Universal Differential Cryptanalysis for Chaotic Ciphers

Differential cryptanalysis is a crucial task in cryptography. Recently, Chen and Zhou discovered that if the differential plaintext is only a function of the differential ciphertext, independent of the key, and the operations between differential plaintext and differential ciphertext are of the same type, attackers can break certain two-level structures of permutation–diffusion and diffusion–permutation, as well as three-level structures of permutation–diffusion–permutation. This paper further reveals that if the operations between differential plaintext and differential ciphertext are of different types, under certain conditions, differential cryptanalysis can still be used to break several types of two-level structures of permutation–diffusion and diffusion–permutation, as well as three-level structures of permutation–diffusion–permutation. This research enhances the theory and application of differential cryptanalysis, expanding its scope from cases where differential plaintext and differential ciphertext operations are of the same type to various scenarios in applications, where these operations can be of different types. It provides a theoretical basis and an implementation method for designing secure chaotic ciphers.