The One-Round Functions of the DES Generate the Alternating Group

Abstract

In each of the 16 DES rounds we have a permutation of 64-bitblocks. According to the corresponding key-block there are 248 possible permutations per round. In this paper we will prove that these permutations generate the alternating group. The main parts of the paper are the proof that the generated group is 3-transitive, and the application of a result from P. J. Cameron based on the classification of finite simple groups. A corollary concerning n-round functions generalizes the result.