Research Of Chaos In Memristor-based Circuit And Image Security

Chaos theory is one of the center researches in nonlinear science which has a very wide range of applications. Memristor is a two-terminal element with variable resistance called memristance. Because of the nonlinearity of memristor element, memristor-based circuits can easily generate a chaotic signal, which can be used in cryptographic systems. Cryptography is the science of cryptology and cryptanalysis. The properties of chaotic maps such as sensitivity to initial conditions and random-like behavior and the properties of cryptography are in common, so chaos theory has a widely used in cryptography. This thesis use theoretical analysis and numerical simulation method to study the chaos in the memristor circuit and chaotic cryptography. The main works are as follows:(1) The author studies the chaotic behavior of both integer-order and fractional-order memristor-based Muthuswamy-Chua circuit. A second order exponent internal state memristor function and fourth degree polynomial memristance function is used in this circuit to increase complexity of the attractor. Simulation results show that both integer-order and fractional-order systems exhibit chaotic behavior over a range of control parameters.(2) The author studies the chaotic behavior of three kinds of Muthuswamy-Chua systems whose memristance functions are obtained from the Chebyshev polynomials. The internal state of memristor is set to second order to increase complexity of the attractor. Simulation results show that all these systems exhibit chaotic behavior over a range of control parameters.(3) A bit-level image encryption algorithm based on spatiotemporal chaotic system and self-adaptive is proposed. The author uses bit-level encryption scheme to reduce the volume of data during encryption and decryption in order to reduce the execution time. And use the adaptive encryption scheme to make the ciphered image dependent on the plain image. Simulation results show that the performance and security of the proposed encryption algorithm can encrypt plaintext effectively and resist various typical attacks.(4) The author proposes a color image encryption algorithm based on chaos. Firstly, convert the color image into three bit-level images and combine them to one bit-level image. Then, only use permutation architecture to encrypt the integrated bit-level image to reduce the execution time. Simulation results show that the algorithm can encrypt the color image effectively and resist various typical attacks.(5) Analyze the security of a chaotic system based fragile watermarking scheme for image tamper detection proposed by Rawat et al.. Some problems and modification attack against Rawat et al.’s scheme are demonstrated. Both theoretical analysis and experimental results show that the fragile watermarking scheme is not security. Besides, improvement measure is presented, the watermark is embedded into the the lowest three bits of image plane based on chaotic sequence, in order to enhance the security of the fragile watermarking scheme.