A image encryption scheme based on dynamical perturbation and linear feedback shift register

Because low-dimensional chaotic precision degradation has seriously affected the security of encryption, compound chaotic function is designed. It is based on two new one-dimensional chaotic functions. By the definition of Devaney chaotic, the properties of compound chaotic functions are rigidly proved. Based on the compound chaotic function and linear feedback shift register (LFSR), a new pseudo-random sequence generator is designed to generate a more random sequence and expand the key space. The properties of compound chaotic functions and LFSR are also established. In the scheme, a dynamic block division of the 3D baker and dynamical perturbation are illustrated using the compound chaotic map to derive the confusion image. The new pseudo-random sequence generator expands the key space and improves the security of image encryption scheme. The results of entropy analysis, difference analysis, weak-key analysis, statistical analysis, cipher random analysis, and cipher sensitivity analysis show that the encryption scheme has a better security. Compared with traditional encryption scheme and one-dimensional logistic chaotic map, the new image encryption scheme has a better performance in speed, complexity, and security. This paper illustrates how to solve the problem of short periods and low precision of one-dimensional chaotic function by perturbation and LFSR together.