suppose you have a password policy that specifies the characters to be used as "A - Z, a - z, 0 - 9, and 10 special characters".
That's 26+26+10+10=72 characters. How many password combinations is that?
If my password is 8 characters, then there are 72^8 = 7*10^14 passwords
If my password is 14 characters, then there are 72^14 = 1*10^26 passwords
If I am interested in passwords of length 1 to 14, then
(72^1) + (72^2) + ... + (72^13) + (72^14) = 1*10^26
Thus, by looking at the power, we see that the maximum number of characters in the password to be guessed is the most important factor. Smaller passwords contribute, but usually an insignificant computational time in comparison.
What if I wanted to divide the keyspace into equal sized chunks?
The number of passwords is
k(m,n) = \sum_{i=1}^m n^i
where m=charset size, n=maximum password length (see cracking math basics)
I would like q equal chunks. Which strings will be in the (r/q)*k chunk [where r is an integer less or equal to q]
what if mod(k,q) \neq 0?