Cryptanalysis against Type-III Generalized Feistel Networks and Its Variants with SP Type Round Functions

The Type-III Generalized Feistel Networks (GFN) was put forward as early as CRYPTO 1989. It is proposed as a generalized cryptographic transformation whose security is supported by profound mathematics bases. At present, the cryptanalysis against Type-III GFN mainly concentrates on the impossible differential properties. In this paper, we improved those impossible differential results by considering the Type-III GFN and its two variants with Substitution-Permutation (SP) type round functions. Based on the miss-in-the-middle strategy, our approach combined the characteristic matrix method proposed at EUROCRYPT 2016 and found
$(k+3)$
-round impossible differentials for Type-III GFN when the number of branches is
$k$
. Moreover, for its two variants with 4 branches, 6-round impossible differentials were detected. Both of those results are 1 round longer than the previous works. Our result moves a step further for the impossible differential attack against Type-III GFN and its variants, and it would help better understand the properties of those structures and the interaction between its structure and round functions.