| Chaos is an especial phenomenon in the nonlinear dynamical systems, which has ergodicity, limitary, sensitivity to initial condition, control parameters and random like behavior. In recent years, chaotic system's application in information security aroused great interest of scholars, and achieved many significant results. As a special chaotic system, hyperchaotic system has more than one positive Lyapunov exponent. Compare with the regular chaotic system, it has higher unpredictability and stronger pseudo-randomness, may be more useful in some fields such as communication, encryption, etc.Fiber laser, as a representative of the third generation of laser technology, has unmatched technical superiority to the other lasers. Furthermore, Erbium-doped fiber laser also has low-loss characteristic and harmless to the human eye. So, it has been widely applied in optical communications, medicine and many other areas. In 1998, LG Luo et al found that there is chaos and hyper chaos in erbium-doped fiber laser system, then, many scholars have started research work about it, and applied it to information security. This paper, taking the hyper-chaotic system of Dual-ring Erbium-doped Fiber laser as the research object, mainly studies the application of hyper-chaos in information security. The paper presents a novel image encryption algorithm and a novel hyper-chaotic pseudo-random sequence generation algorithm based on hyper-chaos of Dual-ring Erbium-doped fiber laser, studies hyper-chaotic synchronization in Dual-ring Erbium-doped fiber laser's complex networks with coupling delays. The thesis can be divided five parts.Part one:It describes the background and significance of the subject research. Firstly, it briefly introduces the concept, characteristics and research methods of chaos, which focuses on the Lyapunov exponent analysis, and on this basis, describes the concept of hyper-chaos. Secondly, the paper introduces the application of chaos in information security and research focus, and points out it can be divided into two main areas of research:chaotic cryptography and secure communication based on synchronization of chaos, and briefly introduces the concept of cryptography and synchronization of chaos. Finally, we review the research course on chaos of the optical laser system, briefly introduce the research of chaos based on some laser, such as CO2 lasers, He-Ne laser, Nd:YV04 laser and erbium-doped fiber laser, and present the research direction and focus of this paper.Part two:It mainly studies chaotic and hyper-chaotic behavior of Dual-ring Erbium-doped Fiber laser. Firstly, we briefly introduce the structure, principle and characteristics of the Erbium-doped Fiber laser, and on this basis, introduce the normalized equation of the system and utilize Lyapunov exponent to analyze chaotic and hyper-chaotic behavior of the system. Secondly, we discuss the relationship between pseudo-random property of chaotic system with Lyapunov exponent, and compare the pseudo-random property of Dual-ring Erbium-doped fiber laser with that of other common hyperchaotic systems, and illustrate the system more suitable for information security. Finally, we briefly discuss hyper-chaotic control and synchronization of Dual-ring Erbium-doped fiber laser. This provides the basis for follow-up study of hyperchaotic synchronization in complex networks.Part three:Firstly, we introduce the development of digital image encryption based on chaos. In 1997, Fridrich firstly proposed image encryption based on chaos. From then on, many algorithms were proposed. However, research has shown that messages masked by regular chaotic systems are not always safe. On the other hand, Fridrich suggested that a chaos-based image encryption scheme should compose of two processes:substitution and diffusion. This architecture forms the basis of a number of chaos-based image ciphers proposed subsequently. However, in these cryptosystems, many rounds of substitution and diffusion are required to achieve a satisfactory level of security and the total encryption time is quite long. The reason is that the confusion effect is contributed solely by the substitution stage while the diffusion effect is only introduced in the diffusion stage. For the above-mentioned issues, we proposed a novel image encryption algorithm based on hyper-chaos of Dual-ring Erbium-doped fiber laser. In the algorithm, the two-dimensional discrete hyper-chaotic mapping is designed to shuffle the positions of pixels and the hyper-chaos of Erbium-doped fiber laser is used to encrypt the shuffled image. Furthermore, a certain logic operation for diffusion is introduced in the substitution stage. Finally, we utilize "XOR" and "add-and-shift" to verify the effectiveness of the algorithm. The experimental results demonstrate that the suggested encryption algorithm has better security performance, and high security level can be achieved by only one total round of substitution and diffusion.Part four:It mainly studies the pseudo-random sequence based on hyper-chaos. We briefly introduce the relevant theory of pseudo-random sequence and the development of the pseudo-random sequence based on chaos; analyze influence of finite precisions on chaotic systems which hinder the application of chaos in the relevant areas. In recent years, scholars have been seeking the resolution to improve it. The common method is to improve the computing precision, the use of multiple chaotic systems, the use of perturbation, etc., in which the most common way is perturbation. However, to the majority of the proposed perturbation method, the disturbance intervals are fixed, that is adverse to the randomness of the sequence. For the above-mentioned issues, we proposed a novel pseudo-random sequence generation algorithm based on hyper-chaos of Dual-ring Erbium-doped fiber laser. The algorithm disturbs evolution of hyper-chaos by a novel method, in which the disturbance interval and disturbance value are both dynamic, effectively avoiding influence of finite precisions. Finally, we analyze the statistical properties and security properties of the sequence, and apply it to digital image encryption. The experimental results demonstrate that the sequences have good pseudo-random properties. At the same time, the sequence generation algorithm is universal, not limited to hyper-chaos of Dual-ring Erbium-doped fiber laser.Part five:Firstly, we introduce the basic concepts of complex networks and the theory of synchronization of nonlinear dynamic system complex networks with coupling delays; present the thought that it is applied to hyper-chaos of Dual-ring Erbium-doped fiber laser. Secondly, we study hyper-chaotic synchronization of ring network and globally coupled network of Dual-ring Erbium-doped fiber laser based on the theory, and give the relevant criteria. Then, hyper-chaotic synchronization criteria of 4-node ring network and 4-node globally coupled network are deduced. The results show that the synchronization may be obtained on the suitable parameters in the system. We verify the conclusion by the numerical experiments and found the synchronization ability of globally coupled network is better than that of ring network. The results of simulation and analysis provide the important theoretical basis for the further research of chaotic synchronization of fiber laser complex networks and the design of secure communication system based on fiber laser network.
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