# Minimizing the Number of Distrustful Nodes on the Path of IP Packet Transmission
## 1 Introduction  
Routing is one of the main tasks in computer networks and its importance and impact on network efficiency are difficult to overestimate. To implement routing in networks, various routing methods, algorithms, and routing protocols are used. One of the main tasks of routing protocols is finding the shortest paths, construction, and maintenance of routing tables. The main protocol widely used within an Internet Service Provider network is an Open Shortest Path First routing protocol (OSPF) [1]. OSPF is a dynamic routing protocol based on link-state technology, which uses [PERSON]'s algorithm for computing least cost paths. The algorithm allows you to find the shortest path using the selected criterion, while not allowing for the provision of other additional requirements. In our work, as such an additional requirement, we set a goal not to include, if possible, destination routers that are not trustful. The reasons why the router will be considered distrustful may be different, for example, due to its location in the temporarily occupied territory, in the area near the fighting, or others. The responsibility for assigning a router to the untrusted class or returning it back to the normal class can be delegated only to Autonomous Systems, since they are the ones who determine the routing policy on the Internet. All routers of the Autonomous System with a unique ASN number are under the control of a single technical administration service, which clearly defines the policy of routing the IP packets within it. Routing problems are widely covered in the world's scientific literature. These are works of a system-wide nature, which analyze, for example, static and dynamic routingor centralized and decentralized routing [2; 3], as well as works that analyze, compare, and improve specific protocols under certain conditions. In particular, many works are devoted to the implementation of the widely used OSPF protocol in Wide Area Networks (WANs) [4; 5; 6; 7; 8; 9]. Different tools are used for routing research, such as the Riverbed Modeler [10], the GNS3 [7], the Cisco Packet Tracer simulator [11], etc. These make it possible to study the behavior of protocols in networks of different topologies, at different data transfer rates, to analyze various indicators using different criteria. The most common criteria of routing in WANs are the number of routers that a packet must pass through to reach the destination network or the channel throughput [12] and, in the sensor networks, the power consumption [13]. The authors of [14] study the potential of using the relatively new metric of Age-of-Information for enhancing delay-tolerant routing protocols. Delays due to signal propagation time in the physical environment, cost, reliability, and security are also often used in various networks. The OSPF protocol allows us to obtain the shortest paths, taking into account one of these criteria. The disadvantage of the single-criteria approach is that the optimal packet transmission path found for this criterion may not be acceptable from the point of view of other criteria, which are also important in this case. In [15], a routing protocol for wireless sensor networks using two criteria is proposed. It involves the classification of data packets into critical and normal ones and, based on this categorization, offers two delivery paths instead of one, as is usually the case. The case in which three criteria are considered is presented in other studies [5; 9]. To provide security at data transmission, different approaches are proposed. For example, a neural network for real-time cryptographic data protection oriented on unmanned aerial vehicles is presented in [16], for which data protection from damage or loss in the wireless channel between it and the remote control center is critical. The study in [17] proposes the concept of calculating the info-communication system reliability indicator of operating under the probable impact of typical cyber-physical attacks.