Discrete Design of Lorenz Chaotic System Based on Euler Method and Image Encryption

Because the chaotic system has very good encryption performance, so in recent years, the research on the chaotic system is more extensive and in-depth. The output data of the chaotic system can be used to encrypt data and other information. But the output of the chaotic system is continuous, so we need to make discretization of the output continuous data. The Runge-Kutta method is the common method to be used to discrete chaotic systems. Its advantage is high accuracy, but the programming is complex and not easy to achieve. This paper presents a discrete design based on Euler method, this method is simple in programming, small footprint, fast running, but the accuracy is relatively low. But we want to get the discrete data for image encryption, so the accuracy requirements are not high, as long as the discretization can be achieved. Because the Lorenz chaotic system is a three-dimensional system, the output are X, Y, Z three groups of data. We compare a set of data with their power spectral density and autocorrelation characteristics, and then use for image encryption. The MATLAB simulation showed that the method can realize the image encryption and decryption, the effect is good, and it can guarantee the security of data transmission.