“…A further purpose for the analysis of group theoretic properties of a block cipher stems from the fact that, if the round functions of the cipher generate the alternating group on the message space, then general security proofs for the cipher are possible with respect to the Markov cipher approach to classical di erential cryptanalysis (cf. [2,10,16]). For the DES [4], AES [22], and other ciphers, several results on the cyclic and group theoretic structure of their components have already been found (see [3,5,8,13,21,23,24]).…”