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Re: Entropy Estimations for die and pass phrases

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On 2015-10-18 02:05:41 +0000, David Eather said:

> Just a short table of entropy estimates (Shannon entropy for the purest 
> hair splitters)

It's not just hair splitting. Shannon entropy is not the right measure 
when the distribution isn't uniform. Going full Kerchoffs here, the 
attacker knows the distribution and is going to guess the most likely 
first. Note that when a distribution is uniform, min-entropy == Shannon 
entropy, but min-entropy is a better measure when assessing threat.

> 6 sided dice 2.58 bits per throw
> 8 sided dice 3.99 bits per throw
> 10 dided dice 3.32 bits per throw

Right. And if you look at the original Diceware(TM) scheme, it took 
five throws of a 6-sided die to select a word, so 12.92 bits per word.

> Letters from a Scrabble set 4.32 bits per tile (this is higher because 
> the distribution of letters is a little more even than in natural 
> language because some letter must have one tile even though they 
> represent less than 1% of language)

But here is where min-entropy should be used. Assuming Scrabble(TM) 
distribution with replacement, the attacker when going after, say, an 
eight character password should guess "eeeeeeee" and "qqqqqqqq" last. 
So we are looking at 3.06 bits per letter.


> Making a password from the first letter of every word in a pass-phrase 
> yield about 3.9 - 4.0 bits per letter.

Again, it is going to be much lower than that when considering that 
some letters are much more common first letters than others.

> However, Professor Unruh has mentioned his experiments with all lower 
> case words taken from his texts which yielded 4.1 bits per word. This 
> accords very well with the Scrabble result and leads me to conclude 
> that although the difference is relatively small there is no reason to 
> use mixed cases when and only when) making a pass phrase from the first 
> letter of words in a sentence.

Yeah. People will only remember "mixed case" if it is the first letter 
of a meaningful unit or the last letter of the password. So it is only 
a few extra bits, and makes typing on a mobile keyboard harder.

Cheers,

-j

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Entropy Estimations for die and pass phrases  "David Eather" <eather@tpg.com.au> - 2015-10-18 12:05 +1000
  Re: Entropy Estimations for die and pass phrases Robert Wessel <robertwessel2@yahoo.com> - 2015-10-18 00:14 -0500
    Re: Entropy Estimations for die and pass phrases "David Eather" <eather@tpg.com.au> - 2015-10-18 16:40 +1000
  Re: Entropy Estimations for die and pass phrases  "David Eather" <eather@tpg.com.au> - 2015-10-18 16:41 +1000
  Re: Entropy Estimations for die and pass phrases Karl-Uwe Frank <karl.frank@freecx.co.uk> - 2015-10-18 23:22 +0200
    Re: Entropy Estimations for die and pass phrases Paulo Marques <pmarques@grupopie.com> - 2015-10-19 15:24 +0100
  Re: Entropy Estimations for die and pass phrases Jeffrey Goldberg <nobody@goldmark.org> - 2015-10-19 00:17 -0500
    Re: Entropy Estimations for die and pass phrases rpw3@rpw3.org (Rob Warnock) - 2015-10-19 12:00 +0000
      Re: Entropy Estimations for die and pass phrases Jeffrey Goldberg <nobody@goldmark.org> - 2015-10-19 14:52 -0500
        Re: Entropy Estimations for die and pass phrases David Malone <dwmalone@walton.maths.tcd.ie> - 2015-10-20 08:00 +0000
          Re: Entropy Estimations for die and pass phrases Jeffrey Goldberg <nobody@goldmark.org> - 2015-10-20 12:32 -0500

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