On the (im)possibility of improving the round diffusion of generalized Feistel structures
Kyoji Shibutani, Tetsu Iwata · Information Processing Letters · 2021
Generalized Feistel structures (GFS) are widely employed as the underlying structure of primitives like block ciphers and hash functions. In order to improve its slow diffusion, several design ideas have been proposed. In this contribution, we explore the (im)possibility of further improving the round diffusion of GFS by modifying its round permutations. First, we generalize a technique called sub-block dividing, which further divides each sub-block into smaller blocks. We prove that the diffusion round of a round permutation with sub-block dividing is four, regardless of the number of sub-blocks. Moreover, we show that the round diffusion of GFS can be improved by alternately using two different round permutations instead of a single permutation. We present the first results that, by using two round permutations, 10- and 12-block GFS partially and fully reach the lower bounds on the diffusion round, respectively.