Impossible differential cryptanalysis of MARS‐like structures

Abstract

The MARS-like structure is a generalised Feistel structure. Unified impossible differential (UID) method is an effective method to discover impossible differential characteristics for block cipher structures. In this study, for a specific kind of MARS-like structure, the authors use UID to show that when n, the number of subblocks, is even, there always exist 3n − 1 rounds impossible differentials. Moreover, the authors prove that when n is odd, the MARS-like structure has impossible differentials for any number of rounds, which is a clear but interesting result.

Revisiting impossible differentials of MARS‐like structures

“…Using the UID method [19], Xue and Lai constructed ‐round impossible differentials of MARS‐like structures as long as the round function is bijective. In this section, we are going to prove the existence of 3 n ‐round impossible differentials when the bijective round function is SP‐type.…”

“…considered the case when the round function is not bijective and showed that there exist 2 n ‐round impossible differentials of MARS‐like structures with n subblocks [18]. In 2015, Xue and Lai [19] constructed ‐round impossible differentials of MARS‐like structures in the setting where the round function is bijective, and they also presented a trivial result about the MARS‐like structure when the subblock number n is odd. The impossible differential properties of Feistel ciphers with SP round function is studied by Wei et al .…”

Revisiting Impossible Differential Distinguishers of Two Generalized Feistel Structures

“…For m-dataline MARS-like structure, when the round function is any bijective transformation, (2m − 1)-round impossible differentials were presented by the U method in [13]. is result was improved to (3m − 1) rounds in [19]. Furthermore, when the round function takes SP type, 3m-round impossible differentials were found in [5].…”

“…(3) For m-dataline MARS-like structure, when the round function takes SPS type (namely, MARS SPS ), the previous best result of MARS SPS was also presented in [19]. ey showed that (3m − 1)-round impossible differentials were constructed with P satisfying the bijective condition.…”

“…ey showed that (3m − 1)-round impossible differentials were constructed with P satisfying the bijective condition. In this paper, if P has 0 element in the diagonal line, we can construct 3m-round impossible differentials which are 1 round longer than those in [19]. is paper is organized as follows.…”