Abstract
Since the mid-1980s it has been known that Byzantine Agreement can be solved with probability 1 asynchronously, even against an omniscient, computationally unbounded adversary that can adaptively corrupt up to f < n/3 parties. Moreover, the problem is insoluble with f ≥ n/3 corruptions. However, Bracha’s [13] 1984 protocol (see also Ben-Or [8]) achieved f < n/3 resilience at the cost of exponential expected latency 2Θ (n), a bound that has never been improved in this model with f = ⌊ (n-1)/3 ⌋ corruptions.
In this article, we prove that Byzantine Agreement in the asynchronous, full information model can be solved with probability 1 against an adaptive adversary that can corrupt f < n/3 parties, while incurring only polynomial latency with high probability. Our protocol follows an earlier polynomial latency protocol of King and Saia [33, 34], which had suboptimal resilience, namely f ≈ n/109 [33, 34].
Resilience f = (n-1)/3 is uniquely difficult, as this is the point at which the influence of the Byzantine and honest players are of roughly equal strength. The core technical problem we solve is to design a collective coin-flipping protocol that eventually lets us flip a coin with an unambiguous outcome. In the beginning, the influence of the Byzantine players is too powerful to overcome, and they can essentially fix the coin’s behavior at will. We guarantee that after just a polynomial number of executions of the coin-flipping protocol, either (a) the Byzantine players fail to fix the behavior of the coin (thereby ending the game) or (b) we can “blacklist” players such that the blacklisting rate for Byzantine players is at least as large as the blacklisting rate for good players. The blacklisting criterion is based on a simple statistical test of fraud detection.
- [1] . 2008. An almost-surely terminating polynomial protocol forasynchronous Byzantine agreement with optimal resilience. In Proceedings of the 27th Annual ACM Symposium on Principles of Distributed Computing. 405–414.
DOI: Google ScholarDigital Library - [2] . 1993. The influence of large coalitions. Combinatorica 13, 2 (1993), 129–145.
DOI: Google ScholarCross Ref - [3] . 1993. Coin-flipping games immune against linear-sized coalitions. SIAM Journal on Computing 22, 2 (1993), 403–417.
DOI: Google ScholarDigital Library - [4] . 1998. Lower bounds for distributed coin-flipping and randomized consensus. Journal of the ACM 45, 3 (1998), 415–450.
DOI: Google ScholarDigital Library - [5] . 2008. Tight bounds for asynchronous randomized consensus. Journal of the ACM 55, 5 (2008), 1–26.Google ScholarDigital Library
- [6] . 2004. Distributed Computing, 2nd Ed.Wiley.Google ScholarCross Ref
- [7] . 2020. The power of shunning: Efficient asynchronous Byzantine agreement revisited. Journal of the ACM 67, 3 (2020), 14:1–14:59.
DOI: Google ScholarDigital Library - [8] . 1983. Another advantage of free choice: Completely asynchronous agreement protocols (extended abstract). In Proceedings of the 2nd Annual ACM Symposium on Principles of Distributed Computing. 27–30.
DOI: Google ScholarDigital Library - [9] . 1985. Collective coin flipping, robust voting schemes and minima of Banzhaf values. In Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science. 408–416.
DOI: Google ScholarDigital Library - [10] . 2006. Byzantine agreement in the full-information model in \({O}(\log n)\) rounds. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing. 179–186.Google ScholarDigital Library
- [11] . 1993. Randomized distributed agreement revisited. In Proceedings of the 23rd Annual International Symposium on Fault-Tolerant Computing. 412–419.
DOI: Google ScholarCross Ref - [12] . 2000. Perfect-information leader election with optimal resilience. SIAM Journal on Computing 29, 4 (2000), 1304–1320.
DOI: Google ScholarDigital Library - [13] . 1987. Asynchronous Byzantine agreement protocols. Information and Computation 75, 2 (1987), 130–143.
DOI: Google ScholarDigital Library - [14] . 1985. Asynchronous consensus and broadcast protocols. Journal of the ACM 32, 4 (1985), 824–840.
DOI: Google ScholarDigital Library - [15] . 2005. Random oracles in Constantinople: Practical asynchronous Byzantine agreement using cryptography. Journal of Cryptology 18, 3 (2005), 219–246.
DOI: Google ScholarDigital Library - [16] . 1993. Fast asynchronous Byzantine agreement with optimal resilience. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing. 42–51.
DOI: Google ScholarDigital Library - [17] . 1985. A simple and efficient randomized Byzantine agreement algorithm. IEEE Transactions on Software Engineering 11, 6 (1985), 531–539.Google ScholarDigital Library
- [18] . 2009. Concentration of Measure for the Analysis of Randomized Algorithms. Cambridge University Press.Google ScholarCross Ref
- [19] . 1988. Consensus in the presence of partial synchrony. Journal of the ACM 35, 2 (1988), 288–323.Google ScholarDigital Library
- [20] . 1999. Noncryptographic selection protocols. In Proceedings 40th Annual IEEE Symposium on Foundations of Computer Science. 142–153.
DOI: Google ScholarCross Ref - [21] . 1997. An optimal probabilistic protocol for synchronous Byzantine agreement. SIAM Journal on Computing 26, 4 (1997), 873–933.
DOI: Google ScholarDigital Library - [22] . 1982. A lower bound for the time to assure interactive consistency. Information Processing Letters 14, 4 (1982), 183–186.
DOI: Google ScholarCross Ref - [23] . 1986. Easy impossibility proofs for distributed consensus problems. Distributed Computing 1, 1 (1986), 26–39.
DOI: Google ScholarDigital Library - [24] . 1985. Impossibility of distributed consensus with one faulty process. Journal of the ACM 32, 2 (1985), 374–382.
DOI: Google ScholarDigital Library - [25] . 1998. Fully polynomial Byzantine agreement for \(n\gt 3t\) processors in \(t+1\) rounds. SIAM Journal on Computing 27, 1 (1998), 247–290.
DOI: Google ScholarDigital Library - [26] . 2006. Fault-tolerant distributed computing in full-information networks. In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science. 15–26.
DOI: Google ScholarDigital Library - [27] . 2020. A tight lower bound on adaptively secure full-information coin flip. In Proceedings of the 61st Annual IEEE Symposium on Foundations of Computer Science. 1268–1276.
DOI: Google ScholarCross Ref - [28] . 2022. Byzantine agreement in polynomial time with near-optimal resilience. In Proceedings of the 54th ACM Symposium on Theory of Computing. 502–514.Google ScholarDigital Library
- [29] . 2023. Byzantine agreement with optimal resilience via statistical fraud detection. In Proceedings of the 34th ACM-SIAM Symposium on Discrete Algorithms. 4335–4353.Google ScholarCross Ref
- [30] . 1988. The influence of variables on boolean functions (extended abstract). In Proceedings of the 29th Annual IEEE Symposium on Foundations of Computer Science. 68–80.
DOI: Google ScholarDigital Library - [31] . 2010. Fast asynchronous Byzantine agreement and leader election with full information. ACM Transactions on Algorithms 6, 4 (2010), 68:1–68:28.
DOI: Google ScholarDigital Library - [32] . 2020. Improvement and partial simulation of King & Saia’s expected-polynomial-time Byzantine agreement algorithm. Master’s Thesis. University of Victoria, Canada.Google Scholar
- [33] . 2016. Byzantine agreement in expected polynomial time. Journal of the ACM 63, 2 (2016), 13:1–13:21.
DOI: Google ScholarDigital Library - [34] . 2018. Correction to Byzantine agreement in expected polynomial time, JACM 2016.
arXiv:1812.10169. Retrieved from http://arxiv.org/abs/1812.10169Google Scholar - [35] . 1982. The Byzantine generals problem. ACM Transactions on Programming Languages and Systems 4, 3 (1982), 382–401.
DOI: Google ScholarDigital Library - [36] . 2011. The contest between simplicity and efficiency in asynchronous Byzantine agreement. In Proceedings of the 25th International Symposium on Distributed Computing (DISC) (Lecture Notes in Computer Science), Vol. 6950. 348–362.
DOI: Google ScholarCross Ref - [37] . 1996. Distributed Algorithms. Morgan Kaufmann.Google ScholarDigital Library
- [38] . 1980. Reaching agreement in the presence of faults. Journal of the ACM 27, 2 (1980), 228–234.
DOI: Google ScholarDigital Library - [39] . 1983. Randomized Byzantine generals. In Proceedings of the 24th Annual IEEE Symposium on Foundations of Computer Science. 403–409.
DOI: Google ScholarDigital Library - [40] . 2002. Lower bounds for leader election and collective coin-flipping in the perfect information model. SIAM Journal on Computing 31, 6 (2002), 1645–1662.
DOI: Google ScholarDigital Library - [41] . 1989. A robust noncryptographic protocol for collective coin flipping. SIAM Journal on Discrete Mathematics 2, 2 (1989), 240–244.
DOI: Google ScholarDigital Library - [42] . 1984. Randomized Byzantine agreements. In Proceedings of the 3rd Annual ACM Symposium on Principles of Distributed Computing. 163–178.
DOI: Google ScholarDigital Library
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- Byzantine Agreement with Optimal Resilience via Statistical Fraud Detection
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