Towards Minimizing Tweakable Blockcipher-Based Generalized Feistel Networks

A generalized Feistel network (GFN) is a classical approach to constructing a blockcipher from pseudorandom functions (PRFs). Recently, Nakaya and Iwata (ToSC, 2022) formalized tweakable blockcipher (TBC)-based counterparts of type-1, type-2, and type-3 GFNs. This paper studies minimizing the number of TBC calls in such GFN variants. Motivated by the so-called extended GFNs of Berger et al. (IEEE TC, 2016) and Zhao et al. (CANS 2023), we consider TBC-based type-2 GFN and replace the blockwise shuffle with a block-oriented linear diffusion layer. We show that when this diffusion layer is moderately strong, 4 TBC-based GFN rounds are sufficient for CCA security, which is independent of the number of lines. This provides a much more efficient approach to TBC-based enciphering schemes.