[talk] passwd entropy and strength

Brian Callahan bcallah at devio.us
Sun Nov 5 11:35:48 EST 2017

One quick though at the bottom.

On 11/5/2017 10:02 AM, George Rosamond wrote:
> This is something I've tinkered with for a long while, and thought I'd
> raise it on talk@ even though it's a bit OT from BSD land.
> Looking for feedback/correction on my argument here.
> I toyed a bit with the xkcd passwds... the well-known https://xkcd.com/936/.
> The passwords in question are:
> Tr0ub4dor &3 (aka "Tr0")
> versus
> correct horse battery staple (aka "correct")
> There is a unix program called ent in all BSD ports
> (https://www.fourmilab.ch/random/) which calculates entropy with a bunch
> of different measurements.  I fully don't understand all the tests, but
> I generally look at the first one "Entropy" which is bits of entropy per
> byte, ie, how much entropy/randomness per digit. So if you have a five
> digit passwd and 3 bits of entropy per byte, the passwd entropy would be
> 5 digits X 3 bits of entropy per byte = 15 bits of entropy.  I think
> that's correct.
> Now the first Tr0... passwd has 3.546... bits per byte, and the second
> correct... has 3.590... Therefore:
> Tr0.. 3.546 x 12 digits (including space) and is 42.48 bits of entropy
> correct... 3.590 x 28 digits and is 100.5 bits of entropy
> This seems to confirm the argument of the xkcd cartoon. The easier
> passwd correct... has more than double the bits of entropy and is easier
> to remember.
> But then look at the password strength wikipedia page, specifically the
> chart entitled "desired password entropy".
> https://en.wikipedia.org/wiki/Password_strength/
> The Tr0 passwd is considered in the column of "All ASCII printable
> characters" and the correct passwd is in the "case insensitive Latin
> alphabet".  Even by this the Tr0 passwd is about 72 bits of entropy and
> the correct passwd is 128 bits of entropy.
> Certainly the recommended method from the cartoon would likely be a
> massive improvement for most users. And with that, I don't think it's a
> bad thing if there is some real mathematical improvement in passwd strength.
> The problem with that argument, however, is the same problem with
> Diceware. The words, like Diceware, are all in standard US English
> dictionaries, and most methods of bits/entropy calculation doesn't take
> that into account. Both xkcd and Diceware only use a "26 character
> universe", ie, they limit their content to lower-case alphabet English.
> So what may look better in terms of some calculations, doesn't add up
> when it comes to determining patterns, ie, English words.
> So someone getting some of the passwd really just needs a "Wheel of
> Fortune" approach to determining a passwd in full.
> co__ect ho_se batte_y staple
> "Can I buy an 'r'?"
> And "universe" is one of the criteria I think matters for password
> strength. All ASCII printable characters is a 95 universe, which is much
> better over the 26 in a lower-case (or upper-case) US English alphabet one.
> Length matters, of course, but I think it's too often the main criteria
> for users and sysadmins, and the think that intimidates users the most.
> But it's third criteria that matters in this case, what I call
> "diversity", ie, can you find it in any dictionary? Does it contain
> common digraphs (in english, th, ng, st, etc).  Both xkcd and Diceware do.
> Going back to the passwd strength chart, how long does a passwd in
> 26-universe alphabet have to be to equal on that uses a 95-character
> ASCII universe?
> alpha only/ascii
> 13/7 (40 bits/entropy in total)
> 25/13 (80 bits)
> 39/20 (128 bits)
> etc.
> The conclusion, to me, is that getting users to use the whole ASCII
> universe of 95 characters with diversity is an achievable goal, and
> removes the easy brute force dictionary attacks so common.

I know it's crazy impractical right now, but when emoji keyboards start
being a thing and passwords can include UTF-8 chars, I imagine we'll
have whole new xkcd cartoons about correct horse battery staple being 4

emojis and it being a stronger password than the entirety of the
combinations of the ASCII table (I'm being facetious but not by much).

But maybe that's something worth implementing more than "user education"
which I think is already a lost cause. Even my mom uses emojis (sorry
mom!), I bet if I told her "put some emojis in your password" she'd come
up with something like "<purple heart emoji>Il0ve<eggplant emoji><sun
emoji>All<female doctor emoji><horse emoji><ice cream emoji>my<umbrella
emoji>children<angel emoji>" -- which she'd probably already have
memorized the first time she typed it in, and now completely defeats
your Pat Sajak attack in the vast majority of cases.
"Il0veAllmychildren" is a terrible password, but the emojis make it much
much better.

I guess those LISP space cadet keyboards will have to make a comeback
for my dreams to come true...
Maybe UTF-8 passwords already exist somewhere, I don't know. But it's my


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