Type 1.x Generalized Feistel Structures

We formalize the Type 1.x Generalized Feistel Structure (GFS) in order to fill the gap between Type 1 and Type 2 GFSs. This is a natural extension of Type 1 and Type 2 GFSs, and covers them as special cases. The diffusion property of GFS is known to vary depending on the permutation used in the round function. When we have two non-linear functions in one round, we propose a permutation that has a good diffusion property, and compare it with the structure that uses a sub-block-wise cyclic shift. We also present experimental results of exhaustively evaluating the diffusion properties of all permutations up to eight sub-blocks.