The comic says "four random common words". It must take some creative reading to interpret that as "four non-random common words".

When the comic first came out there was a bunch of analysis http://www.explainxkcd.com/wiki/index.php/936:_Password_Stre... "xkcd's entropy estimate of 11 bits per word assumes that the password is being brute-forced with a dictionary attack, and that the words are being chosen from a dictionary of 2000 words (log2(2000) ≈ 11). (For comparison, the entropy offered by Diceware's 7776 word dictionary is 13 bits per word.) If a dictionary attack were not used, the "common words" password would take even longer to crack than depicted. (25 random lowercase characters would have 117 bits of entropy, vs 44 bits for the dictionary words.)"

So yeah maybe it is implicit in the comic, but the math is backed by a specific set of assumption on how the words were selected. Or I could be wrong, I haven't verified it personally.

I've validated it myself for an argument when the comic was published for the phrase "correct horse battery staple".

First character is 4 bits: c = 4

The next 7 chars are 2 bits/each: "orrect " = 14

Characters 9-20 are 1.5 bit/each: "horse batter" = 18

Charactes 21-n are 1 bit/each: "y staple" = 8

No bonus for including both upper and non-alpha chars.

No bonus for passwords of length less than 20 chars, not containing dictionary words, because the password is longer than 20 characters.

Total entropy: 4 + 14 + 18 + 8 = 44 bits of entropy.

I think it is cool that both estimates of entropy come to the same number, but that still seems like the wrong way to look at the approach even if Randall didn't intend it that way.

The NIST entropy estimation is based off of characters that aren't chosen at random (I think?) and it is a heuristic.

For the approach I think Randall intended to describe they aren't really words, just glyphs chosen randomly from a set of glyphs. That these glyphs are easy to memorize and drop right into existing password interfaces is orthogonal.

There's a little box for each bit of entropy (this is consistent throughout the comic). There are 11 little boxes by each word.

While it's true that NIST SP 800-63 gives 44 bits of entropy for the comic's password, this is purely a coincidence. The comic certainly isn't using using NIST SP 800-63 to calculate the entropy. The "xkcd" method extended to, say, 10 words would give 110 bits per xkcd's calculations, but I think it's safe to say that very few of these passwords would qualify as 110 bits under NIST SP 800-63.