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View all- Huang SPettie SZhu L(2024)Byzantine Agreement with Optimal Resilience via Statistical Fraud DetectionJournal of the ACM10.1145/363945471:2(1-37)Online publication date: 12-Apr-2024
Byzantine agreement in polynomial time with near-optimal resilience
Pages 502 - 514
Abstract
It has been known since the early 1980s that Byzantine Agreement in the full information, asynchronous model is impossible to solve deterministically against even one crash fault [FLP 1985], but that it can be solved with probability 1 [Ben-Or 1983], even against an adversary that controls the scheduling of all messages and corrupts up to f<n/3 players [Bracha 1987]. The main downside of [Ben-Or 1983, Bracha 1987] is that they terminate with 2Θ(n) latency in expectation whenever f=Θ(n).
King and Saia [KS 2016, KS 2018] developed a polynomial protocol (polynomial latency, polynomial local computation) that is resilient to f < (1.14× 10−9)n Byzantine faults. The new idea in their protocol is to detect—and blacklist—coalitions of likely-bad players by analyzing the deviations of random variables generated by those players over many rounds.
In this work we design a simple collective coin-flipping protocol such that if any coalition of faulty players repeatedly does not follow protocol, then they will eventually be detected by one of two simple statistical tests. Using this coin-flipping protocol, we solve Byzantine Agreement in polynomial latency, even in the presence of up to f<n/4 Byzantine faults. This comes close to the f<n/3 upper bound on the maximum number of faults [LSP 1982, BT 1985, FLM 1986].
References
[1]
Rosa Abrantes-Metz, Sofia B. Villas-Boas, and George G. Judge. 2013. Tracking the Libor Rate. Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series. https://ideas.repec.org/p/cdl/agrebk/qt2p33x7dk.html
[2]
Miklós Ajtai and Nathan Linial. 1993. The influence of large coalitions. Comb., 13, 2 (1993), 129–145. https://doi.org/10.1007/BF01303199
[3]
Noga Alon and Moni Naor. 1993. Coin-Flipping Games Immune Against Linear-Sized Coalitions. SIAM J. Comput., 22, 2 (1993), 403–417. https://doi.org/10.1137/0222030
[4]
James Aspnes. 1998. Lower Bounds for Distributed Coin-Flipping and Randomized Consensus. J. ACM, 45, 3 (1998), 415–450. https://doi.org/10.1145/278298.278304
[5]
James Aspnes. 2003. Randomized protocols for asynchronous consensus. Distributed Computing, 16, 2 (2003), 165–175.
[6]
Hagit Attiya and Keren Censor. 2008. Tight bounds for asynchronous randomized consensus. J. ACM, 55, 5 (2008), 1–26.
[7]
Ziv Bar-Joseph and Michael Ben-Or. 1998. A Tight Lower Bound for Randomized Synchronous Consensus. In Proceedings 17th Annual ACM Symposium on Principles of Distributed Computing (PODC). 193–199. isbn:0897919777 https://doi.org/10.1145/277697.277733
[8]
Amos Beimel, Eran Omri, and Ilan Orlov. 2015. Protocols for Multiparty Coin Toss with a Dishonest Majority. J. Cryptol., 28, 3 (2015), 551–600. https://doi.org/10.1007/s00145-013-9168-3
[9]
Michael Ben-Or. 1983. Another Advantage of Free Choice: Completely Asynchronous Agreement Protocols (Extended Abstract). In Proceedings 2nd Annual ACM Symposium on Principles of Distributed Computing (PODC). 27–30. https://doi.org/10.1145/800221.806707
[10]
Michael Ben-Or and Nathan Linial. 1985. Collective Coin Flipping, Robust Voting Schemes and Minima of Banzhaf Values. In Proceedings 26th Annual IEEE Symposium on Foundations of Computer Science (FOCS). 408–416. https://doi.org/10.1109/SFCS.1985.15
[11]
Michael Ben-Or, Elan Pavlov, and Vinod Vaikuntanathan. 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 (STOC). 179–186.
[12]
Manuel Blum. 1981. Coin Flipping by Telephone. In IEEE Workshop on Communications Security (CRYPTO). 11–15.
[13]
Nicolò Bonettini, Paolo Bestagini, Simone Milani, and Stefano Tubaro. 2020. On the use of Benford’s law to detect GAN-generated images. In Proceedings 25th International Conference on Pattern Recognition (ICPR). 5495–5502. https://doi.org/10.1109/ICPR48806.2021.9412944
[14]
Gabriel Bracha. 1987. Asynchronous Byzantine Agreement Protocols. Inf. Comput., 75, 2 (1987), 130–143. https://doi.org/10.1016/0890-5401(87)90054-X
[15]
Gabriel Bracha and Sam Toueg. 1985. Asynchronous Consensus and Broadcast Protocols. J. ACM, 32, 4 (1985), 824–840. https://doi.org/10.1145/4221.214134
[16]
Niv Buchbinder, Iftach Haitner, Nissan Levi, and Eliad Tsfadia. 2017. Fair Coin Flipping: Tighter Analysis and the Many-Party Case. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). 2580–2600. https://doi.org/10.1137/1.9781611974782.170
[17]
Richard Cleve. 1986. Limits on the Security of Coin Flips when Half the Processors Are Faulty (Extended Abstract). In Proceedings of the 18th Annual ACM Symposium on Theory of Computing (STOC). 364–369. https://doi.org/10.1145/12130.12168
[18]
Miguel Correia, Giuliana Santos Veronese, Nuno Ferreira Neves, and Paulo Verissimo. 2011. Byzantine consensus in asynchronous message-passing systems: a survey. International Journal of Critical Computer-Based Systems, 2, 2 (2011), 141–161.
[19]
Dana Dachman-Soled, Mohammad Mahmoody, and Tal Malkin. 2014. Can Optimally-Fair Coin Tossing Be Based on One-Way Functions? In Proceedings 11th Conference on Theory of Cryptography (TCC) (Lecture Notes in Computer Science, Vol. 8349). 217–239. https://doi.org/10.1007/978-3-642-54242-8_10
[20]
Mark Duggan and Steven D. Levitt. 2002. Winning Isn’t Everything: Corruption in Sumo Wrestling. American Economic Review, 92, 5 (2002), 1594–1605. https://doi.org/10.1257/000282802762024665
[21]
Michael J. Fischer, Nancy A. Lynch, and Michael Merritt. 1986. Easy Impossibility Proofs for Distributed Consensus Problems. Distributed Comput., 1, 1 (1986), 26–39. https://doi.org/10.1007/BF01843568
[22]
Michael J. Fischer, Nancy A. Lynch, and Mike Paterson. 1985. Impossibility of Distributed Consensus with One Faulty Process. J. ACM, 32, 2 (1985), 374–382. https://doi.org/10.1145/3149.214121
[23]
Daniel Gamermann and Felipe Leite Antunes. 2017. Evidence of Fraud in Brazil’s Electoral Campaigns Via the Benford’s Law. CoRR, abs/1707.08826 (2017), arXiv:1707.08826. arxiv:1707.08826
[24]
Iftach Haitner and Yonatan Karidi-Heller. 2020. A Tight Lower Bound on Adaptively Secure Full-Information Coin Flip. In Proceedings 61st Annual IEEE Symposium on Foundations of Computer Science (FOCS). 1268–1276. https://doi.org/10.1109/FOCS46700.2020.00120
[25]
Iftach Haitner, Nikolaos Makriyannis, and Eran Omri. 2018. On the Complexity of Fair Coin Flipping. In Proceedings 16th International Conference on Theory of Cryptography (TCC) (Lecture Notes in Computer Science, Vol. 11239). 539–562. https://doi.org/10.1007/978-3-030-03807-6_20
[26]
Iftach Haitner and Eliad Tsfadia. 2017. An Almost-Optimally Fair Three-Party Coin-Flipping Protocol. SIAM J. Comput., 46, 2 (2017), 479–542. https://doi.org/10.1137/15M1009147
[27]
Shang-En Huang, Seth Pettie, and Leqi Zhu. 2022. Byzantine Agreement in Polynomial Time with Near-Optimal Resilience. CoRR, abs/2202.13452 (2022), arXiv:2202.13452.
[28]
Jeff Kahn, Gil Kalai, and Nathan Linial. 1988. The Influence of Variables on Boolean Functions (Extended Abstract). In Proceedings of the 29th Annual IEEE Symposium on Foundations of Computer Science (FOCS). 68–80. https://doi.org/10.1109/SFCS.1988.21923
[29]
Bruce M. Kapron, David Kempe, Valerie King, Jared Saia, and Vishal Sanwalani. 2010. Fast asynchronous Byzantine agreement and leader election with full information. ACM Trans. Algorithms, 6, 4 (2010), 68:1–68:28. https://doi.org/10.1145/1824777.1824788
[30]
Karlo Kauko. 2019. Benford’s law and Chinese banks’ non-performing loans. Bank of Finland, Institute for Economies in Transition (BOFIT). http://hdl.handle.net/10419/212933
[31]
A Kilani and G P Georgiou. 2021. Countries with potential data misreport based on Benford’s law. Journal of Public Health, 43, 2 (2021), e295–e296. https://doi.org/10.1093/ /fdab001
[32]
Ben Kimmett. 2020. Improvement and partial simulation of King & Saia’s expected-polynomial-time Byzantine agreement algorithm. Master’s thesis. University of Victoria. Canada.
[33]
Valerie King and Jared Saia. 2011. Breaking the O(n^2) bit barrier: scalable Byzantine agreement with an adaptive adversary. J. ACM, 58, 4 (2011), 1–24.
[34]
Valerie King and Jared Saia. 2016. Byzantine Agreement in Expected Polynomial Time. J. ACM, 63, 2 (2016), 13:1–13:21. https://doi.org/10.1145/2837019
[35]
Valerie King and Jared Saia. 2018. Correction to Byzantine Agreement in Expected Polynomial Time, JACM 2016. CoRR, abs/1812.10169 (2018), arXiv:1812.10169. arxiv:1812.10169
[36]
Leslie Lamport, Robert E. Shostak, and Marshall C. Pease. 1982. The Byzantine Generals Problem. ACM Trans. Program. Lang. Syst., 4, 3 (1982), 382–401. https://doi.org/10.1145/357172.357176
[37]
Allison B. Lewko. 2011. The Contest between Simplicity and Efficiency in Asynchronous Byzantine Agreement. In Proceedings 25th International Symposium on Distributed Computing (DISC) (Lecture Notes in Computer Science, Vol. 6950). 348–362. https://doi.org/10.1007/978-3-642-24100-0_35
[38]
Darya Melnyk. 2020. Byzantine Agreement on Representative Input Values Over Public Channels. Ph. D. Dissertation. ETH Zurich.
[39]
Tal Moran, Moni Naor, and Gil Segev. 2016. An Optimally Fair Coin Toss. J. Cryptol., 29, 3 (2016), 491–513. https://doi.org/10.1007/s00145-015-9199-z
[40]
Michael O. Rabin. 1983. Randomized Byzantine Generals. In Proceedings 24th Annual IEEE Symposium on Foundations of Computer Science (FOCS). 403–409. https://doi.org/10.1109/SFCS.1983.48
[41]
Boudewijn F. Roukema. 2014. A first-digit anomaly in the 2009 Iranian presidential election. J. Applied Statistics, 41, 1 (2014), 164–199. https://doi.org/10.1080/02664763.2013.838664
[42]
Alexander Russell, Michael E. Saks, and David Zuckerman. 2002. Lower Bounds for Leader Election and Collective Coin-Flipping in the Perfect Information Model. SIAM J. Comput., 31, 6 (2002), 1645–1662. https://doi.org/10.1137/S0097539700376007
[43]
Michael E. Saks. 1989. A Robust Noncryptographic Protocol for Collective Coin Flipping. SIAM J. Discret. Math., 2, 2 (1989), 240–244. https://doi.org/10.1137/0402020
[44]
Uri Simonsohn. 2013. Just Post It: The Lesson From Two Cases of Fabricated Data Detected by Statistics Alone. Psychological Science, 24, 10 (2013), 1875–1888. https://doi.org/10.1177/0956797613480366
[45]
Uri Simonsohn, Joseph P. Simmons, and Leif D. Nelson. 2015. Better P-curves: Making P-curve analysis more robust to errors, fraud, and ambitious P-hacking, a Reply to Ulrich and Miller (2015). Journal of Experimental Psychology, 144, 6 (2015), 1146–1152. https://doi.org/10.1037/xge0000104
[46]
Cristi Tilden and Troy Janes. 2012. Empirical evidence of financial statement manipulation during economic recessions. J. Finance and Accountancy, 10 (2012).
[47]
Sam Toueg. 1984. Randomized Byzantine Agreements. In Proceedings 3rd Annual ACM Symposium on Principles of Distributed Computing (PODC). 163–178. https://doi.org/10.1145/800222.806744
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- Byzantine agreement in polynomial time with near-optimal resilience
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View all- Huang SPettie SZhu L(2024)Byzantine Agreement with Optimal Resilience via Statistical Fraud DetectionJournal of the ACM10.1145/363945471:2(1-37)Online publication date: 12-Apr-2024
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