Authenticated Adversarial Routing
 Yair Amir,
 Paul Bunn,
 Rafail Ostrovsky
 … show all 3 hide
Abstract
The aim of this paper is to demonstrate the feasibility of authenticated throughputefficient routing in an unreliable and dynamically changing synchronous network in which the majority of malicious insiders try to destroy and alter messages or disrupt communication in any way. More specifically, in this paper we seek to answer the following question: Given a network in which the majority of nodes are controlled by a nodecontrolling adversary and whose topology is changing every round, is it possible to develop a protocol with polynomiallybounded memory per processor that guarantees throughputefficient and correct endtoend communication? We answer the question affirmatively for extremely general corruption patterns: we only request that the topology of the network and the corruption pattern of the adversary leaves at least one path each round connecting the sender and receiver through honest nodes (though this path may change at every round). Out construction works in the publickey setting and enjoys bounded memory per processor (that is polynomial in the network size and does not depend on the amount of traffic). Our protocol achieves optimal transfer rate with negligible decoding error. We stress that our protocol assumes no knowledge of which nodes are corrupted nor which path is reliable at any round, and is also fully distributed with nodes making decisions locally, so that they need not know the topology of the network at any time.
The optimality that we prove for our protocol is very strong. Given any routing protocol, we evaluate its efficiency (rate of message delivery) in the “worst case,” that is with respect to the worst possible graph and against the worst possible (polynomially bounded) adversarial strategy (subject to the above mentioned connectivity constraints). Using this metric, we show that there does not exist any protocol that can be asymptotically superior (in terms of throughput) to ours in this setting.
We remark that the aim of our paper is to demonstrate via explicit example the feasibility of throughputefficient authenticated adversarial routing. However, we stress that out protocol is not intended to provide a practical solution, as due to its complexity, no attempt thus far has been made to reduce constants and memory requirements.
Our result is related to recent work of Barak, Goldberg and Xiao in 2008 [9] who studied fault localization in networks assuming a privatekey trusted setup setting. Our work, in contrast, assumes a publickey PKI setup and aims at not only fault localization, but also transmission optimality. Among other things, our work answers one of the open questions posed in the Barak et. al. paper regarding fault localization on multiple paths. The use of a publickey setting to achieve strong errorcorrection results in networks was inspired by the work of Micali, Peikert, Sudan and Wilson [14] who showed that classical errorcorrection against a polynomiallybounded adversary can be achieved with surprisingly high precision. Our work is also related to an interactive coding theorem of Rajagopalan and Schulman [15] who showed that in noisyedge statictopology networks a constant overhead in communication can also be achieved (provided none of the processors are malicious), thus establishing an optimalrate routing theorem for statictopology networks.
Finally, our work is closely related and builds upon to the problem of EndToEnd Communication in distributed networks, studied by Afek and Gafni [1], Awebuch, Mansour, and Shavit [8], and Afek, Awerbuch, Gafni, Mansour, Rosen, and Shavit[2] , though none of these papers consider or ensure correctness in the setting of a nodecontrolling adversary that may corrupt the majority of the network.
 Afek, Y., Gafni, E.: EndtoEnd Communication in Unreliable Networks. In: PODC (1988)
 Afek, Y., Awebuch, B., Gafni, E., Mansour, Y., Rosen, A., Shavit, N. (1997) Slide– The Key to Poly. EndtoEnd Communication. J. of Algorithms 22: pp. 158186 CrossRef
 Afek, Y., Gafni, E., Rosén, A.: The Slide Mechanism With Applications In Dynamic Networks. In: Proc. of the 11th ACM Symp. on PoDC, pp. 35–46 (1992)
 Aiello, W., Kushilevitz, E., Ostrovsky, R., Rosén, A. (2000) Adaptive Packet Routing For Bursty Adversarial Traffic. J. Comput. Syst. Sci. 60: pp. 482509 CrossRef
 Amir, Y., Bunn, P., Ostrovsky, R.: Authenticated Adversarial Routing, Full Version. Cornell Univ. Library arXiv, Article No. 0808.0156 (2008), http://arxiv.org/abs/0808.0156
 Awerbuch, B., Holmer, D., NinaRotaru, C., Rubens, H. (2002) A Secure Routing Protocol Resilient to Byzantine Failures. WiSE. ACM, New York, pp. 2130 CrossRef
 Awerbuch, B., Leighton, T.: Improved Approximation Algorithms for the MultiCommodity Flow Problem and Local Competitive Routing in Dynamic Networks. In: STOC (1994)
 Awerbuch, B., Mansour, Y., Shavit, N.: EndtoEnd Communication With Polynomial Overhead. In: Proc. of the 30th IEEE Symp. on Foundations of Computer Science, FOCS (1989)
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 Title
 Authenticated Adversarial Routing
 Book Title
 Theory of Cryptography
 Book Subtitle
 6th Theory of Cryptography Conference, TCC 2009, San Francisco, CA, USA, March 1517, 2009. Proceedings
 Pages
 pp 163182
 Copyright
 2009
 DOI
 10.1007/9783642004575_11
 Print ISBN
 9783642004568
 Online ISBN
 9783642004575
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 5444
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 Springer Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 Network Routing
 EndtoEnd Communication
 Fault Localization
 ErrorCorrection
 MultiParty Computation
 Communication Complexity
 Industry Sectors
 eBook Packages
 Editors

 Omer Reingold ^{(16)}
 Editor Affiliations

 16. Faculty of Mathematics and Computer Science, The Weizmann Institute of Science
 Authors

 Yair Amir ^{(17)}
 Paul Bunn ^{(18)}
 Rafail Ostrovsky ^{(19)}
 Author Affiliations

 17. Department of Computer Science, Johns Hopkins University, Baltimore, MD, 21218, USA
 18. Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA
 19. Department of Computer Science and Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA
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