A Novel Piecewise Chaotic Map for Image Encryption

Abstract

This paper investigates the issue of chaos-based image encryption. A new one-dimensional piecewise chaotic map based on the z-shaped fuzzy number is proposed and investigated, exhibiting regions of constant chaos and high Lyapunov exponent values. A pseudorandom bit generator based on the novel chaotic map is designed and successfully passes the National Institute of Standards and Technology (NIST) statistical tests. This PRBG is applied to the problem of image encryption, introducing a new image encryption scheme by using row and column permutation, chaotic pixel shuffling, and the exclusive OR operation. To demonstrate the robustness of this image encryption technique, various tests, such as differential attack and correlation, entropy and histogram analysis are performed.