In this paper, the notion of 2-tuples distribution matrices of the rotation symmetric orbits is proposed, by using the properties of the 2-tuples distribution matrix, a new characterization of 2-resilient rotation symmetric Boolean functions is demonstrated. Based on the new characterization of 2-resilient rotation symmetric Boolean functions, constructions of 2-resilient rotation symmetric Boolean functions (RSBFs) are further studied, and new 2-resilient rotation symmetric Boolean functions with prime variables are constructed.

We present a rebound attack on the 4-branch type-2 generalized Feistel structure with an SPS round function, which is called the type-2 GFN-SPS in this paper. Applying a non-full-active-match technique, we construct a 6-round known-key truncated differential distinguisher, and it can deduce a near-collision attack on compression functions of this structure embedding the MMO or MP modes. Extending the 6-round attack, we build a 7-round truncated differential path to get a known-key differential distinguisher with seven rounds. The results give some evidences that this structure is not stronger than the type-2 GFN with an SP round function and not weaker than that with an SPSP round function against the rebound attack.