Abstract
This paper presents a new statistical testing of symmetric ciphers and hash functions which allow us to detect biases in a few of these systems. We first give a complete characterization of the Algebraic Normal Form (ANF) of random Boolean functions by means of the Möbius transform. Output bits of a cryptosystem are here described by a set of Boolean functions. The new testing is based on the comparison between their Algebraic Normal Form and those of purely random Boolean functions. Detailed testing results on several cryptosystems are presented. As a main result we show that AES, DES, Snow, and Lili-128 fail the tests wholly or partly and thus present strong biases.KeywordsBoolean functionstatistical testingsymmetric cipherrandomnesshash functionMöbius transformWalsh Transform
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