Analysis of permutation choices for enhanced generalised Feistel structure with SP-type round function

Since the proposition of improved generalised Feistel structure (GFS), many researches and applications have been published. In this study, the authors further enhance the improved GFS with SP-type round function by extending the sub-block-wise permutation to word-wise permutation which can have better diffusion and security effect. Then, they study the security effect of different permutation choices for this kind of enhanced GFS cipher with SP-type round function. By proving several propositions about the equivalent situation, they can eliminate isomorphic permutations so as to narrow down the candidate space notably and propose a method to compute the number of effective permutation candidates. Finally, they take three typical scenes as example, and for each experimental scene, they compute the number of effective permutation candidates and exhaustively evaluate their security results. They also give an optimum permutation as example for each scene.