Known key distinguishers on 15 round 4 branch type 2 generalised Feistel network

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 sing