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I saw in another thread: Is using 7-8 random words from all words of a language as password a good idea?

These calculations:

If we assume that English has 171,476 words. Then with 8 words the entropy is:

$$P(171476,8) \approx 7.474 \times 10^{41} \approx 2^{140}$$

Therefore you will have lower entropy than Bip-39, again. And with 7 words:

$$P(171476,7)≈4.358×10^{36}≈2^{122}$$

I like to use this calculation method myself. I have the following related questions:

  1. What is the name of this mathematical formula called $P(x,y)$?

  2. Any online calculator available? Or even better, a formula for MS Excel or python?

  3. Is this method commonly used to calculate entropy? If not please hint me to a more widely used formula.

Maarten Bodewes
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johnsmiththelird
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  • https://crypto.stackexchange.com/q/374/18298 – kelalaka Jan 15 '20 at 14:14
  • thx! and do u know if there is ready Excel formula or python formula available? – johnsmiththelird Jan 15 '20 at 14:18
  • I did not read, however, first with google search password entripy calculator excel – kelalaka Jan 15 '20 at 15:34
  • Your $P$ is named power, with $P(x,y)=x^y$. In many languages it is called pow. It does not return the password entropy, but the number of distinct passwords. The password entropy in bit for uniform choice among these is the base-2 logarithm of the number of password, in other words $\log_2(x^y)=y\log_2(x)=y\log(x)/\log(2)$. In many languages $\log_2$ is called log2 and $\log$ is called log (but in others log could also be $\log_{10}$). – fgrieu Jan 15 '20 at 16:06
  • @fgrieu there it is Permutation. $P(n,r)$ – kelalaka Jan 15 '20 at 20:10
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    @kelalaka: Right. And, checking, the numbers are closer to your hypothesis than mine, and could have been obtained (checking the source: by you!) using a rounding down of the result with permutation. However the question is about 7 or 8 random words, not 7 or 8 random distinct words, therefore the mathematically correct function is power, and there is no reason to invoke permutation. With the numbers at hand the difference is <0.00024 bit of entropy. – fgrieu Jan 15 '20 at 20:25
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    @fgrieu I've updated. – kelalaka Jan 15 '20 at 23:00

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