Is this password entropy calculation correct?

Question

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.

Answer 1

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.