A 6 dimensional chaotic generalized synchronization system and design of pseudorandom number generator with application in text encryption

Abstract

In this paper, a novel 3-dimensional discrete chaotic system is introduced. The calculated Lyapunov exponents of the system are 1.0287, 0.024615 and −0.58505. Numerical simulations show that the dynamic behaviors of the chaotic system have chaotic attractor characteristics. Based on the chaotic system and a chaos generalized synchronization (GS) theorem, a 6-dimensional chaotic generalized synchronic system is constructed. Using the chaotic generalized synchronic 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 tests the CPRNG. The result show that the CPRNG are all passed the FIPS 140-2 criteria. Numerical simulations show that for the perturbations of the keys of the CPRNG which are larger than 10−16, the keystreams have an average 50.0067% different codes which are different from the codes generated by unperturbed keys. And the keystreams have an average 49.9763% different codes which are different from the codes generated by the function of Matlab. The results imply that the key stream of the CPRNG has sound pseudorandomness. Using the pseudorandom number generator, a text encryption example is given. Experimental results show that, the resulting ciphertext can be well hidden plaintext.