>Assume for a moment that we have a random number generator which is
>non-uniform, and we are using it to generate a key.
>
>What I'd like to do is characterize the work factor involved in
>brute-force search of the key space, assuming that the adversary
>has knowledge of the characteristics of the random number generator?

You may want to use the guessing entropy.
I've written about it before here:

http://www.cs.berkeley.edu/~daw/my-posts/entropy-measures 

Christian Cachin's thesis is a wonderful introduction to entropy
measures, including the guessing entropy.

By the way, I'll make the obvious recommendation: Try to avoid
using a non-uniform random number generator to generate a cryptographic
key, if you can.

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