Secure Overlay Network Design

• Published in: Algorithmic Aspects in Information and Management pp. 354 - 366
• Main Authors: Li, Li (Erran), Mahdian, Mohammad, Mirrokni, Vahab S.
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2006
• Series: Lecture Notes in Computer Science
• Subjects: combinatorics; network design; network security; optimization
• ISBN: 3540351574; 9783540351573
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11775096_33

Due to the increasing security threats in the Internet, new overlay network architectures have been proposed to secure privileged services. In these architectures, the application servers are protected by a defense perimeter where only traffic from entities called servelets are allowed to pass. End users must be authorized and can only communicate with entities called access points (APs). APs relay authorized users’ requests to servelets, which in turn pass them to the servers. The identity of APs are publicly known while the servelets are typically secret. All communications are done through the public Internet. Thus all the entities involved forms an overlay network. The main component of this distributed system consists of n APs. and m servelets. A design for a network is a bipartite graph with APs on one side, and the servelets on the other side. If an AP is compromised by an attacker, all the servelets that are connected to it are subject to attack. An AP is blocked, if all servelets connected to it are subject to attack. We consider two models for the failures: In the average case model, we assume that each AP i fails with a given probability pi. In the worst case model, we assume that there is an adversary that knowing the topology of the network, chooses at most k APs to compromise. In both models, our objective is to design the connections between APs and servelets to minimize the (expected/worst-case) number of blocked APs. In this paper, we give a polynomial-time algorithm for this problem in the average-case model when the number of servelets is a constant. We also show that if the probability of failure of each AP is at least 1/2, then in the optimal design each AP is connected to only one servelet (we call such designs star-shaped), and give a polynomial-time algorithm to find the best star-shaped design. We observe that this statement is not true if the failure probabilities are small. In the worst-case model, we show that the problem is related to a problem in combinatorial set theory, and use this connection to give bounds on the maximum number of APs that a perfectly failure-resistant design with a given number of servelets can support. Our results provide the first rigorous theoretical foundation for practical secure overlay network design.