Discrete Chaotic Systems with One-Line Equilibria and Their Application to Image Encryption

Abstract

This paper introduces nine four-dimensional discrete chaotic systems with one-line equilibria (DCSLE), consisting of some simple sine functions. Based on the generalized chaos synchronization (GCS) theorem, a DCSLE is used to construct an eight-dimensional DCSLE GCS system. The new DCSLE GCS system is verified by numerical simulation and then used to design a chaotic pseudorandom number generator (CPRNG). The randomness of ten 100-key streams generated by the CPRNG, two GCS-based CPRNGs, the RC4 PRNG and the ZUC PRNG are tested by the SP800-22/FIPS 140-2 tests. The test results confirm that the randomness performances of the three CPRNGs are promising, for there are no significant correlations between a keystream and any perturbed keystream generated by such CPRNG. Also, the key space of the CPRNG is larger than [Formula: see text]. Finally, the CPRNG is used with an avalanche-effect encryption scheme to encrypt an RGB image, demonstrating that the CPRNG is able to generate the avalanche effects which are similar to those generated by ideal CPRNGs.

A Chaotic System with Infinite Equilibria and Its S-Box Constructing Application

“…It is noted that memristor-based systems often have a line of equilibrium points [18]. It is interesting that Chen et al have found nine discrete chaotic systems with one-line equilibria and applied them for image encryption [19]. Chaotic systems with infinite equilibria and their applications should be further investigated.…”

A fractional-order form of a system with stable equilibria and its synchronization

“…Applications of chaos have been witnessed in various areas ranging from path planning generator [4], secure communications [5][6][7], audio encryption scheme [8], image encryption [9][10][11], to truly random number generator [12,13]. Many three-dimensional (3D) autonomous chaotic systems have been found and reported in the literature [14].…”

The fast image encryption algorithm based on substitution and diffusion

“…Chaotic image cryptology research has become a hotspot in the field of information security. And that includes three main research directions: First is to study the new chaotic systems which can produce cryptographic key streams [1][2][3][4][5]. The direction serves as an important application of chaos theory to give birth to the study of new chaotic systems.…”