Document Open Access Logo

Fast Agreement in Networks with Byzantine Nodes

Authors Bogdan S. Chlebus, Dariusz R. Kowalski, Jan Olkowski



PDF
Thumbnail PDF

File

LIPIcs.DISC.2020.30.pdf
  • Filesize: 0.6 MB
  • 18 pages

Document Identifiers

Author Details

Bogdan S. Chlebus
  • School of Computer and Cyber Sciences, Augusta University, GA, USA
Dariusz R. Kowalski
  • School of Computer and Cyber Sciences, Augusta University, GA, USA
  • SWPS Uniwersytet Humanistycznospołeczny, Warsaw, Poland
Jan Olkowski
  • WydziałMatematyki, Informatyki i Mechaniki, Uniwersytet Warszawski, Warsaw, Poland

Cite AsGet BibTex

Bogdan S. Chlebus, Dariusz R. Kowalski, and Jan Olkowski. Fast Agreement in Networks with Byzantine Nodes. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 30:1-30:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.DISC.2020.30

Abstract

We study Consensus in synchronous networks with arbitrary connected topologies. Nodes may be faulty, in the sense of either Byzantine or proneness to crashing. Let t denote a known upper bound on the number of faulty nodes, and D_s denote a maximum diameter of a network obtained by removing up to s nodes, assuming the network is (s+1)-connected. We give an algorithm for Consensus running in time t + D_{2t} with nodes subject to Byzantine faults. We show that, for any algorithm solving Consensus for Byzantine nodes, there is a network G and an execution of the algorithm on this network that takes Ω(t + D_{2t}) rounds. We give an algorithm solving Consensus in t + D_{t} communication rounds with Byzantine nodes using authenticated messages of polynomial size. We show that for any numbers t and d > 4, there exists a network G and an algorithm solving Consensus with Byzantine nodes using authenticated messages in fewer than t + 3 rounds on G, but all algorithms solving Consensus without message authentication require at least t + d rounds on G. This separates Consensus with Byzantine nodes from Consensus with Byzantine nodes using message authentication, with respect to asymptotic time performance in networks of arbitrary connected topologies, which is unlike complete networks. Let f denote the number of failures actually occurring in an execution and unknown to the nodes. We develop an algorithm solving Consensus against crash failures and running in time 𝒪(f + D_{f}), assuming only that nodes know their names and can differentiate among ports; this algorithm is also communication-efficient, by using messages of size 𝒪(mlog n), where n is the number of nodes and m is the number of edges. We give a lower bound t+D_t-2 on the running time of any deterministic solution to Consensus in (t+1)-connected networks, if t nodes may crash.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Distributed algorithms
Keywords
  • distributed algorithm
  • network
  • Consensus
  • Byzantine fault
  • message authentication
  • node crash
  • lower bound

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Marcos Kawazoe Aguilera and Sam Toueg. A simple bivalency proof that t-resilient consensus requires t + 1 rounds. Information Processing Letters, 71(3-4):155-158, 1999. Google Scholar
  2. Hagit Attiya and Faith Ellen. Impossibility Results for Distributed Computing. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, 2014. Google Scholar
  3. Hagit Attiya and Jennifer Welch. Distributed Computing: Fundamentals, Simulations, and Advanced Topics. Wiley, Second edition, 2004. Google Scholar
  4. Piyush Bansal, Prasant Gopal, Anuj Gupta, Kannan Srinathan, and Pranav K. Vasishta. Byzantine agreement using partial authentication. In Proceedings of the 25th International Symposium on Distributed Computing (DISC), volume 6950 of Lecture Notes in Computer Science, pages 389-403. Springer, 2011. Google Scholar
  5. Amotz Bar-Noy, Danny Dolev, Cynthia Dwork, and H. Raymond Strong. Shifting gears: Changing algorithms on the fly to expedite Byzantine agreement. Information and Computation, 97(2):205-233, 1992. Google Scholar
  6. Piotr Berman and Juan A. Garay. Cloture votes: n/4-resilient distributed consensus in t+1 rounds. Mathematical Systems Theory, 26(1):3-19, 1993. Google Scholar
  7. Piotr Berman, Juan A. Garay, and Kenneth J. Perry. Optimal early stopping in distributed consensus (extended abstract). In Proceedings of the 6th International Workshop on Distributed Algorithms (WDAG), volume 647 of Lecture Notes in Computer Science, pages 221-237. Springer, 1992. Google Scholar
  8. Armando Castañeda, Yoram Moses, Michel Raynal, and Matthieu Roy. Early decision and stopping in synchronous consensus: A predicate-based guided tour. In Proceedings of 5th International Conference on Networked Systems (NETYS), volume 10299 of Lecture Notes in Computer Science, pages 206-221. Springer, 2017. Google Scholar
  9. Bogdan S. Chlebus and Dariusz R. Kowalski. Robust gossiping with an application to consensus. Journal of Computer System and Sciences, 72(8):1262-1281, 2006. Google Scholar
  10. Bogdan S. Chlebus and Dariusz R. Kowalski. Time and communication efficient consensus for crash failures. In Proceedings of the 20th International Symposium on Distributed Computing (DISC), volume 4167 of Lecture Notes in Computer Science, pages 314-328. Springer, 2006. Google Scholar
  11. Bogdan S. Chlebus and Dariusz R. Kowalski. Locally scalable randomized consensus for synchronous crash failures. In Proceedings of the 21st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 290-299. ACM, 2009. Google Scholar
  12. Bogdan S. Chlebus, Dariusz R. Kowalski, and Michał Strojnowski. Fast scalable deterministic consensus for crash failures. In Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC), pages 111-120. ACM, 2009. Google Scholar
  13. Bogdan S. Chlebus, Dariusz R. Kowalski, and Michał Strojnowski. Scalable quantum consensus for crash failures. In Proceedings of the 24th International Symposium on Distributed Computing (DISC), volume 6343 of Lecture Notes in Computer Science, pages 236-250. Springer, 2010. Google Scholar
  14. Danny Dolev. The Byzantine generals strike again. Journal of Algorithms, 3(1):14-30, 1982. Google Scholar
  15. Danny Dolev and Christoph Lenzen. Early-deciding consensus is expensive. In Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC), pages 270-279. ACM, 2013. Google Scholar
  16. Danny Dolev and Rüdiger Reischuk. Bounds on information exchange for Byzantine agreement. Journal of the ACM, 32(1):191-204, 1985. Google Scholar
  17. Danny Dolev, Rüdiger Reischuk, and H. Raymond Strong. Early stopping in Byzantine agreement. Journal of the ACM, 37(4):720-741, 1990. Google Scholar
  18. Danny Dolev and H. Raymond Strong. Authenticated algorithms for Byzantine agreement. SIAM Journal on Computing, 12(4):656-666, 1983. Google Scholar
  19. Michael J. Fischer and Nancy A. Lynch. A lower bound for the time to assure interactive consistency. Information Processing Letters, 14(4):183-186, 1982. Google Scholar
  20. Michael J. Fischer, Nancy A. Lynch, and Michael Merritt. Easy impossibility proofs for distributed consensus problems. Distributed Computing, 1(1):26-39, 1986. Google Scholar
  21. Zvi Galil, Alain J. Mayer, and Moti Yung. Resolving message complexity of Byzantine agreement and beyond. In Proceedings of the 36th IEEE Symposium on Foundations of Computer Science (FOCS), pages 724-733. IEEE, 1995. Google Scholar
  22. Juan A. Garay and Yoram Moses. Fully polynomial Byzantine agreement for n > 3t processors in t + 1 rounds. SIAM Journal on Computing, 27(1):247-290, 1998. Google Scholar
  23. Maurice Herlihy and Nir Shavit. The Art of Multiprocessor Programming. Morgan Kaufmann, 2012. Google Scholar
  24. Idit Keidar and Sergio Rajsbaum. A simple proof of the uniform consensus synchronous lower bound. Information Processing Letters, 85(1):47-52, 2003. Google Scholar
  25. Muhammad Samir Khan, Syed Shalan Naqvi, and Nitin H. Vaidya. Exact Byzantine consensus on undirected graphs under local broadcast model. In Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC), pages 327-336. ACM, 2019. Google Scholar
  26. Leslie Lamport, Robert E. Shostak, and Marshall C. Pease. The Byzantine generals problem. ACM Transactions on Programming Languages and Systems, 4(3):382-401, 1982. Google Scholar
  27. Nancy A. Lynch. Distributed Algorithms. Morgan Kaufmann Publishers, 1996. Google Scholar
  28. Philippe Raipin Parvédy and Michel Raynal. Optimal early stopping uniform consensus in synchronous systems with process omission failures. In Proceedings of the Sixteenth Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 302-310. ACM, 2004. Google Scholar
  29. Marshall C. Pease, Robert E. Shostak, and Leslie Lamport. Reaching agreement in the presence of faults. Journal of the ACM, 27(2):228-234, 1980. Google Scholar
  30. Michel Raynal. Fault-tolerant Agreement in Synchronous Message-passing Systems. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, 2010. Google Scholar
  31. T. K. Srikanth and Sam Toueg. Simulating authenticated broadcasts to derive simple fault-tolerant algorithms. Distributed Computing, 2(2):80-94, 1987. Google Scholar
  32. Lewis Tseng. Recent results on fault-tolerant consensus in message-passing networks. In Proceedings of the 23rd International Colloquium on Structural Information and Communication Complexity (SIROCCO), volume 9988 of Lecture Notes in Computer Science, pages 92-108. Springer, 2016. Google Scholar
  33. Lewis Tseng and Nitin H. Vaidya. Fault-tolerant consensus in directed graphs. In Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC), pages 451-460. ACM, 2015. Google Scholar
  34. Lewis Tseng and Nitin H. Vaidya. A note on fault-tolerant consensus in directed networks. SIGACT News, 47(3):70-91, 2016. Google Scholar
  35. Xianbing Wang, Yong Meng Teo, and Jiannong Cao. A bivalency proof of the lower bound for uniform consensus. Information Processing Letters, 96(5):167-174, 2005. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail