> We establish that for source words originally constructed from an i.i.d. sequence of letters, as a function of word length it is exponentially easier to guess

> We establish that for source words originally constructed from an i.i.d. sequence of letters, as a function of word length it is exponentially easier to guess a word conditioned to be in the source’s typical set in comparison to the corresponding equipartition approximation. Maybe I'm missing something, but this seems like a known and fairly trivial result. I read that as basically saying that if you don't pick the letters in your passwords from an uniform distribution, they are easier to guess. I don't see what that adds when people are already using Markov chains and dictionary attacks to brute force passwords, and I see no implication at all for secure keys chosen by good PRNGs. I guess it could have some use in entropy estimation for PRNG state, but assuming uniform distribution of input seems like a naive mistake to make. Is there some application of this that I'm missing?