Abstract
Chaotic signals generated by nonlinear dynamic systems can play a vital role in communications. Namely, the broadband frequency spectrum associated with chaotic signals is very natural in sending and receiving private communication signals. They are also attractive due to the ease of generation whether digitally or in analog form from nonlinear circuits, lasers, or even acoustic and mechanical sources. This dissertation has proposed a hybrid synchronized chaotic circuits for the purpose of secure communications. A novel secure communication system and cryptosystem are generated based on the hybrid synchronized chaotic circuits. First, a three-dimensional phase-locked loop (PLL) has been proven the existence of horseshoe chaos through the perturbation method that is based on the ideas of Melnikov method. Then, the Lyapunov exponents and Lyapunov dimension are calculated to confirm our theoretical results. Based on the architecture of synchronized chaotic circuits, a secure communication system and cryptosystem are proposed. In this secure communication system, the information sequence can be dynamically mapped to different portions of a chaotic time series. Using this method for communication has a variety of advantages. For example, a chaotic attractor contains infinite long time of chaotic series. Different time series can be mapped to the same information signal. Moreover, chaos has the noise like property, the mapped information sequence is also noise like. This hybrid synchronized chaotic circuit can also be used for cryptography. Using this synchronized chaotic circuit to replace the conventional encryption and decryption systems, this cryptosystem can achieve the purpose of security. The same plaintext will be encrypted to different ciphertext at different time. This cryptosystem can protect every single bit during the transmission. The architecture of the novel secure communication system and cryptosystem are also proposed. Simulation results indicate that it can not be broken by statistical methods. It is believed that the proposed secure communication system and cryptosystem are secure and will definitely help us in understanding the application of synchronized chaotic circuits.