This paper shows the rebound attack on the Feistel-SPS structure, which has the Feistel network with a Substitution-Permutation-Substitution (SPS) round function. A 6-round known-key truncated differential distinguisher is obtained by studying the diffusion properties of differences. Based on the distinguisher, a near- collision attack on the compression functions of this structure embedding the Matyas-Meyer-Oseas (MMO) and Miyaguchi-Preneel (MP) modes is given. Besides, the 6-round distinguisher is extended and a 7-round truncated differential path is constructed to get a 7-round truncated differential distinguisher of the compression function for the two modes mentioned before.
