Almost Independence and Secrecy Capacity

In information-theoretic models of secure transmission or cooperative secret key generation, the usual secrecy criterion is per letter mutual information. For familiar models, the same secrecy capacity is shown to be achievable with a much stronger criterion. The main tool is a general theorem about a function of a random variable almost uniformly distributed on a large set and almost independent of another random variable, a consequence of a recent result of Ahlswede and the author about robust uniform randomness.