Abstract
We consider the problem of uniform sampling in large scale open systems. Uniform sampling is a fundamental primitive that guarantees that any individual in a population has the same probability to be selected as sample. An important issue that seriously hampers the feasibility of uniform sampling in open and large scale systems is the unavoidable presence of malicious nodes. In this paper we show that restricting the number of requests that malicious nodes can issue and allowing for a full knowledge of the composition of the system is a necessary and sufficient condition to guarantee uniform and ergodic sampling. In a nutshell, a uniform and ergodic sampling guarantees that any node in the system is equally likely to appear as a sample at any non malicious node in the system and that infinitely often any node has a non-null probability to appear as a sample of honest nodes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jelasity, M., Voulgaris, S., Guerraoui, R., Kermarrec, A.M., van Steen, M.: Gossip-based Peer Sampling. ACM Transaction on Computer System 25(3) (2007)
Bertier, M., Busnel, Y., Kermarrec, A.M.: On Gossip and Populations. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 72–86. Springer, Heidelberg (2009)
Karger, D.R., Ruhl, M.: Simple Efficient Load Balancing Algorithms for Peer-to-Peer. In: Voelker, G.M., Shenker, S. (eds.) IPTPS 2004. LNCS, vol. 3279, pp. 131–140. Springer, Heidelberg (2004)
Lv, Q., Cao, P., Cohen, E., Li, K., Shenker, S.: Search and Replication in Unstructured Peer-to-Peer Networks. In: Proceedings of the International Conference on Supercomputing (ICS), pp. 84–95 (2002)
Massoulié, L., Merrer, E.L., Kermarrec, A.M., Ganesh, A.: Peer Counting and Sampling in Overlay Networks: Random Walk Methods. In: Proceedings of the 25th Annual Symposium on Principles of Distributed Computing (PODC), pp. 123–132. ACM Press, New York (2006)
Busnel, Y., Beraldi, R., Baldoni, R.: A Formal Characterization of Uniform Peer Sampling Based on View Shuffling. In: Proceedings of the International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT), pp. 360–365. IEEE Computer Society, Los Alamitos (2009)
Gurevich, M., Keidar, I.: Correcness of Gossip-Based Membership under Message Loss. In: Proceedings of the 28th Annual Symposium on Principles of Distributed Computing (PODC), Calgary, AL, Canada. ACM Press, New York (2009)
Bakhshi, R., Gavidia, D., Fokkink, W., van Steen, M.: An Analytical Model of Information Dissemination for a Gossip-based Protocol. Computer Networks 53(13), 2288–2303 (2009)
Karp, R., Schindelhauer, C., Shenker, S., Vocking, B.: Randomized Rumor Spreading. In: the 41st Annual Symposium on Foundations of Computer Science (FOCS), p. 565. IEEE Computer Society, Los Alamitos (2000)
Voulgaris, S., Gavidia, D., van Steen, M.: CYCLON: Inexpensive Membership Management for Unstructured P2P Overlays. Journal of Network System Management 13(2), 197–217 (2005)
Stutzbach, D., Rejaie, R., Duffield, N., Sen, S., Willinger, W.: On Unbiased Sampling for Unstructured Peer-to-Peer Networks. IEEE/ACM Transactions on Networking 17(02), 377–390 (2009)
Bollobás, B.: Random Graphs, 2nd edn. Cambridge University Press, Cambridge (2001)
Zhong, M., Shen, K., Seiferas, J.: Non-uniform Random Membership Management in Peer-to-Peer Networks. In: Proceedings of the 24th Annual Joint Conference of the Computer and Communications Societies (INFOCOM). IEEE Press, Los Alamitos (2005)
Awan, A., Ferreira, R.A., Jagannathan, S., Grama, A.: Distributed Uniform Sampling in Unstructured Peer-to-Peer Networks. In: Proceedings of the 39th Annual Hawaii International Conference on System Sciences, HICSS (2006)
Sit, E., Morris, R.: Security Considerations for Peer-to-Peer Distributed Hash Tables. In: Druschel, P., Kaashoek, M.F., Rowstron, A. (eds.) IPTPS 2002. LNCS, vol. 2429, pp. 261–269. Springer, Heidelberg (2002)
Bortnikov, E., Gurevich, M., Keidar, I., Kliot, G., Shraer, A.: Brahms: Byzantine Resilient Random Membership Sampling. Computer Networks 53, 2340–2359 (2009); A former version appeared in the 27th ACM Symposium on Principles of Distributed Computing (PODC) (2008)
Awerbuch, B., Scheideler, C.: Group Spreading: A Protocol for Provably Secure Distributed Name Service. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 183–195. Springer, Heidelberg (2004)
Jesi, G.P., Montresor, A., van Steen, M.: Secure Peer Sampling. Computer Networks (2010) (to appear)
Singh, A., Ngan, T.W., Druschel, P., Wallach, D.S.: Eclipse Attacks on Overlay Networks: Threats and Defenses. In: Proceedings of the 25th IEEE International Conference on Computer Communications, INFOCOM (2006)
Liu, D., Ning, P., Du, W.: Detecting Malicious Beacon Nodes for Secure Location Discovery in Wireless Sensor Networks. In: Proceedings of the 25th IEEE International Conference on Distributed Computing Systems, ICDCS (2005)
Douceur, J., Donath, J.S.: The Sybil Attack. In: Druschel, P., Kaashoek, M.F., Rowstron, A. (eds.) IPTPS 2002. LNCS, vol. 2429, pp. 251–260. Springer, Heidelberg (2002)
Awerbuch, B., Scheideler, C.: Towards a Scalable and Robust Overlay Network. In: Proceedings of the 6th International Workshop on Peer-to-Peer Systems, IPTPS (2007)
Anceaume, E., Brasileiro, F.V., Ludinard, R., Sericola, B., Tronel, F.: Analytical Study of Adversarial Strategies in Cluster-based Overlays. In: Proceedings of the International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT), pp. 293–298 (2009)
Castro, M., Druschel, P., Ganesh, A., Rowstron, A., Wallach, D.S.: Secure Routing for Structured Peer-to-peer Overlay Networks. In: Proceedings of the 5th Symposium on Operating Systems Design and Implementation (OSDI), pp. 299–314. ACM, New York (2002)
Hildrum, K., Kubiatowicz, J.: Asymptotically Efficient Approaches to Fault-tolerance in Peer-to-Peer Networks. In: Fich, F.E. (ed.) DISC 2003. LNCS, vol. 2848, pp. 321–336. Springer, Heidelberg (2003)
Fiat, A., Saia, J., Young, M.: Making Chord Robust to Byzantine Attacks. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 803–814. Springer, Heidelberg (2005)
Anceaume, E., Brasileiro, F., Ludinard, R., Ravoaja, A.: PeerCube: an Hypercube-based P2P Overlay Robust against Collusion and Churn. In: Proceedings of the IEEE International Conference on Self-Adaptive and Self-Organizing Systems, pp. 15–24 (2008)
Condie, T., Kacholia, V., Sank, S., Hellerstein, J.M., Maniatis, P.: Induced Churn as Shelter from Routing-Table Poisoning. In: Proceedings of the International Network and Distributed System Security Symposium, NDSS (2006)
Yu, H., Kaminsky, M., Gibbons, P.B., Flaxman, A.: SybilGuard: Defending against Sybil Attacks via Social Networks. In: Proceedings of the ACM Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (SIGCOMM), pp. 267–278 (2006)
Yu, H., Gibbons, P.B., Kaminsky, M., Xiao, F.: SybilLimit: A Near-Optimal Social Network Defense against Sybil Attacks. In: Proceedings of the IEEE Symposium on Security and Privacy (SP), pp. 3–17 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Anceaume, E., Busnel, Y., Gambs, S. (2010). Uniform and Ergodic Sampling in Unstructured Peer-to-Peer Systems with Malicious Nodes. In: Lu, C., Masuzawa, T., Mosbah, M. (eds) Principles of Distributed Systems. OPODIS 2010. Lecture Notes in Computer Science, vol 6490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17653-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-17653-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17652-4
Online ISBN: 978-3-642-17653-1
eBook Packages: Computer ScienceComputer Science (R0)