Differential property of Present-like structure

Present is a lightweight block cipher designed by Bogdanov et al. We define the Present-like structure and study its differential property. Present has the 2-dimensional Present-like structure. With a new proof technique, we confirm that Bogdanov et al.'s proof for differential property of Present is true: any 5-round differential characteristic has at least 10 active S-boxes. We prove that for dimensions 3, 4, and 5, any 7-, 9-, and 11-round differential characteristics have at least 20, 28, and 43 active S-boxes, respectively. Especially, the result for dimension 3 can be applied to security analysis of the lightweight hash function Spongent with b≥256. Furthermore, we find that this differential property is deeply related to permutations with maximal cycle length.