Collision Attack on 4-Branch, Type-2 GFN Based Hash Functions Using Sliced Biclique Cryptanalysis Technique

In this work, we apply the sliced biclique cryptanalysis technique to show 8-round collision attack on a hash function H based on 4-branch, Type-2 Generalized Feistel Network (Type-2 GFN). This attack is generic and works on 4-branch, Type-2 GFN with any parameters including the block size, type of round function, the number of S-boxes in each round and the number of SP layers inside the round function. We rst construct a 8-round distinguisher on 4-branch, Type-2 GFN and then use this distinguisher to launch 8-round collision attack on compression functions based on Matyas-Meyer-Oseas (MMO) and Miyaguchi-Preneel (MP) modes. The complexity of the attack on 128bit compression function is 2. The attack can be directly translated to collision attack on MP and MMO based hash functions and pseudocollision attack on Davies-Meyer (DM) based hash functions. When the round function F is instantiated with double SP layer, we show the rst 8 round collision attack on 4-branch, Type-2 GFN with double SP layer based compression function. The previous best attack on this structure was a 6-round near collision attack shown by Sasaki at Indocrypt'12. His attack cannot be used to generate full collisions on 6-rounds and hence our result can be regarded the best so far in literature on this structure.