## 3 Materials and Methods  
Steganography is a scientific field concerned with concealing confidential messages, focusing on the efficient hiding of messages. Steganography is divided into three main approaches: classical (non-computer), computer-based (utilizing data formats in networks),and digital (hiding information in multimedia). Our research concentrates on computer-based and digital steganography.  
Currently, the field of computer-based steganography is not yet complete, but it has seen numerous research proposals. Among them, the EMBSS model (Steganographic ally Systems Interconnection basic reference model--SSI model), proposed by the authors of [54], elucidates the meanings of several terms in steganography theory. This model is built upon popular concepts in steganography theory, communication system theory, and information security theory, as well as introducing new terminology.  
One research approach for enhancing security in the field of steganography is the development of algorithms for finding paths for packets in a network to ensure safety and optimization. Survey results reveal that the Dijkstra algorithm [13] has been widely adopted for solving shortest path finding tasks in routing protocols.  
The Dijkstra algorithm is one of the most popular algorithms for solving the shortest path problem on a directed graph. This algorithm finds the shortest path from a source vertex to all other vertices in a weighted directed graph, given that all edges in the graph have non-negative weights. The length (or weight) of a graph is the sum of the weights of its edges.  
The essence of the Dijkstra algorithm is to gradually build the tree of shortest paths from the source node. In this case, the necessary factor is that after adding a communication link and a node at each stage, the newly formed shortest path is the minimum path that can serve all the untaken destination nodes into the tree. While constructing the tree of shortest paths, the weight vectors of the paths are calculated and the vectors of the initial components of the shortest paths are adjusted. The complexity of the Dijkstra method depends on how the vertex v is found, how the set of unvisited vertices is stored, and how the labels are updated. In graph G, with n and m being the number of vertices and edges, respectively, finding a vertex with the shortest path to that vertex less than or equal to v requires searching through the entire n. The Dijkstra method is widely used in networking and network programming, for example, it is employed in the OSPF (Open Shortest Path First) protocol to eliminate routing loops.  
The author [55] proposes modifying the formula for calculating the metric \(M\) of steganographic communication channels to take into account the loss index in the OSPF protocol:  
\[M_{stego}=\left(k_{1}\cdot\frac{10^{8}}{C}+k_{2}\cdot T_{delay}\right)\cdot \frac{k_{3}}{P_{con}+k_{4}} \tag{1}\]  
In this context, \(M_{stego}\) is the modified metric of the stego communication channel; by default, for OSPF, \(k_{1}\) = 1 and \(k_{2}\) = 0, while \(k_{3}\) and \(k_{4}\) are coefficients to determine the confidential components. \(P_{con}\) is the secrecy index of the message transmitted through the covert channel, assumed to have values within the range \([0,1]\). This index ensures that sensitive information is safeguarded from unauthorized disclosure during transmission, with a value of 1 corresponding to maximum secrecy and 0 indicating no secrecy.  
In this study, we will employ a modified version of the Dijkstra algorithm in the steganographic network, as presented by the authors [13]. This modified version not only facilitates finding the shortest path from the source node to other nodes but also enables the identification of backup paths from the source node to other nodes.