This paper presents a new, powerful statistical testing of symmetric ciphers and hash functions which allowed us to detect biases in both of these systems where previously known tests failed. We first give a complete characterization of the Algebraic Normal Form (ANF) of random Boolean functions by means of the M obius transform. Then we built a new testing based on the comparison between the structure of the different Boolean functions Algebraic Normal Forms characterizing symmetric ciphers and hash functions 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 all or part of the tests and thus present strong biases.

This note summarizes the results of Babbage's cryptanalysis of COS ciphers and shows that in fact COS ciphers are not weak as claimed. COS ciphers have been designed according a novel conception of encryption directly determined by the context of use. This concept is here de ned more precisely. Keywords: stream cipher, cryptanalysis, COS, nonlinear feedback shift register, adaptable encryption, dual technology, copyright protection, IFIC. 1