Double SP-Functions: Enhanced Generalized Feistel Networks

Abstract

This work deals with the security and efficiency of type-I and type-II generalized Feistel networks (GFNs) with 4 lines. We propose to instantiate the GFNs with double SP-functions (substitutionpermutation layer followed by another substitution-permutation layer) instead of single SP-functions (one substitution-permutation layer). We provide tight lower bounds on the number of differentially and linearly active functions and S-boxes in such ciphers. Based on these bounds, we show that the instantiation with double SP-functions using MDS diffusion has a proportion of differentially and linearly active S-boxes by up to 33% and 50% higher than that with single SP-functions for type-I and type-II GFNs, respectively. This opens up the possibility of designing more efficient block ciphers based on GFN structure. Note that type-I and type-II GFNs are the only non-contracting GFNs with 4 lines under a reasonable definition of a GFN.