A simplified and generalized treatment of DES related ciphers
This provides theoretical insights into cryptographic structure for cryptographers, but is incremental as it extends known limitations.
The paper tackled the problem of analyzing DES-like ciphers by replacing XOR with arbitrary group operations in Feistel networks, and found that simplified versions do not form groups under composition, with proofs for up to 6 rounds.
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.