Abstract: The diffusion performance of diffusion layer affects the anti-attack ability of all the  cipher structure,and the linear branch number is an important indicator to measure the diffusion performance;the bigger the branch number is,the stronger the ability to resist differential and linear cryptanalysis.The optimal diffusion layer composed by cyclic matrix can recycle the existing resources,so the implementation performance is more superior.As the necessary and sufficient condition of branch number to achieve maximum is that each sub-determinant is not zero,the paper constructs an algorithm based on this condition which can generate cyclic matirx with optimal diffusion and verify whether a matrix meets the optimal diffusion.A lot of eight order cyclic matrixes with optimal diffusion are obtained for the first time.A construction method of a class of four order cyclic matrix with the optimal diffusion is presented,and an error in reference is also corrected.The experiment results show that the number of the cyclic matrix with optimal diffusion is distributed evenly.

Key words: diffusion layer, branch number, cyclic matrix, optimal diffusion