On Feistel Structures Using a Diffusion Switching Mechanism

We study a recently proposed design approach of Feistel structure which employs diffusion matrices in a switching way. At ASIACRYPT 2004, Shirai and Preneel have proved that large numbers of S-boxes are guaranteed to be active if a diffusion matrix used in a round function is selected among multiple matrices. However the optimality of matrices required by the proofs sometimes pose restriction to find matrices suitable for actual blockciphers. In this paper, we extend their theory by replacing the condition of optimal mappings with general-type mappings, consequently the restriction is eliminated. Moreover, by combining known lower bounds for usual Feistel structure, we establish a method to estimate the guaranteed number of active S-boxes for arbitrary round numbers. We also demonstrate how the generalization enables us to mount wide variety of diffusion mappings by showing concrete examples.