Study On Theory And Applications Of Encryption Algorithms Based On Multiple Chaotic Systems

Many properties of chaotic systems, such as ergodic, mixing, deterministic features and sensitive dependence on initial conditions, are related to diffusion and confusion of cryptography. Therefore, chaos is suitable for realizing cipher algorithms that are usually realized by digital circuits or computer software, and the algorithms are called digital chaotic ciphers or chaotic cipher algorithms in this dissertation.Chaotic cipher algorithms are facing up the following problems: lack of systematic theories for proving the security of chaotic ciphers, and degradation of chaotic dynamic properties caused by finite computer precisions. Because of the former, tests of chaotic ciphers are extremely important. As for the latter, it can be amended by adopting multiple chaotic systems and perturbation schemes. On the other hand, security of classical ciphers can be proved mathematically, so it is suggested that chaotic ciphers should be combined with classical ciphers to construct highly secure cryptosystems. Thus, the subject of this dissertation deals with new complexity measurements and random tests of chaotic sequences, multiple chaotic cryptosystems, and mixed cryptosystems constructed by classical ciphers and chaotic ciphers.To be more specific, this dissertation mainly illustrates the following research findings.1. Test and compare the randomness of some chaotic sequences. The results show that Sequence Tests, Runs Tests and Approximate Entropy Tests are extremely significant for chaotic pseudorandom sequences. Meantime, some crucial conclusions are drawn on how iteration times and discretization precisions influence the randomness of chaotic sequences.2. New parameters for measuring the complexity and the local randomness of chaotic pseudorandom sequences, the index in primitive production process (IPP) and the maximum length of primitive production subsequences (LHmax), are proposed in this dissertation. Moreover, the weight IPP and the weight LHmax are defined. Absolute difference and relative difference of IPP and LHmax, i.e., ?IPP,k , LH max,k, dΔIPP,k and , are used for measuring and comparing the randomness stability of chaotic sequences. Numerical analyses show that the methods are effective. d LHmax,k3. Influence of finite computer precisions on chaotic systems is discussed. Then, a perturbation scheme is proposed. In the scheme, both chaotic system and the longest Linear Feedback Shift Register (LFSR) are adopted. Besides, its perturbation time space is varied randomly. Based on the perturbation scheme, a pseudorandom generator mLC-PRNG, composed by Logistic strong chaotic map, 4-order Chebyshev chaotic map and one LFSR, is presented and tested by NIST test suites.4. A cryptosystem based on multiple chaotic systems is designed. In the cryptosystem, digital chaotic maps are used and differential equations are not needed. Cascaded multiple chaotic maps and varied iteration times are adopted to weaken the effect of finite computer precisions and to strengthen the complexity and unpredictability of ciphers. Besides, once chaotic orbits fall into steady states, tiny perturbation 2-P (P presents the finite computer precision) will be put into force to eliminate the influence of steady states on cipher security. Test results prove that the cipher is not only sensitive to plaintext and key change, but also resistant to statistical attacks, differential attacks and state space reconstruction attacks.5. Image encryption schemes constructed by multiple chaotic systems are researched. Moreover, an image encryption algorithm based on forward-backward stream ciphers is designed with two pseudorandom generators mLC-PRNGs. Then, an image encryption algorithm with wavelet transform is proposed. Both of the two proposed algorithms are featured by large key space and high security.6. Cryptanalyses of two multiple chaotic image encryption algorithms in literatures are discussed and the causes for their insecurity are illustrated. In order to improve the security of the algorithms, it is suggested that ciphertext feedback, two rounds or even more rounds encryption architecture, more complex nonlinear transform should be adopted. By this way, cipher image sensitivity can be greatly enhanced and resistance against attacks be highly improved.7. A variable block cipher, GCIDEA, is designed on the basis of IDEA and spatiotemporal chaotic maps. In GCIDEA, both the advantages of classical ciphers and chaotic ciphers are fully utilized and the unpredictability of ciphers is improved by varying cipher block size. GCIDEA is characterized by large key space, high sensitivity to plaintext and key change, and strong resistance against statistical attacks and differential attacks.Finally, the dissertation is concluded and future work is stated.