## 8 Security Analysis  
Now, let us consider the security of data transmission through MANET by the proposed method. As noted earlier, security is based on the strength of the RRNS-SSS. The computationally secure SSS has a sufficient level of security without leading to high redundancy, unlike ideal SSSs [39]. Due to the properties of RRNS, this scheme allows not only secure data transmission in networks but also load balancing using distributed transmission of data divided into small shares. The strength of a particular network configuration depends on the resistance of each node to capture, the network topology, the number of node-separated routes built, the configuration of the SSS, and the moduli selection of the RRNS. It is necessary to consider that the condition for data interception (and at the same time confidentiality violation) is the interception of any number of nodes on \(n\) or more routes. Because it is not known in advance which nodes will be intercepted, it is impossible to select and exclude a compromised route in the data transmission protocol. Let us introduce the following notations:  
_Pr_--the probability of secure data transmission when data will not be intercepted during the time interval \(T_{0}\). _Pr__node_--the probability of the node attack-resistance (the probability that during the time interval \(T_{0}\) the data on the node will not be intercepted). _Q_--the probability of interception of \(z\) nodes. _E_--the probability of secret loss with \(z\) intercepted nodes. _Pr_--the probability of secure data transmission with \(z\) intercepted nodes  
node_ij_--node \(j\) in the route \(i\). _Z_--the total number of nodes. _z_--number of intercepted nodes. Let us consider the probability \(Pr\) for the example of the network with the same number of nodes on each route. Note, that it can be extended to the case with an arbitrary number of nodes on each route. Let us have four possible data transmission routes (Figure 6), each of which has two nodes, with \(\Pr\)\(\mathrm{node}=0.99\). We use a suitable RRNS configuration \((3,4)\) with three working and one redundant modulo. The probability of interception is 1-\(Pr\). The interception of data at any of the nodes of the route means the loss of confidentiality of the data transmitted by this route. To intercept the secret, at least three different routes must be intercepted (according to the number of moduli \(k=3\), the minimum necessary for recovery). Therefore, the probability of interception when less than three nodes are intercepted is zero. If exactly three nodes are attacked, then there are two options:  
* An attacker will be able to recover the original message, for example, if nodes are \(\mathrm{node}_{11}\), \(\mathrm{node}_{21}\), \(\mathrm{node}_{42}\);
* An attacker will not be able to recover the original message, for example, if nodes are \(\mathrm{node}_{11}\), \(\mathrm{node}_{12}\), \(\mathrm{node}_{22}\). The number of possible permutations of 8 nodes taken 3 intercepted at a time that leads to loss of secret (we denote this value by \(E_{3}\)), multiplied by the probability of intercepting exactly three nodes, gives the probability \(\Pr_{3}\) of intercepting data when intercepting any three nodes:  
\[\Pr_{3}=Q_{3}E_{3}, \tag{30}\]  
where \(Q_{3}=(1-\Pr\)\(\mathrm{node})^{3}\Pr_{\mathrm{node}}^{5}\)--the probability of intercepting exactly three nodes.