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Comment by sidedishes | Hacker News Reader

To your first point, I think it's about priors about password choices. To take an extreme example, even if a site allows up to 32 alphanumeric characters, we don't just say passwords on this site are uniformly secure under metric (26+26+10)^32 because theoretically a brute-force approach would have to go through up that many permutations. (Such a number is an upper bound on your password security.)

In particular, short passwords with up to 8 characters are weaker because they form a small and common subset of passwords that people often draw from, and attackers exploit that by trying short passwords first.

Passwords that are 3 dictionary words, with possibly some small perturbations like punctuation inserts or replacements (which helps but only expands the space so much), also form a relatively small subset of passwords that people increasingly draw upon, and attackers aware of this will tailor their brute-force search accordingly.

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I might be misunderstanding your first paragraph, but I'm not saying that the exponent is constant, just the base.

What I was saying is if the rules of the site allow for all lower, all upper, special characters, and numerals, the sum of that is your base. If your password is purplepenguinparade, the expectation is you've cracked it by the time you've completed combined_base^1 through combined_base^19. They could artificially limit it (most people use lowercase characters and this site allows just lowercase characters, so let's try 26^n), but they'd run the risk of never cracking it because characters could've been added that deviate from their parameters.

Oops, that was my misunderstanding in the first paragraph :)

Maybe a clearer example w.r.t. the base^exponent value would be another highly structured class of long passwords, instead of short passwords. For example, those that are just a 2-character sequence repeated 20 times (e.g. abab...ab). You can still say that it'll take maybe up to 26^40 tries for an attacker to guess this, but that number should be more obviously too charitable, since less entropic classes of passwords are more likely to be guessed first.

More generally, this kind of counting analysis depends on your choice of attacker, and it's plausible for attackers to be more sophisticated than just trying all the strings in lexicographical order. A more concrete but still practical attack sketch adapted to the frequency of password schemes today could be: guess dictionary word combinations first, starting with common/short words/phrase lengths, then repeat with small perturbations, then more perturbations, and so on until you search all the remaining strings.

Then, the number of tries for such an attacker to find a 3-word passphrase with a few changes would be much closer to (some small constant) * (# dictionary words)^3 than (# characters)^(string length). Of course, you can still say that such an attacker would take at most (# characters)^(string length) tries to get it, but such an upper bound isn't as useful when the password is much more structured and easy to guess with a slightly more sophisticated attacker.

(Yet another way to put it: one shouldn't expect a password that's 'slightly out of reach' to be significantly more secure than a password that follows a scheme exactly - a more sophisticated attacker would test neighbouring passwords as it brute-forces the combinations in the scheme)

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