Security analysis of epsilon-almost dual universal2 hash functions: smoothing of min entropy vs. smoothing of Rényi entropy of order 2

Abstract

Recently, $\epsilon$-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 Rényi entropy of order 2 and/or min entropy. We clarify the difference between these two methods.

Several errors are fixed. Introduction and presentation have been improved. This paper consists of a part of the older version of arXiv:1202.0322 and several additional result. This part of the older version of arXiv:1202.0322 has been removed in the current version of arXiv:1202.0322. So, there is no overlap between this paper and the current version of arXiv:1202.0322

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