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 structures with four and six partitions and explain how to analyze them by MILP when they have more than one MDS2 matrices (like Clefia) in their structure. Moreover, we propose a new four partitions Feistel structure with three multiple MDS matrices which have more active S-boxes rather than Clefia structure. We also generalize Clefia structure in to six partitions Feistel structure by three multiple MDS matrices for 192 bits block size.