# Constellation Encryption Design Based on Chaotic Sequence and the RSA Algorithm
## 1 Introduction  
Because satellite communication has many advantages, such as long communication distance, small restrictions and flexible signal configuration, it is widely used in communication broadcasting, secure communication, positioning, navigation and other fields [1; 2; 3; 4; 5; 6]. However, since the essence of satellite communication is wireless communication, the main problem is that communication signals are easily exposed to illegal interceptors in the process of wireless transmission, and the rapid improvement of computer data processing capabilities now means that the anti-interception ability of communication signals has improved. It is easy to cause potential security risks, especially in the field of military communications. If the concealment and security of the communication process cannot be guaranteed, it is possible to miss opportunities on the battlefield. Therefore, how todesign according to the characteristics of wireless communication is more secure. It is an urgent problem of wireless communication that needs to be solved in the future [7; 8; 9; 10; 11; 12; 13]. Low intercept probability communication is a comprehensive physical layer of wireless security technology, which guarantees the security of wireless communication from three levels: 1. Signal concealment to prevent communication signals from being discovered; 2. Feature hiding to prevent communication signal features from being extracted; 3. Information concealment to prevent communication information from being eavesdroppedped [14; 15; 16]. In Ref. [17], in order to improve the security of the physical layer, a novel chaotic technique was designed to make the symbol period change according to the behavior of the chaotic spreading sequence during communication. Ref. [18] proposed a new symbol-level constellation shift scheme based on phase ambiguity, so that the encrypted symbols are still on the ideal constellation points. However, the computational complexity still needs to be improved. The constellation is also mapped using digital chaos, adding a dynamic radius and phase offset to the standard constellation diagram [19], thus providing ahigh level of security during data transmission. However, under low signal-to-noise ratio conditions, it will affect the transmission's reliability. Ref. [20] designed a fast, dual-polarization frequency hopping system and applied virtual polarization technology to satellite communication to enhance the secure transmission of the physical layer. In Ref. [21], a scheme based on constellation rotation and weighted fractional Fourier transform was proposed, so that the processed signal resembles a Gaussian distribution, which is not easy to detect. Additionally, the constellation points are also distorted to ensure strong confidentiality. Ref. [22] proposed a multiple encryption scheme, scrambled the already modulated symbols, and distributed them independently on the complex plane. Additionally, the dynamic parameters of the constellation shift were generated by 3-D hyper-digital chaos. Combining two asymmetric encryption algorithms, RSA (Rivest-Shamir-Adleman) and ECC (Ellipse Curve Cryptography), generates a new hybrid key generation, which enhances the key strength in Ref. [23]. In Ref. [24], a six-dimensional model for generating chaotic sequences was first constructed, and encrypted sequences were generated according to the principles of the RSA asymmetric algorithm. In order to achieve better confidentiality of satellite communications and to improve the ability to resist interception, many methods have emerged at the level of physical layer encryption, but there are certain shortcomings in terms of high computational complexity, low reliability at low signal-to-noise ratios, and specific requirements for certain parameters. We found that chaos-based wireless secure communication systems and some algorithms in cryptography are widely used. This provided us with new ideas and methods.