Evaluation and proof of routing algorithm in Tor anonymity network

Tor is one of the most popular networks providing anonymity and privacy on the Internet that works using volunteer systems from around the world. Low latency operation makes it suitable for things like web browsing. The way to select a path in tor network is one of the influential factors in the efficiency and security of this network. The path selection algorithm in the tor network has undergone many changes over its original design. These changes have been made for reasons such as increased efficiency, reliability, and load balancing, sometimes even in response to introduced attacks, they have to change the path selection algorithm. So far, many papers have looked at how to choose relays in the creation of circuits, but none of them, despite the open-source of the tor code, did not analyze the routing algorithm and the weighting method of the relays. And they have not proved logically and mathematically the relations used in this algorithm. In this paper, we attempt after fully analyzing the tor routing algorithm, for the first time, the exact logical and mathematical proofs of the relationships used in this algorithm are discussed. In this paper, we tried to investigate the anonymous network routing algorithm as the largest current anonymous network in the world.