256 choose 8 with replacement. Do the math. :)

Why not? tedu’s password would still be as strong as 9 random ASCII characters.

How big was your dictionary? It’s actually fairly easy to compute how many passwords a given generation scheme can produce.

For example, my /usr/share/dict/words has 99,171 words in it. Picking five at random (without replacement) with cat /usr/share/dict/words|sort -R|head -n 5|tr $'\n' ' ' allows for (99,171 choose 5) different passwords, which is 79,927,903,812,879,014,029,704, or about 76 bits or 13 case-sensitive alphanumeric characters. (Choosing with replacement makes for a significantly easier to calculate but only marginally bigger 83 bits/14 characters.)

I generated a couple of 13-character alphanumeric passwords and got an average score between 80 and 90, and a couple of five-word passphrases, which mostly got 100, so that seems in line to me. However, it heavily penalizes passphrases that consist entirely of lowercase letters and space, and my dictionary has lots of proper nouns and possessives. Filtering those, the passphrase scores were much worse—50-60-ish. (Interestingly, a 5-word passphrase generated from this shorter dictionary—66,005 words—is still worth a 12-character password. This is why experts advise you to concentrate on length over alphabet/dictionary size.)

So it’s safe to say this checker isn’t consistent with the actual amount of entropy in a given password. But it looks like it’s trying to penalize the sorts of habits that result in bad passwords, even if that results in a very skewed “good” password space. It’s much more important to it that “password1” get a bad score than that “signals constriction punchy rejoinders titanic” get a good one. I’m not sure it’s biased in the best way (“signals constriction etc.” is far more likely to be remembered and used than the otherwise-equivalent “8inHpcw47jUdD”), and I don’t think I’d recommend it for that reason, but the premise is probably sound.

Well, let’s do the math. According to a quick search there are about 171,476 words in current usage–that’s about 2^17.387647.

So, assuming that you pick each word at random and allow duplicates, getting your password is:

P(5word_pass) = 1/171476 * 1/171476 * 1/171476 * 1/171476 * 1/171476
P(5word_pass) = ( 2^-17.387647 ) ^ 5
P(5word_pass) = ( 2^-86.938235 )

So, we’ll setup the same trick using uppercase letters (26), lowecase letters (26), digits (10), and other characters (33). So, at random, we can choose a character from those sets, and that’s a 1/95 chance of any particular character being picked.

Let’s see how many characters we need to match the 5-word password!

P(5word_pass) = ( 2^-86.938235 )
( 2^-86.938235 ) = (1/95)^N
( 2^-86.938235 ) = (2^- 6.569856)^N
( 2^-86.938235 ) = 2^(- 6.569856N)
-86.938235 = -6.569856N
N = 13.232898

And to double check:

(1/95) ^ 13.232989 = 6.7422567e-27
2^(-86.948235) = 6.7422567e-27

So, it looks like you’d have to use about 14 characters from that class defined above to get the same strength as 5 dictionary words.

I think the concern is dictionary based brute force attacks. People love talking about entropy with regards to password strength, but I think that ignores search space. A long passphrase has very high entropy on a per-character basis, but a memorable series of lowercase words chosen from common vocabulary (not a dictionary) is more likely to be attempted first before a similar length string with special characters. Another thing that I think complicates the discussion is whether you’re protecting against login attempts, hash cracking (from a credential db leak), or a targeted attack that may have already obtained a passphrase you use elsewhere. Different patterns and recommendations tend to focus on addressing one or more of these concerns, but any strategy requiring memorization (no password manager) will compromise on these. All that is to say a long passphrase is good, but a long passphrase with some special characters is even better at guarding against one type of attack.

You should consider attack vectors. If you have a list of all known usernames like say a forum has a directory of users, then my first attack would be to try every known username against common passwords like password, password1, hunter2, Password, dog, etc.

Another attack vector is you know the user you want to compromise, so you try potential passwords like names of family, friends, significant things in their life. You can open it up to just all English words, then vary that by special characters trying some leet speak substitutions.

In summary, I’m just saying that an attacker knows the total solution space is gigantic, but could also assume some basic human nature that were lazy so we make passwords easy and memorable. An attacker might be able to exploit this and reduce their search space enough to have a feasible attack.

Why would they have to assume that? Especially knowing that XKCD has made series of words passwords popular. Plus, you don’t know how long a password is based on its hash.

Seems like a totally reasonable attack vector nowadays to me to just randomly assemble the most common couple thousand words.