Improving the Generalized Feistel

Abstract

Abstract. The generalized Feistel structure (GFS) is a generalized form of the classical Feistel cipher. A popular version of GFS, called Type-II, divides a message into k > 2 sub blocks and applies a (classical) Feistel transformation for every two sub blocks, and then performs a cyclic shift of k sub blocks. Type-II GFS has many desirable features for implementation. A drawback, however, is its low diffusion property with a large k. This weakness can be exploited by some attacks, such as impossible differential attack. To protect from them, Type-II GFS generally needs a large number of rounds.In this paper, we improve the Type-II GFS's diffusion property by replacing the cyclic shift with a different permutation. Our proposal enables to reduce the number of rounds to attain a sufficient level of security. Thus, we improve the security-efficiency treading off of Type-II GFS. In particular, when k is a power of two, we obtain a significant improvement using a highly effective permutation based on the de Bruijn graph.

LBlock: A Lightweight Block Cipher

“…Moreover, we specifically choose the rotation offsets of right half in each round as 8 bits which can be omitted in 8-bit platform implementation. On the other hand, in the aspect of security requirement, we choose the word-wise permutation carefully so that the structure of LBlock satisfies that in both encryption and decryption directions it can achieve best diffusion [32] in 8 rounds.…”

Zero-correlation linear cryptanalysis of reduced-round LBlock

“…The nibble-wise permutation has been chosen such that it achieves the best diffusion as proposed in [14]. To verify the theoretical model of zero-correlation attacks [3] we implement the described attack on a small variant of LBlock with block length 32-bit.…”

“…To verify the theoretical model of zero-correlation attacks [3] we implement the described attack on a small variant of LBlock with block length 32-bit. Two optimal word-wise permutations for improved Type II GFC with 8 branches were suggested in [14]. To make the small variant cipher similar as much as possible to the original one, we choose the permutation which is not based on the Bruijn graph.…”

Extended Generalized Feistel Networks Using Matrix Representation

“…In [30], Suzaki and Minematsu proposed to use a non-cyclic permutation instead and applied it to Type-2 GFNs. More precisely, they studied the maximum diffusion round.…”

“…Following the work of [30], Yanagihara and Iwata [32] studied the case of Type-1, Type-3, SH and TH GFNs with non-cyclic permutation. For Type-1 and Type-3 GFNs, they showed that the maximum diffusion round can be improved by changing the permutation while for SH and TH GFNs it cannot.…”