Security Analysis of Some Diffusion Mechanisms Used in Chaotic Ciphers

As a variant of the substitution-permutation network, the permutation-diffusion structure has received extensive attention in the field of chaotic cryptography over the last three decades. Because of the high implementation speed and nonlinearity over GF(2), the Galois field of two elements, mixing modulo addition/multiplication and Exclusive OR becomes very popular in various designs to achieve the desired diffusion effect. This paper reports that some diffusion mechanisms based on modulo addition/multiplication and Exclusive OR are not resistant to plaintext attacks as claimed. By cracking several recently proposed chaotic ciphers as examples, it is demonstrated that a good understanding of the strength and weakness of these crypto-primitives is crucial for designing more practical chaotic encryption algorithms in the future.