Security analysis of epsilon-almost dual universal2 hash functions

Recently, epsilon-almost dual universal2 hash functions has been proposed as a new and wider class of hash functions. This class well works even when the random seeds of hash function are subject to non-uniform distribution. This paper evaluates the security performance when we apply this kind of hash functions. We evaluate the security in several kinds of setting based on the L_1 distinguishability criterion and the modified mutual information criterion. The obtained evaluation is based on smoothing of Renyi entropy of order 2 and/or min entropy. Further, we apply this analysis to the secret key generation with error correction.