# Constellation Encryption Design Based on Chaotic Sequence and the RSA Algorithm
## 3 The Proposed Design Method  
### Design Thinking  
The chaotic sequence is iteratively generated by the deterministic equation, so that the receiver can reproduce the exact same sequence under the condition of mastering the parameters. At the same time, chaotic sequences are often used in the encryption process because they are sensitive to initial conditions and control parameters, and because they  
Figure 1: Bifurcation diagram.  
can generate a large number of different sequences. However, due to the influence of calculation accuracy, periodic characteristics will appear, which will have a great impact on the security of the communication system.  
The RSA algorithm is often used in asymmetric encryption. It has a pair of public key and private key, and has the advantage of high cracking difficulty. Butthe secrecy strength of the RSA algorithm increases with the length of its key. Butthe longer the key, the longer it takes to encrypt and decrypt.  
The idea of the design method we proposed is that the digitally modulated signal shows several fixed points on the constellation diagram. Such a fixed modulation method makes the communication parameters of the transmitted signal easy to decipher, which brings great challenges to wireless link transmission communication. Taking this as a starting point, chaotic sequences are used to scramble the constellation points, so that the points on the original constellation map lose their original physical significance, and achieve the purpose of physical layer encryption. The essence is to use the chaotic sequence to remap the constellation points according to certain rules, and the parameters generated by the chaotic sequence use the RSA algorithm, that is, combine the advantages of the above two and avoid, their defects as much as possible.  
The specific method is: we use the public key and the key to encrypt and decrypt the information at the sender and receiver, respectively. For partners, the rules and public keys for information encryption can be obtained. After the receiving end receives the signal, first demodulate it, then use the key and pre-agreed rules to decrypt it, and then continue to process the signal, the flowchart is shown in Figure 2 For non-cooperating parties, the difficulty of intercepting information comes from three aspects: First, there is no encryption rule; Second, it is unclear which chaotic map to use and the specific parameters; and Third, it is difficult to know how to solve the key.  
The model we designed provides a set of constellation encryption flowcharts, in which both communicating parties have a lot of choice for the chaotic sequence used in encryption, and the parameters of the RSA algorithm can also be adjusted in real time, so the model has a strong flexibility, which further improves the anti-interception ability of information. At the same time, the simplicity of the entire model does not increase the computational complexity and does not reduce the reliability of communication under low signal-to-noise ratios. However, there are also some flaws, namely, the model is mainly designed for the sender and receiver, the channel only uses Gaussian white noise for scrambling, the whole process does not involve the synchronization of the transmit and receive time of the public key and the key and target signal, and the does not consider how to ensure that the ciphertext is not lost and distorted.