Imprimitive permutation groups and trapdoors in iterated block ciphers

Abstract

An iterated block cipher can be regarded as a means of pro- ducing a set of permutations of a message space. Some properties of the group generated by the round functions of such a cipher are known to be of cryptanalytic interest. It is shown here that if this group acts impri- mitively on the message space then there is an exploitable weakness in the cipher. It is demonstrated that a weakness of this type can be used to construct a trapdoor that may be dificult to detect. An example of a DES-like cipher, resistant to both linear and differential cryptanalysis that generates an imprimitive group and is easily broken, is given. Some implications for block cipher design are noted.