Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Abstract

Based on some analyses of existing chaotic image encryption frameworks and a new designed three-dimensional improved logistic chaotic map (3D-ILM), an asymmetric image encryption algorithm using public-key Rivest–Shamir–Adleman (RSA) is presented in this paper. In the first stage, a new 3D-ILM is proposed to enhance the chaotic behavior considering analysis of time sequence, Lyapunov exponent, and Shannon entropy. In the second stage, combined with the public key RSA algorithm, a new key acquisition mathematical model (MKA) is constructed to obtain the initial keys for the 3D-ILM. Consequently, the key stream can be produced depending on the plain image for a higher security. Moreover, a novel process model (NPM) for the input of the 3D-ILM is built, which is built to improve the distribution uniformity of the chaotic sequence. In the third stage, to encrypt the plain image, a pre-process by exclusive OR (XOR) operation with a random matrix is applied. Then, the pre-processed image is performed by a permutation for rows, a downward modulo function for adjacent pixels, a permutation for columns, a forward direction XOR addition-modulo diffusion, and a backward direction XOR addition-modulo diffusion to achieve the final cipher image. Moreover, experiments show that the the proposed algorithm has a better performance. Especially, the number of pixels change rate (NPCR) is close to ideal case 99.6094%, with the unified average changing intensity (UACI) close to 33.4634%, and the information entropy (IE) close to 8.