Assume that a transaction is paid to a brain wallet address. (not P2SH, or M of N)
Is there any statistical approximation (or tiers of approximation) of how secure a Brain Wallet is to
A key generated from pure random
The non-random keys created by a broken random on Android pre 2013
any other key generation technique
My goal is to get an approximation based on complexity relative to the other methods. A constructive thing that this would help with is what complexity is necessary for the Brain Wallet to have 2^64 bits of pure random?
Some additional question that may come of this line of thinking include:
In a Brain Wallet, what is the relationship between complexity, length and the random output?
What patterns are there to avoid? (vowel frequency, other letter statistical distribution)
Is a Brain Wallet more secure if written in a foreign language that has more characters in it (more entropy)?
Much of this may be in a Cryptanalysis book, but I'm looking for someone who may have studied passwords in the past and can offer suggestions on how to brute force a Brain Wallet.