A 6 Dimensional Chaotic Generalized Synchronization System and Design of Pseudorandom Number Generator with Application in Image Encryption

Abstract

This paper introduce a novel 3-dimensional discrete chaotic map. The calculated Lyapunov exponents of the map are 1.1638, 0.8946 and -0.2177. Numerical simulations show that the dynamic behaviors of the map have chaotic attractor characteristics. Based on the chaotic map and a chaos generalized synchronization (GS) theorem, a 6-dimensional chaotic GS system is constructed. Using the chaotic GS system and a transformation T form R to an integer set {0, 1} designs a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2 test suit tests the randomness of two 1000 key streams consisting of 20000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/97.7% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that for the perturbations of the keys of the CPRNG, the keystreams have an average 49.995% codes which are different from the codes generated by the unperturbed key. The results imply that CPRNG has sound pseudo randomness, the key space of the CPRNG is larger than 2747. As an application, an image encryption example via the CPRNG is given. Experimental results show that the correlation parameters between the plaintext and the ciphertext and the decrypted cipher texts via the 100 key streams with perturbed keys is less than 0.00414. The results suggest that the plaintext can be well hidden in the ciphertext, and brute attacks are needed to break the cryptographic system.