## 3 Confidential Transmission Methods for High-Speed Power Line Carrier Communications  
### High-Speed Power Line Carrier Communication Network Formation  
In high-speed power line carrier communication, establishing a stable link requires careful selection of appropriate power lines and nodes, forming the essential foundation for subsequent data transmission. A stable and reliable network guarantees that chaotic sequences generated by chaotic mapping maintain their complexity and unpredictability without causing transmission interference, thereby improving communication confidentiality and security. The minimal connected dominating set method enables the identification and construction of key node sets that preserve full network connectivity while minimizing node count, effectively reducing data transmission redundancy and delays [13]. This approach is implemented through a power line carrier routing algorithm to construct the high-speed power line carrier communication network. The concept of vertex domination in graph theory can be defined as a vertex dominating other vertices. In an undirected graph \(G(V,F)\), for a vertex subset \(V^{\prime}\subseteq V\), if for \(u\in(V-V^{\prime})\), there exist \(u\in V^{\prime}\) such that \((u,v)\in F\), then \(u\) is said to dominate \(v\), and \(V^{\prime}\) is considered a dominating set of \(G\). If any two vertices in an undirected graph \(G\) are connected by a path, then \(G\) is considered a connected graph. Let \(S\) be a dominating set of \(G(V,F)\). If there exists an edge set \(F^{\prime}\subseteq F\) that makes \(G\) a connected graph, then \(S\) is considered a connected dominating set of graph \(G(V,F)\). If for \(\forall v\in S\), \(S-\{v\}\) is not a connected dominating set, then \(S\) is considered a minimal connected dominating set of graph \(G(V,F)\). The primary objective of the high-speed power line carrier routing and networking algorithm is to construct an optimal network structure among the carrier nodes. A high-speed power line carrier communication network with bidirectional communication can be modeled as an undirected connected graph \(G(V,F)\), where \(V\) denotes the set of all carrier nodes, and \(F\) is the set of edges, with each edge of \(f\in F\) indicating the existence of a communication path between two carrier nodes. The research on high-speed power line carrier communication networking strategies primarily centers on dividing the network into logically interconnected subnetworks and ensuring reliable communication between devices [14]. Within a given area containing \(n\) carrier devices, maximizing network utilization efficiency requires selecting a minimal set of \(m\) devices with superior communication capabilities to serve as routing nodes, thereby guaranteeing reliable network-wide communication. This challenge is mathematically formulated as a minimal connected dominating set problem in graph theory. From a graph theory perspective, this work establishes a weighted network analysis model employing the minimal connected dominating set concept. Building upon this model, we propose a novel high-speed power line carrier routing algorithm that executes the following procedure: First, the algorithm selects initial routing nodes via maximum weight priority determination. Specifically, for each carrier node, it verifies whether the node exhibits the largest weight among its neighbors, thus ensuring the selection of the highest signal-to-noise ratio node as a dominating node. Second, the method performs network connectivity re-optimization on preliminary routing nodes to derive the minimal connected dominating set solution. During optimization, when any neighbor remains unconnected through existing dominating nodes, the algorithm designates it a new dominating node. Therefore, in the algorithm implementation, each carrier device is classified into one of three states: undetermined, a dominating node, or a dominated node. The undetermined state occurs during initial network formation when a device's role remains undefined.