Analysis Of Coexisting And Hidden Attractor Chaotic Systems And Application Of Image Encryption

Chaotic motion is an important research object in nonlinear systems.Chaotic systems have excellent characteristics such as extremely sensitive to initial conditions,unpredictability and high complexity,which are widely concerned by scholars and are gradually applied to engineering fields.The rapid development of communication technology and computer networks has made digital images more versatile and convenient as information carriers.However,the security of image information is becoming increasingly serious,and it is crucial to design secure and reliable image encryption schemes.With the maturity of chaos theory and chaotic cryptography,chaotic image encryption technology has developed into an important branch of image cryptography research.The main research work of this paper is as follows.The common chaotic systems in image encryption algorithms are described,the single dynamical property of chaotic systems in image encryption schemes is improved and two chaotic systems with complex characteristics are constructed.The rich dynamical behavior of the system is analyzed by using bifurcation diagrams,Lyapunov exponential spectra and phase diagrams.The first new four-wing hyperchaotic system has two Lyapunov exponents greater than zero,and multiple states of motion such as periodic,chaotic and hyperchaotic can be observed as the parameters change.The system exhibits the coexistence of multiple types of attractors when different initial values and fixed parameters.The second equilibrium-free chaotic system does not have equilibrium states and can generate single-wing hidden attractors and double-wing hidden attractors with a wide range of chaotic parameters as the parameters change.In addition,the complexity of two new chaotic systems is calculated to verify the complexity of chaotic sequences and to determine the range of parameters in subsequent cryptographic applications.Combining the constructed chaotic system with coexisting attractors,a two-level image encryption scheme associated to plaintext is proposed.The scheme introduces Logistic mapping to generate the key stream associated with the plaintext,uses global dislocation algorithm to disrupt the pixel positions,and uses cyclic diffusion algorithm to change the pixel values so that the change of each pixel point affects the whole image in the encryption process.The advantage of this scheme is that it achieves "one key at a time",enhances the randomness and security of the algorithm,and has the ability to resist common attacks.The color image encryption scheme is proposed in conjunction with the constructed chaotic system with hidden attractors.The scheme obtains a key associated with the plaintext through the Hash function.The confusion stage uses the idea of matrix blocking and combines the Zigzag algorithm to achieve pixel point permutation.During the diffusion process,the Sine map is used to achieve dynamic encoding of DNA,and a bidirectional diffusion algorithm is designed to complete the encryption process.Experimental analysis shows that the algorithm has good encryption and decryption performance,and has a certain degree of robustness.