New Directions in Design of Binary Matrices for SPN Block Ciphers

. Di usion layer plays an important role in a block cipher. Some block ciphers, such as ARIA, Camellia, and Skinny use binary matrices as di usion layers which can be e ciently implemented in hardware and software. In this paper, the goal is to propose some new binary matrices with suitable values for number of active S-boxes for R rounds. Firstly, some new 16 16 matrices are proposed whose software implementation are better than corresponding one for ARIA block cipher. Also, the values for minimum number of active S-boxes for these matrices are greater than corresponding values for ARIA block cipher for R 5. To design 32 32 matrices, a structure with a special form is proposed. Using this structure, a 32 32 binary matrix is proposed which guarantees at least 48 active S-boxes for 8 rounds of an SPN structure with this matrix as its di usion layer. By extending this structure, a 32 32 nonbinary matrix is presented which results in at least 60 active S-boxes after 8 rounds.