Design of optimal diffusion layers for SPN block ciphers

The diffusion layers in substitution-permutation network (SPN) block ciphers are almost invertible linear transformations, which is optimal if the branch number reaches the maximum value. The method of constructing involutory optimal diffusion layers is proposed based on the Cauchy matrix, which can decrease the cost of implementation. The analysis to experimental results indicates that the diffusion layer ensures the security of the SPN block cipher against differential cryptanalysis (DC) and linear cryptanalysis (LC), and decreases half the cost of implementation.