## 4 Proposed Methodology
### Using Multiple Routes in Each Transmission  
Figure 7 illustrates the sequentially connected steganographic communication channels:  
From the reliability formula for a serial connection, the secrecy index of the message transmitted along the pathway created through one individual consecutive channel:  
\[P_{con}=P_{con\;1}\cdot P_{con\;2}\cdot\ldots\cdot P_{con\;l}=\prod_{i=1}^{l}P_ {i}\]  
where \(P_{con\;i}\) represents the secrecy index of the information transmitted through the \(i\)-th covert channel. Figure 8 depicts the parallel-connected steganographic communication channels:  
From the formula for calculating the reliability of parallel connections, the secrecy index of the transmitted information of the entire system, created through one individual parallel channel, is obtained. \[P_{con}=1-(1-P_{con\;1})\cdot(1-P_{con\;2})\cdot\ldots\cdot(1-P_{con\;l})=1- \prod_{i}^{l}(1-P_{con\;i})\]  
where \(P_{con\;i}\) is the secrecy index of the information transmitted through the \(i\)-th covert channel. If we combine the sequential and parallel connection models (Figure 9) (Case 2). Figure 8: Example of the parallel-connected steganographic communication channels. Figure 7: An example of sequentially connected steganographic communication channels. From the formula for calculating the reliability when combining sequential and parallel connections, the secrecy index of the transmitted message (when transmitted through multiple paths). \[P_{con}=1-\prod\limits_{i}^{n}{(1-\prod\limits_{j}^{m}{P_{con\ j}})}=1-\prod \limits_{i}^{n}{(1-P_{con\ i})} \tag{4}\]  
\(P_{con\ j}\)--secrecy index of the message transmitted through the \(j\)-th steganographic communication channel of the \(i\)-th path. \(P_{con\ i}\)--secrecy index of the message transmitted along the \(i\)-th path. \(n\)--the number of parallel paths used between the sender and the receiver. \(m\)--the number of steganographic communication channels in each path. Because of the probability of a breach in the confidentiality of the transmitted message between the sender and the receiver \(P_{nk}=1-P_{con}\), and the probability of a breach in the confidentiality of the message transmitted through \"\(i\)-th\" route is \(P_{nk\ i}=1-P_{con\ i}\), therefore \((4)\Leftrightarrow P_{nk}=\prod\limits_{i}^{n}{P_{nk\ i}}\), combined with \(P_{nk\ i}\leq 1,i=\overline{1,n}\). Thus, \(n\geq 1\Rightarrow P_{nk}\leq P_{nk\ i}\Rightarrow P_{con\ i}\
eq 1 \overline{1,n}\). From the results \(P_{con}\geq P_{con\ i}\)\(i=\overline{1,n}\), it has been demonstrated that combining serial and parallel connections enhances the secrecy index of the message transmitted between the sender and the receiver. Alternating the Use of Groups of Paths \(N\) Out of the Total \(M\) Paths (Case 3--A Combination of Case 1 and Case 2)  
This case is a combination of Case 1 and Case 2, and it is the proposed model. When alternating the use of \(N\) groups of paths out of the total \(M\) paths, the number of groups of paths (each consisting of \(N\) paths) is calculated as \(L=\left\lfloor\frac{M}{N}\right\rfloor\). \"Alternating\" here means that the proportion of using these groups of paths is equal and follows the ratio:  
\[\alpha=\frac{1}{L}=\frac{1}{\left\lfloor\frac{M}{N}\right\rfloor} \tag{5}\]  
Figure 9: Example of combined steganographic communication channels (sequential and parallel connections). In the case where the secrecy index of each path is \(P_{con\;i}=P_{con\;c}=\text{const}\), \(i=\overline{1..M}\), according to Formula (4), the secrecy index of the group of N paths is:  
\[P_{con\;N}=1-\prod_{i}^{N}(1-P_{con\;i})=1-(1-P_{con\;c})^{N} \tag{6}\]  
Combining Formulas (3) and (6) and Condition (5), the secrecy index when alternating the use of \(N\) path groups out of the total of \(M\) paths will be calculated using the following formula:  
\[P_{con\;M}=1-\prod_{i=1}^{L}\alpha(1-P_{con\;N})=1-[\alpha(1-P_{con\;N})]^{L}=1 -\frac{1}{L^{L}}(1-P_{con\;c})^{N\times L} \tag{7}\]  
where: \(L=\left\lfloor\frac{M}{N}\right\rfloor\).