## 3 Confidential Transmission Methods for High-Speed Power Line Carrier Communications
### Confidential Transmission Method Based on Generalized Two-Dimensional Polynomial Chaotic Mapping
The system architecture of the encrypted high-speed power line carrier communication network, implementing generalized two-dimensional polynomial chaotic mapping for information transmission, is shown in Figure 1.  
The operational process of the encrypted high-speed power line carrier communication network implementing generalized two-dimensional polynomial chaotic mapping is as follows:  
Step 1: Load the key \(K_{x}=x_{1}d_{1}x_{2}d_{2}\cdots x_{\tau}d_{\tau}\) generated by the generalized two-dimensional polynomial chaotic mapping equations. Step 2: Encrypt the transmission information \(\chi\) of the high-speed power line carrier communication network using the following encryption formula:  
\[P_{K_{x}}(\chi)=\cdots(x_{1}d_{1}\oplus\chi_{1})\cdots(x_{\tau}d_{\tau}\oplus \chi_{\tau})\cdots(x_{1}d_{1}\oplus\chi_{\tau+1})\cdots(x_{\tau}d_{\tau}\oplus \chi_{2\tau})\cdots \tag{5}\]  
Step 3: Generate the temporary ciphertext \(\chi^{\prime}=\chi^{\prime}_{1}\chi^{\prime}_{2}\cdots\chi^{\prime}_{\tau} \cdots\chi^{\prime}_{\tau+1}\chi^{\prime}_{\tau+2}\cdots\chi^{\prime}_{2\tau}\). Step 4: Load the key \(K_{y}=y_{1}d_{1}y_{2}d_{2}\cdots y_{\tau}d_{\tau}\) generated by the generalized two-dimensional polynomial chaotic mapping equations. Step 5: Perform secondary encryption on the temporary ciphertext \(\chi^{\prime}\) using the following formula:  
\[P_{K_{y}}\big{(}\chi^{\prime}\big{)}=\cdots\big{(}y_{1}d_{1}\oplus\chi^{\prime} _{1}\big{)}\cdots\big{(}y_{\tau}d_{\tau}\oplus\chi^{\prime}_{\tau}\big{)}\cdots \big{(}y_{1}d_{1}\oplus\chi^{\prime}_{\tau+1}\big{)}\cdots\big{(}y_{\tau}d_{ \tau}\oplus\chi^{\prime}_{2\tau}\big{)}\cdots \tag{6}\]  
Step 6: Generate the final ciphertext \(\chi^{\prime\prime}=\chi^{\prime\prime}_{1}\chi^{\prime\prime}_{2}\cdots\chi^ {\prime\prime}_{\tau}\cdots\chi^{\prime\prime}_{\tau+1}\chi^{\prime\prime}_{ \tau+2}\cdots\chi^{\prime\prime}_{2\tau}\). The decryption flow of the information transmitted by a high-speed power line carrier communication network using generalized two-dimensional polynomial chaotic mapping is shown in Figure 2.  
The decryption process using two-dimensional polynomial chaotic mapping for high-speed power line carrier communication networks is as follows:  
Figure 1: Encryption process of transmission information in high-speed power line carrier communication network. Figure 2: Decryption process of transmission information in high-speed power line carrier communication network. Step 1: Extract the encrypted ciphertext \(\chi^{\prime\prime}=\chi_{1}^{\prime\prime}\chi_{2}^{\prime\prime}\cdots\chi_{ \tau}^{\prime\prime}\cdots\chi_{\tau+1}^{\prime\prime}\chi_{\tau+2}^{\prime \prime}\cdots\chi_{2\tau}^{\prime\prime}\) through sequential reading [20]. Step 2: Load the decryption key \(K_{y}=y_{1}d_{1}y_{2}d_{2}\cdots y_{\tau}d_{\tau}\) generated by the generalized two-dimensional polynomial chaotic mapping equations. Step 3: Decrypt the ciphertext \(\chi^{\prime\prime}\) transmitted by the high-speed power line carrier communication network, using the following formula:  
\[P_{K_{y}}(\chi^{\prime})=\cdots\left(y_{1}d_{1}\oplus\chi_{1}^{\prime\prime} \right)\cdots\left(y_{\tau}d_{\tau}\oplus\chi_{\tau}^{\prime\prime}\right) \cdots\left(y_{1}d_{1}\oplus\chi_{\tau+1}^{\prime\prime}\right)\cdots\left(y_{ \tau}d_{\tau}\oplus\chi_{2\tau}^{\prime\prime}\right)\cdots \tag{7}\]  
Step 4: Generate the decrypted temporary ciphertext \(\chi^{\prime}=\chi_{1}^{\prime}\chi_{2}^{\prime}\cdots\chi_{\tau}^{\prime} \cdots\chi_{\tau+1}^{\prime}\chi_{\tau+2}^{\prime}\cdots\chi_{2\tau}^{\prime}\). Step 5: Load the decryption key \(K_{x}=x_{1}d_{1}x_{2}d_{2}\cdots x_{\tau}d_{\tau}\) generated by the generalized two-dimensional polynomial chaotic mapping equations.