**Guidong Zhang, Weikang Ding and Lian Li \***

School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China; zhanggd@lzu.edu.cn (G.Z.); dingwk15@lzu.edu.cn (W.D.)

**\*** Correspondence: lil@lzu.edu.cn

Received: 4 February 2020; Accepted: 19 February 2020; Published: 1 March 2020

**Abstract:** 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.

**Keywords:** chaotic map; image encryption; simultaneous confusion and diffusion
