N-phase logistic chaotic sequence and its application for image encryption

Abstract

In this study, the authors use a non-symmetric partition to generate N-phase pseudorandom sequences using the logistic maps. The theoretical analysis shows that this N-phase logistic sequence is with uniform distribution, as well as independent and identically distributed. Numerical experiments show that these N-phase logistic sequences have high complexity and are with good randomness. A fast algorithm with its time complexity be O(M) is proposed to generate these N-phase sequences. Furthermore, they propose a new image encryption algorithm based on the N-phase logistic sequence, which is combined with both shuffling and substitution algorithms. Several security tests are carried out to demonstrate that the authors’ new algorithm is with a high security level, and can resist various attacks, which can be competitive with some other recently proposed image encryption algorithms.