Security analysis of epsilon-almost dual universal2 hash functions: smoothing of min entropy vs. smoothing of R\'enyi entropy of order 2

Recently, $\varepsilon$-almost dual universal$_2$ hash functions has been proposed as a new and wider class of hash functions. Using this class of hash functions, several efficient hash functions were proposed. 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 R\'{e}nyi entropy of order 2 and/or min entropy. We clarify the difference between these two methods.