## 3 Confidential Transmission Methods for High-Speed Power Line Carrier Communications
### Confidential Transmission Method Based on Generalized Two-Dimensional Polynomial Chaotic Mapping
#### 3.3.3 Confidential Transmission Scheme for High-Speed Power Line Carrier  
Communications Based on Generalized Two-Dimensional Polynomial Chaotic Mapping  
The inherent unpredictability and ergodicity of chaotic mapping make it particularly suitable for secure data transmission in networks. When ciphertext encrypted via the generalized two-dimensional polynomial chaotic mapping (Section 3.3.2) is employed for data transmission, its output distribution critically impacts the bit error rate (BER) performance. The generalized 2D polynomial chaotic mapping proposed in this work achieves a near-uniform output distribution across the entire value space, thereby enhancing secure communication performance. By integrating the reference-modulated differential chaotic shift keying (RM-DCSK) with the ciphertext encrypted via the generalized 2D polynomial chaotic mapping (Section 3.3.2), the RM-DCSK secure transmission scheme ensures robust and secure high-speed power line carrier communication. The schematic diagram of the ciphertext interface of chaotic map and RM-DCSK modulation is shown in Figure 3.  
The advantages of a high-speed power line carrier communication secure transmission scheme based on generalized two-dimensional polynomial chaotic mapping over traditional secure transmission methods are as follows:  
(1) Confidentiality enhancement  
Figure 3: Schematic diagram of ciphertext interface of chaotic map and RM-DCSK modulation. The scheme leverages the complex dynamic behavior of generalized two-dimensional polynomial chaotic mapping to generate cryptographically strong key sequences with high randomness and unpredictability. This significantly elevates the confidentiality level of transmitted data and substantially increases the computational complexity for potential attackers. The expanded key space in two-dimensional space provides superior anti-deciphering capability compared to traditional methods, effectively mitigating the risks of information leakage and malicious attacks. Anti-Interference performance  
The proposed encryption scheme demonstrates exceptional resistance to power line channel impairments including electromagnetic interference, equipment noise, and signal attenuation. The inherent randomness and complexity of the chaotic mapping ensure consistent communication stability and reliability, while preserving data integrity and accuracy during transmission. This enhanced robustness enables reliable operation in highly dynamic communication environments. Transmission efficiency  
The scheme fully exploits the high-bandwidth characteristics of power line carrier communication to support high-throughput, low-latency data transmission. Through optimized modulation/demodulation algorithms, the system achieves superior spectral efficiency and overall performance. This meets and exceeds the stringent requirements of smart grid applications, while providing scalable infrastructure for future power system advancements. The RM-DCSK secure transmission scheme consists of transmitter and receiver components. The transmitter first encrypts the message bits with a key generated by the generalized 2D polynomial chaotic mapping in Section 3.3.2, produces a high-speed power line carrier communication ciphertext, and then transmits the transmitter and receiver components. The receiver decodes the received ciphertext using the key generated by the generalized 2D polynomial chaotic mapping in Section 3.3.2 to recover the message bits. Transmitting end: \(\chi_{2l}\) serves as the information bits for \(2l\), and \(\chi_{l}^{\prime\prime}\) represents the high-speed power line carrier communication ciphertext encrypted using the generalized 2D polynomial chaotic mapping described in Section 3.3.2, with a line length of \(H\). This is expressed as \(\chi_{l}^{\prime\prime}=\left\{\chi_{i}^{\prime\prime}|2H<i<(2l+1)H\right\}\), where \(H\) denotes the spreading index. The first time slot within the high-speed power line carrier communication network, established in Section 3.1, is designated as the reference time slot.