Distinguishers for 4-Branch and 8-Branch Generalized Feistel Network

TLDR: It is concluded that eight-branch type-2 generalized Feistel network (GFN) with SSP functions is weaker than four-br branch type-two GFN with DSP functions in the KKA model.

Abstract: In this paper, we present an eight round distinguisher for four-branch type-2 generalized Feistel network (GFN) with double-SP (DSP) functions and two distinguishers for eight-branch type-2 GFN with single-SP (SSP) functions in a known key attack (KKA) model. We improved the result presented by Sasaki in Indocrypt 2012 by extending the number of rounds attacked from seven to eight for four-branch GFN. Furthermore, for eight-branch type-2 GFN with SSP functions, we present the first known key distinguishers. Our attack works up to 15 rounds of this GFN for all practical parameters. Subsequently, we extend the attack to 17 rounds for the same GFN, which works for most practical parameters. On the basis of our second result and the number of rounds attacked, we conclude that eight-branch type-2 GFN with SSP functions is weaker than four-branch type-two GFN with DSP functions in the KKA model. We apply rebound attack technique to mount all three distinguishers. However, a limitation of all the distinguishers presented in this paper is that they are useful only if the input size of S-boxes in bits is greater than or equal to the number of S-boxes in one S-box layer.