  This work is a study of DES-like ciphers where the bitwise exclusive-or (XOR)
operation in the underlying Feistel network is replaced by an arbitrary group
operation. We construct a two round simplified version of DES that contains all
the DES components and show that its set of encryption permutations is not a
group under functional composition, it is not a pure cipher and its set of
encryption permutations does not generate the alternating group. We present a
non-computational proof that for n\leq6 the set of n-round Feistel permutations
over an arbitrary group do not constitute a group under functional composition.

Group Theory;Cryptography and Security