AES, the Advanced Encryption Standard, is one of the most important algorithms in modern cryptography. Certain randomness properties of AES are of vital importance for its security. At the same time, these properties make AES an interesting candidate for a fast nonlinear random number generator for stochastic simulation. In this article, we address both of these two aspects of AES. We study the performance of AES in a series of statistical tests that are related to cryptographic notions like confusion and diffusion. At the same time, these tests provide empirical evidence for the suitability of AES in stochastic simulation. A substantial part of this article is devoted to the strategy behind our tests and to their relation to other important test statistics like Maurer's Universal Test.
(Salzburg) 1. Introduction. In either one of the following two problems: (A) generation of uniform pseudorandom numbers (in the normalized domain [0, 1[), (B) quasi-Monte Carlo methods (i.e. random samples in a Monte Carlo method are replaced by deterministic points) a well-chosen finite point set P = {x 0 , x 1 ,. .. , x N −1 } in the s-dimensional unit cube [0, 1[ s has to be generated. To assess the quality of P, it is essential to determine the deviation of the (empirical) distribution of P from uniform distribution on [0, 1[ s (see Niederreiter [5, Chapters 2 and 7] for a thorough discussion). Discrepancy has turned out to be the appropriate concept to measure this deviation. There are several notions of discrepancy. The most important are the following.
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