# Teletraffic Analysis of DoS and Malware Cyber Attacks on P2P Networks under Exponential Assumptions
## 1 Introduction  
Peer-to-peer networks are computer networks in which all or some aspects function without fixed clients or servers [1]. They have elementary operating principles; their maintenance cost is low because they do not have centralized servers, and, therefore, thy are very popular, especially in data transmission and file-sharing services of any kind. Moreover, they avoid bottlenecks at the server since high traffic loads imply that many users are active in the system, and each of these contributes resources (memory, processing, and communication bandwidth) to the overall operation of the network. They are organized in a flat structure that allows a direct exchange of information between clients. That is why they are ideal for file dissemination to many computers. Figure 1 shows the operation of this kind of network. Indeed, a _peer_ acts as a server and as a client in a self-organized and dynamically coordinating structure, since the number of nodes can be increased or decreased at any time. Peers share the file with each other, which is divided into chunks that are distributed throughout the system. Then, a given peer uploads a set of chunks to other peers thatdo not have them, while it downloads missing chunks from other peers. The respective peer is responsible for finding the correct information. If the data are common, it is easy to find them, but it is difficult to find rare data from other peers. Peers with the complete file usually are called _Seeds_, while peers without the complete file are called _Leechers_[2]. Hence, seeds can share the complete file with any given leecher. In this regard, it is important for seeds to remain in the system after they have downloaded the file to increase the capacity of the system. P2P networks can be divided into three categories: unstructured P2P, structured P2P, and hybrid P2P networks [3; 4; 5]. An unstructured P2P network does not tell the exact location of the data, so it looks for the requested data in its network. This type of network represents a degree distribution of power law and is dominant in real-life deployment. The disadvantage of this type of network is that it does not seem to know if it can access the data. A structured P2P network uses a globally consistent protocol for efficient searching. It uses a hash table called a distributed hash table (DHT). This table provides information about where a particular file comes from based on several important factors. A hybrid P2P network combines the topology of a structured and an unstructured one. This type of network defines so-called _Superpeers_, which act as servers to a small portion of the network, and each of them has a list of file information. From this description, it is clear that, for any P2P network, nodes share the chunks directly among themselves without the need for previous verification from a centralized authority. Hence, it would be relatively easy for a malicious node to modify a given chunk to propagate malware throughout the network. Furthermore, since the P2P network entirely relies on users sharing their communication resources, a simple denial of service attack (DoS), which impedes neighbor nodes' communication, can drastically hinder the operation and performance of the system [6]. Taking BitTorrent as an example, when a file is downloaded, part of the file is downloaded, and the other part is received at the same time by different peers who may have downloaded a chunk or the whole file [7]. This download mechanism in peer-to-peer networks improves the download speed, avoiding bottlenecks at the server and taking advantage of the user's resources to increase the system bandwidth. However, the adequate operation of the system heavily relies on nodes trusting each other. Hence, in the case of malware inserted in one or several chunks, it can be spread and affect many users. To the best of our knowledge, the malware propagation dynamics in a P2P network have been largely overlooked.