A 4-Dimensional Discrete Chaotic System and Application in Image Encryption with Avalanche Effects

This paper introduces a 4-dimensional chaotic map, consisting of sine, and cosine functions. Using this map and a generalized synchronization (GCS) theorem designs an 8-dimensional GCS system. The GCS system is used to design a chaotic pseudorandom number generator (CPRNG). Using the FIPS 140-2 test suit/generalized FIPS 140-2 test suit tests the randomness of three 1000-key streams consisting of 20000bits generated by the CPRNG, the RC4 algorithm and the ZUC algorithm, respectively. The results show that there are100%/98.9%, 99.9%/98.8%, 100%/97.9% key streams passing the tests, respectively. The analysis of the keys sensitivity suggests that there are no significant correlations between the key stream and the perturbed key streams. The key space of the CPRNGis larger than 2 1195. The CPGNG with an avalanche effect encryption scheme is used to encrypt an RGB image. The numerical calculations demonstrate that the CPRNG can generate the avalanche effects which are similar to those generated by ideal CPRNGs.