Apple Passwords’ generated strong password format

I'm glad someone is thinking about UX and ergonomics when it comes to passwords. Most people I interact with have by now realized that generating passwords is a good idea. But if you are already generating the password, please do not include special characters. I regularly use different keyboard layouts (sometimes it is not even clear which layout is active, like in the vSphere web console), and the fact that passwords are often not shown on the screen when typing them makes for terrible UX and causes frustration.

The usual advice about character classes is only for casual users who don't know what makes a secure password. Entropy is the deciding factor: Ten random lower case letters is much more secure than "Summer2024!", which satisfies most password rules and has more characters.

Personally I stick to lower case letters for things like my Netflix password or Wifi key, because typing with a TV remote can be a huge pain. To keep a similar entropy, just increase the length by one or two characters.

> The usual advice about character classes is only for casual users who don't know what makes a secure password.

Arguably, it was to make early rainbow tables less feasible.

> if you are already generating the password, please do not include special characters.

This would make your generator useless on most sites. Since it's not the generator making up this rule, it's the web site's password "complexity" requirements.

I do agree password strength tests should just measure bits of entropy and allow whatever's typed that's high enough.

It's not really meaningful to measure entropy of a single password, only of a distribution of passwords. You could assume a password comes from some distribution, but how would you know? Does "grefn" come from a distribution of "pick a 5 letter dictionary word and then randomly change one letter or a distribution of "pick 4-7 random ASCII characters"?

> It's not really meaningful to measure entropy of a single password

Here’s a ‘not meaningful’ formula then: E = L × log₂(R)

• E is the entropy, in bits, representing how hard the password is to crack.

• L is the password length (number of characters).

• R is the size of the character set (e.g., 26 for lowercase letters, 52 for upper/lowercase, 62 if digits are included).

• log₂(R) is the number of bits needed to represent each character.

I hear your point: a single password might not actually use all character types, so the actual entropy could be less than its potential. Maybe they could have drawn from a wider range and didn’t.

But for everyday user feedback, assuming the fewest sets seems fine to nudge people toward picking stronger passwords.

One definition for the randomness of a finite string is the size of the smallest program that produces it. The definition is dependent on how programs are interpreted.

If my string is "aaaa", does that mean its entropy is zero? There is at least information about its length. And by your definition, how do we know that this password isn't from a 256 character set? Does "Aaab" have 26 times the entropy of "aaab"?

Topics like this make more sense to me when the strings are infinite, or when the population of strings is known.