ABSTRACT
Consider a completely asynchronous network consisting of n parties where every two parties are connected by a private channel. An adversary At with unbounded computing power actively controls at most t = ([n/3] − 1) out of n parties in Byzantine fashion. In this setting, we say that π is a t-resilient, (1 − ε)-terminating Asynchronous Byzantine Agreement (ABA) protocol, if π satisfies all the properties of Byzantine Agreement (BA) in asynchronous settings tolerating At and terminates (i.e every honest party terminates π with probability at least (1 − ε). In this work, we present a new t-resilient, (1 − ε)-terminating ABA protocol which privately communicates O(Cn6 κ) bits and A-casts1 O(Cn6 κ) bits, where ε = 2−Ω(κ) and C is the expected running time of the protocol. Moreover, conditioned on the event that our ABA protocol terminates, it does so in constant expected time; i.e., C = O(1). Our ABA protocol is to be compared with the only known t-resilient, (1 − ε)-terminating ABA protocol of [5] in the same settings, which privately communicates O(Cn11 κ4) bits and A-casts O(Cn11 κ2 log(n)) bits, where ε = 2−Ω(κ) and C = O(1). So our ABA achieves a huge gain in communication complexity in comparison to the ABA of [5], while keeping all other properties in place. In another landmark work, in PODC 2008, Abraham et. al [1] proposed a t-resilient, 1-terminating (called as almost-surely terminating in [1]) ABA protocol which privately communicates O(Cn6 log n) bits and A-casts O(Cn6 log n) bits. But ABA protocol of Abraham et. al. takes polynomial (C = O(n2)) expected time to terminate. Hence the merits of our ABA protocol over the ABA of Abraham et. al. are: (i) For any κ < n2 log n, our ABA is better in terms of communication complexity (ii) conditioned on the event that our ABA protocol terminates, it does so in constant expected time (the constant is independent of n, t and κ), whereas ABA of Abraham et. al. takes polynomial expected time. Summing up, in a practical scenario where a faster and communication efficient ABA protocol is required, our ABA fits the bill better than ABA protocols of [5, 1].
For designing our ABA protocol, we present a novel and simple asynchronous verifiable secret sharing (AVSS) protocol which significantly improves the communication complexity of the only known AVSS protocol of [5] in the same settings. We believe that our AVSS can be used in many other applications for improving communication complexity and hence is of independent interest.
- I. Abraham, D. Dolev, and J. Y. Halpern. An Almost Surely Terminating Polynomial Protocol for Asynchronous Byzantine Agreement with Optimal Resilience. In PODC, pages 405--414, 2008. Google ScholarDigital Library
- M. Ben-Or, S. Goldwasser, and A. Wigderson. Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation. In STOC,pages 1--10, 1988. Google ScholarDigital Library
- G. Bracha. An Asynchronous {(n &#8722; 1)/3}-Resilient Consensus Protocol. In PODC, pages 154--162, 1984. Google ScholarDigital Library
- R. Canetti. Studies in Secure Multiparty Computation and Applications. PhD thesis, Weizmann Institute, Israel, 1995.Google Scholar
- R. Canetti and T. Rabin. Fast Asynchronous Byzantine Agreement with Optimal Resilience. In STOC, pages 42--51, 1993. Google ScholarDigital Library
- B. Chor and C. Dwork. Randomization in Byzantine Agreement. Advances in Computing Research, 5:443--497, 1989.Google Scholar
- R. Cramer, I. Damg&#229;rd, S. Dziembowski, M. Hirt, and T. Rabin. Efficient Multiparty Computations Secure Against an Adaptive Adversary. In EUROCRYPT, pages 311--326, 1999. Google ScholarDigital Library
- P Feldman and S. Micali. An Optimal Probabilistic Protocol for Synchronous Byzantine Agreement. SIAM Journal of Computing, 26(4):873--933, 1997. Google ScholarDigital Library
- M. Fischer. The Consensus Problem in Unreliable Distributed System. Technical Report, Department of Computer Science, Yale University, 1983.Google Scholar
- M. J. Fischer, N. A. Lynch, and M. Paterson. Impossibility of Distributed Consensus with One Faulty Process. JACM, 32(2):374--382, 1985. Google ScholarDigital Library
- M. Fitzi, J. Garay, S. Gollakota, C. Pandu Rangan, and K. Srinathan. Round-Optimal and Efficient Verifiable Secret Sharing. In TCC, pages 329--342, 2006. Google ScholarDigital Library
- R. Gennaro, Y. Ishai, E. Kushilevitz, and T. Rabin. The Round Complexity of Verifiable Secret Sharing and Secure Multicast. In STOC, pages 580--589, 2001. Google ScholarDigital Library
- N. A. Lynch. Distributed Algorithms. Morgan Kaufmann, 1996. Google ScholarDigital Library
- M. Pease, R. E. Shostak, and L. Lamport. Reaching Agreement in the Presence of faults. JACM, 27(2):228--234, 1980. Google ScholarDigital Library
- M. Rabin. Randomized Byzantine Generals. In FOCS, pages 403--409, 1983. Google ScholarDigital Library
- T. Rabin and M. Ben-Or. Verifiable Secret Sharing and Multiparty Protocols with Honest Majority. In STOC, pages 73--85, 1989. Google ScholarDigital Library
Index Terms
- Simple and efficient asynchronous byzantine agreement with optimal resilience
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