Improving Clefia and six partitions Feistel structures by Multiple MDS Matrices

Counting the minimum number of differential active S-boxes is a common way to evaluate the security of block ciphers against differential and linear cryptanalysis. In this paper, we use mixed-integer linear programming (MILP)to calculate minimum number of active S-boxes of the some Feistel structures. We focus on Type-II of Feistel structureswith four and six partitions and explain how to analyze them by MILP when they have more than one MDS۲ matrices (likeClefia) in their structure. Moreover, we propose a new four partitions Feistel structure with three multiple MDS matriceswhich have more active S-boxes rather than Clefia structure. We also generalize Clefia structure in to six partitions Feistelstructure by three multiple MDS matrices for ۱۹۲ bits block size.

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Keywords— Clefia Structure ، Linear Programming ، Switching Method ، Generalized Feistel Structure ، Active S-boxes