# Is this password entropy calculation correct?

I'm trying to compute the entropy of a passphrase of the following pattern:

`.... .... .... ....`

Where `.` represent lowercase characters.

The passphrase follows the rule that the two parts of each 4-character sequence have a vowel and a consonant, e.g.:

`anno domi arip keto`

Which has the pattern `:: :: :: ::` where `:` represents a vowel-consonant pair.

Assuming an attacker knows all this, is the following entropy calculation correct?

log_2((2*5*21)^8) = 61.7 bits

Since there are 5*21 ways to create a vowel-consonant and 21*5 ways to create a consonant-vowel, we get 2*5*21, and because there are 8 of these the value is raised to the 8th power.

## 1 Answer

Yes, your calculations appear to be correct.

5 (vowels, if you don't count y) * 21 (consonants) = number of possible two-character arrangements. So 105 different two-character arrangements in the 1 vowel and 1 consonant order. And like you said the reverse order is also possible, so 105 more for a total of possible 210 arrangements.

210 arrangements ^ 8 two character groupings = number of combined total character combinations. So approximately 3,782,285,936,100,000,000 possible combinations.

Log2 of 3,782,285,936,100,000,000 gives you the number of possible combinations represented in bits. So approximately 61.7 bits.