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On Complexity and Approximability of Optimal DoS Attacks on Multiple-Tree P2P Streaming Topologies
March/April 2011 (vol. 8 no. 2)
pp. 270-281
Sascha Grau, Technische Univerität Ilmenau, Ilmenau
Mathias Fischer, Technische Universität Ilmenau, Ilmenau
Michael Brinkmeier, Technische Universität Ilmenau, Ilmenau
Günter Schäfer, Technische Universität Ilmenau, Ilmenau
We investigate the hardness of malicious attacks on multiple-tree topologies of push-based Peer-to-Peer streaming systems. In particular, we study the optimization problem of finding a minimum set of target nodes to achieve a certain damage objective. For this, we differentiate between three natural and increasingly complex damage types: global packet loss, service loss when using Multiple Description Coding, and service loss when using Forward Error Correction. We show that each of these attack problems is NP-hard, even for an idealized attacker with global knowledge about the topology. Despite tree-based topologies seem susceptible to such attacks, we can even prove that (under strong assumptions about NP) there is no polynomial time attacker, capable of guaranteeing a general solution quality within factors of c_1 \log (n) and c_2 2^{\log^{1-\delta } n} (with n topology nodes, \delta = 1 / \log \log^d n for d<1/2 and constants c_1, c_2), respectively. To our knowledge, these are the first lower bounds on the quality of polynomial time attacks on P2P streaming topologies. The results naturally apply to major real-world DoS attackers and show hard limits for their possibilities. In addition, they demonstrate superior stability of Forward Error Correction systems compared to Multiple Description Coding and give theoretical foundation to properties of stable topologies.

[1] Y.H. Chu, S.G. Rao, S. Seshan, and H. Zhang, "A Case for End System Multicast," IEEE J. Selected Areas in Comm., vol. 20, no. 8, pp. 1456-1471, Oct. 2002.
[2] M. Castro, P. Druschel, A.-M. Kermarrec, A. Nandi, A. Rowstron, and A. Singh, "Split Stream: High-Bandwidth Multicast in Cooperative Environments," Proc. Nineteenth ACM Symp. Operating Systems Principles (SOSP '03), ACM, pp. 298-313, 2003.
[3] T. Strufe, J. Wildhagen, and G. Schäfer, "Towards the Construction of Attack Resistant and Efficient Overlay Streaming Topologies," Electronic Notes in Theoretical Computer Science, vol. 179, pp. 111-121, 2007.
[4] V. Fodor and G. Dan, "Resilience in Live Peer-to-Peer Streaming," IEEE Comm. Magazine, vol. 45, no. 6, pp. 116-123, June 2007.
[5] V.K. Goyal, "Multiple Description Coding: Compression Meets the Network," IEEE Signal Processing Magazine, vol. 18, no. 5, pp. 74-93, Sept. 2001.
[6] G. Dan, V. Fodor, and G. Karlsson, "On the Stability of End-Point-Based Multimedia Streaming," Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communications Systems, pp. 678-690, Springer, 2006.
[7] V. Venkataraman, K. Yoshida, and P. Francis, "Chunkyspread: Heterogeneous Unstructured Tree-Based Peer-to-Peer Multicast," Proc. 2006 IEEE Int'l Conf. Network Protocols (ICNP '06), pp. 2-11, 2006.
[8] M. Haridasan and R. van Renesse, "Defense Against Intrusion in a Live Streaming Multicast System," Proc. Sixth IEEE Int'l Conf. Peer-to-Peer Computing, pp. 185-192, 2006.
[9] R.H. Wouhaybi and A.T. Campbell, "Building Resilient Low-Diameter Peer-to-Peer Topologies," Computer Networks, vol. 52, no. 5, pp. 1019-1039, 2008.
[10] W. Wang, Y. Xiong, Q. Zhang, and S. Jamin, "Ripple-Stream: Safe Guarding P2P Streaming Against Dos Attacks," Proc. IEEE Int'l Conf. Multimedia and Expo, pp. 1417-1420, 2006.
[11] W. Conner, K. Nahrstedt, and I. Gupta, "Preventing DoS Attacks in Peer-to-Peer Media Streaming Systems," Proc. Multimedia Computing and Networking, 2006.
[12] J. Yang, Y. Li, B. Huang, and J. Ming, "Preventing DDoS Attacks Based on Credit Model for P2P Streaming System," Autonomic and Trusted Computing, pp. 13-20, Springer, 2008.
[13] X. Jin, S.-H. Chan, W.-P. Yiu, Y. Xiong, and Q. Zhang, "Detecting Malicious Hosts in the Presence of Lying Hosts in Peer-to-Peer Streaming," Proc. IEEE Int'l Conf. Multimedia and Expo, pp. 1537-1540, July 2006.
[14] P. Dhungel, X. Hei, K.W. Ross, and N. Saxena, "The Pollution Attack in p2p Live Video Streaming: Measurement Results and Defenses," Proc. 2007 Workshop Peer-to-peer Streaming and IP-TV (P2P-TV '07), pp. 323-328, 2007.
[15] S. Yang, H. Jin, B. Li, X. Liao, H. Yao, and X. Tu, "The Content Pollution in Peer-to-Peer Live Streaming Systems: Analysis and implications," Proc. 37th Int'l Conf. Parallel Processing, pp. 652-659, 2008.
[16] A. Singh, M. Castro, P. Druschel, and A. Rowstron, "Defending Against Eclipse Attacks on Overlay Networks," Proc. 11th Workshop ACM SIGOPS European Workshop (EW11), p. 21, 2004.
[17] J.R. Douceur, "The Sybil Attack," Proc. Revised Papers from the First Int'l Workshop Peer-to-Peer Systems (IPTPS '01), pp. 251-260, 2002.
[18] F. Wang, J. Liu, and Y. Xiong, "Stable Peers: Existence, Importance, and Application in Peer-to-Peer Live Video Streaming," Proc. IEEE INFOCOM '08, 2008.
[19] M. Brinkmeier, M. Fischer, S. Grau, and G. Schaefer, "Towards the Design of Unexploitable Construction Mechanisms for Multiple-Tree Based P2P Streaming Systems," Proc. 16. ITG/GI-Fachtagung, Kommunikation in Verteilten Systemen (KiVS '09), pp. 193-204, Mar. 2009.
[20] A. Brieg, M. Brinkmeier, S. Grau, M. Fischer, and G. Schäfer, "Attacker Independent Stability Guarantees for Peer-2-Peer-Live-Streaming Topologies," Proc. Second Int'l Conf. Comm. Theory, Reliability, and Quality of Service, pp. 20-25, July 2009.
[21] M. Brinkmeier, G. Schaefer, and T. Strufe, "Optimally DOS Resistant P2P Topologies for Live Multimedia Streaming," IEEE Trans. Parallel and Distributed Systems, vol. 20, no. 6, pp. 831-844, June 2009.
[22] M.G. Luby, M. Mitzenmacher, M.A. Shokrollahi, D.A. Spielman, and V. Stemann, "Practical Loss-Resilient Codes," Proc. 29th Ann. ACM Symp. Theory of Computing (STOC '97), pp. 150-159, May 1997.
[23] I. Wegener, Complexity Theory: Exploring the Limits of Efficient Algorithms. Springer, 2005.
[24] Approximation Algorithms for NP-hard Problems. D.S. Hochbaum, ed. PWS Publishing Co., 1997.
[25] P. Crescenzi, "A Short Guide to Approximation Preserving Reductions," Proc. 12th Ann. IEEE Conf. Computational Complexity (CCC '97), p. 262, 1997.
[26] G. Ausiello, A. D'Atri, and M. Protasi, "Structure Preserving Reductions Among Convex Optimization Problems," J. Computational System Sciences, vol. 21, pp. 136-153, 1980.
[27] S. Khanna, R. Motwani, M. Sudan, and U.V. Vazirani, "On Syntactic Versus Computational Views of Approximability," Proc. IEEE Symp. Foundations of Computer Science, pp. 819-830, 1994.
[28] U. Feige, "A Threshold of ln n for Approximating Set Cover," J. ACM, vol. 45, no. 4, pp. 634-652, 1998.
[29] T. Fujito, "Approximation Algorithms for Submodular Set Cover With Applications," IEICE Trans. Comm. Electronics Information and Systems, vol. 83, pp. 480-487, 2000.
[30] P. Slavík, "Improved Performance of the Greedy Algorithm for Partial Cover," Information Processing Letters, vol. 64, no. 5, pp. 251-254, 1997.
[31] R. Bar-Yehuda and S. Moran, "On Approximation Problems Related to the Independent Set and Vertex Cover Problems," Discrete Applied Math., vol. 9, pp. 1-10, 1984.
[32] R.D. Carr, S. Doddi, G. Konjevod, and M. Marathe, "On the Red-Blue Set Cover Problem," Proc. 11th Ann. ACM-SIAM Symp. Discrete Algorithms (SODA '00), pp. 345-353, 2000.
[33] I. Dinur and S. Safra, "On the Hardness of Approximating Label Cover," Proc. Electronic Colloquium Computational Complexity (ECCC), vol. 6, no. 015, 1999.
[34] P. Chou, V. Padmanabhan, and H. Wang, "Resilient Peer-to-Peer Streaming," Technical Report MSR-TR-2003-11, Microsoft Research, Redmond, WA, Mar. 2003.

Index Terms:
P2P streaming, topology, attack stability, approximation, complexity theory.
Sascha Grau, Mathias Fischer, Michael Brinkmeier, Günter Schäfer, "On Complexity and Approximability of Optimal DoS Attacks on Multiple-Tree P2P Streaming Topologies," IEEE Transactions on Dependable and Secure Computing, vol. 8, no. 2, pp. 270-281, March-April 2011, doi:10.1109/TDSC.2009.51
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