Weikang Ding

We propose a new chaotic map combined with delay and cascade, called tent delay-sine cascade with logistic map (TDSCL). Compared with the original one-dimensional simple map, the proposed map has increased initial value sensitivity and internal randomness and a larger chaotic parameter interval. The chaotic sequence generated by TDSCL has pseudo-randomness and is suitable for image encryption. Based on this chaotic map, we propose an image encryption algorithm with a symmetric structure, which can achieve confusion and diffusion at the same time. Simulation results show that after encryption using the proposed algorithm, the entropy of the cipher is extremely close to the ideal value of eight, and the correlation coefficients between the pixels are lower than 0.01, thus the algorithm can resist statistical attacks. Moreover, the number of pixel change rate (NPCR) and the unified average changing intensity (UACI) of the proposed algorithm are very close to the ideal value, which indicates that it can efficiently resist chosen-plain text attack.

Considering that a majority of the traditional one-dimensional discrete chaotic maps have disadvantages including a relatively narrow chaotic range, smaller Lyapunov exponents, and excessive periodic windows, a new nonlinearly modulated Logistic map with delay model (NMLD) is proposed. Accordingly, a chaotic map called a first-order Feigenbaum-Logistic NMLD (FL-NMLD) is proposed. Simulation results demonstrate that FL-NMLD has a considerably wider chaotic range, larger Lyapunov exponents, and superior ergodicity compared with existing chaotic maps. Based on FL-NMLD, we propose a new image encryption algorithm that joins the pixel plane and bit-plane shuffle (JPB). The simulation and test results confirm that JPB has higher security than simple pixel-plane encryption and is faster than simple bit-plane encryption. Moreover, it can resist the majority of attacks including statistical and differential attacks.

With the popularity of the Internet, the transmission of images has become more frequent. It is of great significance to study efficient and secure image encryption algorithms. Based on traditional Logistic maps and consideration of delay, we propose a new one-dimensional (1D) delay and linearly coupled Logistic chaotic map (DLCL) in this paper. Time delay is a common phenomenon in various complex systems in nature, and it will greatly change the dynamic characteristics of the system. The map is analyzed in terms of trajectory, Lyapunov exponent (LE) and Permutation entropy (PE). The results show that this map has wide chaotic range, better ergodicity and larger maximum LE in comparison with some existing chaotic maps. A new method of color image encryption is put forward based on DLCL. In proposed encryption algorithm, after various analysis, it has good encryption performance, and the key used for scrambling is related to the original image. It is illustrated by simulation results that the ciphered images have good pseudo randomness through our method. The proposed encryption algorithm has large key space and can effectively resist differential attack and chosen plaintext attack.