Known-key distinguishers on 15-round 4-branch type-2 generalised Feistel networks with single substitution–permutation functions and near-collision attacks on its hashing modes

Generalised Feistel network (GFN) is a popular design for block ciphers and hash functions. The round function of the network often chooses a substitution-permutation (SP) transformation (consists of a subkey XOR, an S-boxes layer and a linear layer). In 2011, Bogdanov and Shibutani provided another choice to build round functions, namely the double SP-functions, which has two SP-layers in series. They showed that a 4-branch type-2 GFN with double SP-functions was stronger than the one with single SP-function in terms of the number of active S-boxes in a differential or linear cryptanalysis, but some subsequent results showed that the double SP-function is the weaker one in some known-key scenarios and hashing modes. In this study, the authors present a new result of the 4-branch type-2 GFN, whose round function is a single SP-function. They show some 15-round truncated differential distinguishers for this network with four usual parameters by utilising some rebound attack techniques. Based on these distinguishers, they construct some 15-round near-collision attacks on the Matyas-Meyer-Oseas and Miyaguchi-Preneel compression function modes in which the 4-branch type-2 GFN with the single SP-function is used.