4n × 4n Diffusion Layers Based on Multiple 4 × 4 MDS Matrices

In terms of security, MDS matrices are one of the best choices for the diffusion layer of block ciphers. However, as these matrices grow in size, their software implementation becomes a challenge. In this paper, to benefit from the properties of MDS matrices and avoid the mentioned challenge, we use 4 × 4 MDS matrices to build some 16 × 16 matrices with a low number of zero elements. We show that if these matrices are used as diffusion layers of software-based SPN structures, the resulting block ciphers have similar properties as AES in software implementation complexity (i.e. the number of required CPU instructions) and resistance against linear and differential attacks. Moreover, the best impossible differential and square distinguishers for the proposed 16 × 16 structures have a similar length as SPN structures with 16 × 16 MDS matrices. Thus, the new structures outperform AES concerning the impossible differential and square attacks. Additionally, we show that if the proposed SPN structure uses the AES key schedule, its results for the differential related-key attacks are better than those for AES. We also extend the idea and use 4×4 MDS matrices to design 24×24 and 32×32 matrices with acceptable properties for SPN structure design. Finally, we extend the idea to propose some matrices for Feistel structures with SP-type F-functions. We show that the resulting structures are more secure than the improved Type-II GFS.