| Summary: | 碩士 === 國立臺南大學 === 電機工程學系碩博士班 === 104 === In order to obtain double encryption via elliptic curve cryptography (ECC) and chaotic synchronization, this study presents a design methodology for neural-network (NN)-based secure communications in multiple time-delay chaotic (MTDC) systems. ECC is an asymmetric encryption and its strength is based on the difficulty of solving the elliptic curve discrete logarithm (ECDL) problem in finite field. Moreover, the difficulty of solving the ECDL problem depends on the size of the largest prime divisor of the order of the group of points of the curve. Therefore, it is time-consuming to process ECC when the prime divisor is much larger. If a smaller prime divisor is used to decrease the ECC processing time, it leads to a less secure cryptosystem. In order to enhance the strength of the cryptosystem, this study conducts double encryption that combines chaotic synchronization with ECC. First, ECC and the public key are used to encrypt the original message (plaintext) to produce the ciphertext, and the ciphertext is then re-encrypted via chaotic synchronization. A robust fuzzy control design is presented to overcome the effects of modeling errors between the MTDC systems and the NN models. Second, this study derives a delay-dependent exponential stability criterion in terms of Lyapunov’s direct method to guarantee the exponential stability of the error system between the master and the slave systems, thereby ensuring that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are reformulated into linear matrix inequalities (LMIs). Genetic algorithms (GAs) have been the focus of much attention from researchers because of their capability at random searches for near-optimal solutions. The lower and upper bounds of the search space, according to the LMI approach, can be set, thus GA seeks better feedback gains of fuzzy controllers, in order to accelerate the synchronization process. However, the traditional GA fails in both local searches and premature convergence. Therefore, this study presents an improved genetic algorithm (IGA) to effectively overcome this problem. According to the IGA, a fuzzy controller is synthesized to realize the exponential synchronization and achieve optimal H∞ performance by minimizing the disturbances attenuation level. Finally, a numerical example with simulations is given to demonstrate the effectiveness of the proposed approach.
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