[talk] passwd entropy and strength

George Rosamond george at ceetonetechnology.com
Sun Nov 5 10:51:00 EST 2017

Ariel Sanchez Mora:
> Love the topic and kudos on a very clear explanation :)

Why, thank you.

> Personally, I combined both - long password combined with an easy to
> remember but more complex character like # at the end, so the password
> wasnt entirely derived from the "simple" character universe. Still easy to
> remember :)

That's cool, but also possibly considered predictable, in that if you
ask users to add numbers, they append passwds with 0, etc.

This post, though, is directed to those who could critique my view.


> On Nov 5, 2017 10:03 AM, "George Rosamond" <george at ceetonetechnology.com>
> 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.
> Can't imagine a more perfect Sunday morning post.
> g
> --
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