like "mountain blue sky eagle" comes from a much smaller pool than the list suggests, and cracking tools generate such phrases. "Marble fence cloud bicycle", picked by dice or a generator, has no link between the words, to you, or to any known text. That is why Diceware uses real dice.

When to use which

• Passphrase for what you have to type from memory: your password manager's master password, a laptop login.
• Generated random password for everything a password manager fills in for you.
• Anything short, predictable or built on a real phrase is the actual mistake, whichever format you choose.

You can make both kinds in the browser, with nothing sent or stored: passphrase generator, password generator, and the strength checker. The full article is on the site: Passphrases vs Passwords.

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