Dynamics Analysis And Research On Image Encryption Algorithm Based On Chaos Systems

Due to the characteristics of chaos systems such as good pseudorandom, ergodic,high sensibility to the initial values, and long inscrutability, chaos has great potentialapplication in practical engineering. For example, the encryption algorithms based onchaos are presented to protect digital information against illegal copying and distributionover the Internet; and the weak signal can be tested by the sensibility. The analysis ofdesigned chaotic systems and their application in encryption are researched in this paper.Firstly, a image encryption algorithm based on Logistic mappings is designed.According to simulation results, the algorithm has good improvements on encryptioneffect, but still has some disadvantages which are brought by low-dimensional chaossystems, such as small key space, low randomicity and insecurity. What is more, thehigh-dimensional chaotic maps can exponentially enhance the security.Secondly, in order to make the information more secure over the Internet, twothree-dimensional chaotic systems are discussed. Some basic dynamical properties of thetwo systems are not only investigated by theoretical analysis but also demonstrated bycomputer simulations. What is more, changing the values can switch the states of the twosystems among periodic, equilibrium point and chaotic state. At the same time, the Lorenzsystem and the Chen system are compared with the two chaos systems.Thirdly, a color image encryption scheme based on the two chaos systems isproposed. Simulation results demonstrate that the algorithm has good performances andcan be used in practical engineering.Finally, in order to generate complex chaotic attractors, a four-dimensionalhyper-chaotic system is constructed by adding a nonlinear control to the three dimensionalchaotic system. Compared with the hyper-chaotic Chen system, the designed chaos systemhas larger positive Lyapunov exponent, better sensitivity and larger chaotic range.