# A New One-Dimensional Compound Chaotic System and Its Application in High-Speed Image Encryption  
[PERSON]  
1 Software School, Xinjiang University, Urumqi 830091, China; [EMAIL_ADDRESS] (S.Z. ); [EMAIL_ADDRESS] (X.D. )1 Software School, Xinjiang University, Urumqi 830091, China; [EMAIL_ADDRESS] (S.Z. ); [EMAIL_ADDRESS] (X.D. )1 Software School, Xinjiang University, Urumqi 830091, China; [EMAIL_ADDRESS] (S.Z. )1 Software School, Xinjiang University, Urumqi 8  
high-dimensional continuous time systems described by differential equations and low-dimensional discrete time systems described by iterative maps. The structure of a low-dimensional discrete chaotic map is simple, the software calculation speed is fast, and the hardware implementation is easier. However, some common low-dimensional discrete chaotic maps have the following defects: the number of parameters is small, and the map is easy to predict. Moreover, the range of parameters with chaotic behavior are narrow and the distribution of state values is not uniform. For example, there are such systems as the famous logistic map [10], tent map [11], sine map [12], etc. Due to the above shortcomings of such chaotic systems, information encryption brings the risk of security reduction. On the contrary, the high-dimensional continuous time chaotic system has more variables and parameters, and the parameter interval of chaotic behavior is large. However, this kind of complex dynamical system described by differential equations is more difficult to implement by hardware and requires more time overhead for software calculation, so it is not suitable for real-time encryption applications. Constructing new chaotic systems with a simple structure and high unpredictability has become an important issue for many cryptologists and researchers [13; 14; 15; 16; 17]. [PERSON] et al. [18] proposed an enhanced logistic map (ELM) and applied it in an image encryption scheme based on block scrambling and modified zigzag transformation. The authors claim that the method is secure and computationally efficient based on the analysis of the proposed method. [PERSON] et al. [19] proposed a lightweight image encryption algorithm based on a logistic-tent map and crossover operator. The extensive experiments of performance and security assessment show that the proposed image encryption scheme is secure enough to withstand all potential cryptanalytic attacks. [PERSON] et al. [20] proposed a new perturbed high-dimensional chaotic map and applied it to design a new encryption scheme. Although the encryption scheme can obtain satisfactory security, its encryption speed cannot meet the requirements of real-time encryption. [PERSON] et al. [21] proposed a new 1D chaotic system and applied it to color image encryption. Although the encryption system has acceptable speed, it has security defects. Some researchers have analyzed the encryption system [22; 23]. [PERSON] et al. [24] proposed a new two-dimensional (2D) chaotic system called a 2D-LASM and applied it to design an image encryption scheme. Although the authors claim that the system has a high security level, [PERSON] et al. [25] did a detailed cryptanalysis for it and cracked the cryptosystem. [PERSON] et al. [26] proposed a fast image encryption algorithm based on a logistic map, which has high encryption speed. However, the logistic map is not secure enough because of its small chaotic space and is vulnerable to brute force attacks. Although some existing image encryption algorithms have high security [6; 27; 28; 29; 30; 31; 32], many of them are only suitable for specific types of image encryption, such as color image and medical image, and cannot handle all types of digital images. The defects of these existing image encryption schemes have aroused our motivation to design a new image encryption scheme that is safe, fast and universal. In this paper, a new discrete chaotic map composed of a logistic map and tent map is proposed.