Improving the Permutation Layer of Type 1, Type 3, Source-Heavy, and Target-Heavy Generalized Feistel Structures

Abstract

The Generalized Feistel Structure (GFS) generally uses the sub-block-wise cyclic shift in the permutation layer, the layer between the two F function layers. For Type 2 GFS, at FSE 2010, Suzaki and Minematsu showed that a better diffusion property can be obtained if one uses some other sub-block-wise permutation. In this paper, we consider Type 1, Type 3, Source-Heavy (SH), and Target-Heavy (TH) GFSs, and study if their diffusion properties can be improved by changing the sub-block-wise cyclic shift. For Type 1 GFS and Type 3 GFS, we show that better permutations in terms of diffusion exist. For SH and TH GFSs, we show that the diffusion property does not change even if we change the sub-block-wise cyclic shift. We also experimentally derive optimum permutations in terms of diffusion, and evaluate the security of the resulting schemes against saturation, impossible differential, differential, and linear attacks.