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Simple Is COOL: Graded Dispersal and Its Applications for Byzantine Fault Tolerance

Authors Ittai Abraham , Gilad Asharov , Anirudh Chandramouli

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Author Details

Ittai Abraham
  • Intel Labs, Petah Tikva, Israel
Gilad Asharov
  • Bar-Ilan University, Ramat-Gan, Israel
Anirudh Chandramouli
  • Bar-Ilan University, Ramat-Gan, Israel

Funding

  • Asharov, Gilad: Supported by the Israel Science Foundation (grant No. 2439/20), and by JPM Faculty Research Award.
  • Chandramouli, Anirudh: Same as Gilad Asharov.

Cite As Get BibTex

Ittai Abraham, Gilad Asharov, and Anirudh Chandramouli. Simple Is COOL: Graded Dispersal and Its Applications for Byzantine Fault Tolerance. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.1

Abstract

The COOL protocol of Chen (DISC'21) is a major advance that enables perfect security for various tasks (in particular, Byzantine Agreement in Synchrony and Reliable Broadcast in Asynchrony). For an input of size L bits, its communication complexity is O(nL+n² log n), which is optimal up to a log n factor. Unfortunately, Chen’s analysis is rather intricate and complex.
Our main contribution is a simple analysis of a new variant of COOL based on elementary counting arguments. Our main consistency proof takes less than two pages (instead of over 20 pages), making the COOL protocol much more accessible. In addition, the simple analysis allows us to improve the protocol by reducing one round of communication and reducing the communication complexity by 40%.
In addition, we suggest a new way of extracting the core properties of COOL as a new primitive, which we call Graded Dispersal. We show how Graded Dispersal can then be used to obtain efficient solutions for Byzantine Agreement, Verifiable Information Dispersal, Gradecast, and Reliable Broadcast (in both Synchrony and Asynchrony, where appropriate). Our improvement of COOL directly applies here, and we improve the state-of-the-art in all those primitives by reducing at least one round and 40% communication.

Subject Classification

ACM Subject Classification
  • Security and privacy
  • Security and privacy → Cryptography
  • Security and privacy → Information-theoretic techniques
  • Security and privacy → Distributed systems security
Keywords
  • Byzantine Agreement
  • Broadcast

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References

  1. Ittai Abraham and Gilad Asharov. Gradecast in synchrony and reliable broadcast in asynchrony with optimal resilience, efficiency, and unconditional security. In PODC '22: ACM Symposium on Principles of Distributed Computing, 2022, pages 392-398. ACM, 2022. URL: https://doi.org/10.1145/3519270.3538451.
  2. Ittai Abraham, Gilad Asharov, Shravani Patil, and Arpita Patra. Asymptotically free broadcast in constant expected time via packed VSS. In Theory of Cryptography - 20th International Conference, TCC 2022, volume 13747 of Lecture Notes in Computer Science, pages 384-414. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-22318-1_14.
  3. Ittai Abraham, T.-H. Hubert Chan, Danny Dolev, Kartik Nayak, Rafael Pass, Ling Ren, and Elaine Shi. Communication complexity of byzantine agreement, revisited. Distributed Comput., 36(1):3-28, 2023. URL: https://doi.org/10.1007/S00446-022-00428-8.
  4. Ittai Abraham, Philipp Jovanovic, Mary Maller, Sarah Meiklejohn, Gilad Stern, and Alin Tomescu. Reaching consensus for asynchronous distributed key generation. In PODC '21: ACM Symposium on Principles of Distributed Computing, 2021, pages 363-373. ACM, 2021. URL: https://doi.org/10.1145/3465084.3467914.
  5. Ittai Abraham and Andrew Lewis-Pye. Phase-king through the lens of gradecast: A simple unauthenticated synchronous byzantine agreement protocol. Decentralized Thoughts, Blog Post, 2022. URL: https://decentralizedthoughts.github.io/2022-06-09-phase-king-via-gradecast/.
  6. Nicolas Alhaddad, Sourav Das, Sisi Duan, Ling Ren, Mayank Varia, Zhuolun Xiang, and Haibin Zhang. Balanced byzantine reliable broadcast with near-optimal communication and improved computation. In PODC '22: ACM Symposium on Principles of Distributed Computing, pages 399-417. ACM, 2022. URL: https://doi.org/10.1145/3519270.3538475.
  7. Gilad Asharov and Anirudh Chandramouli. Perfect (parallel) broadcast in constant expected rounds via statistical VSS. In Advances in Cryptology - EUROCRYPT 2024, volume 14655 of Lecture Notes in Computer Science, pages 310-339. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-58740-5_11.
  8. Michael Ben-Or. Another advantage of free choice: Completely asynchronous agreement protocols (extended abstract). In Proc. of the Annual Symposium on Principles of Distributed Computing (PODC), 1983. Google Scholar
  9. Michael Ben-Or, Danny Dolev, and Ezra N. Hoch. Brief announcement: Simple gradecast based algorithms. In Distributed Computing, 24th International Symposium, DISC 2010., volume 6343 of Lecture Notes in Computer Science, pages 194-197. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-15763-9_18.
  10. Piotr Berman, Juan A Garay, and Kenneth J Perry. Bit optimal distributed consensus. In Computer science. 1992. Google Scholar
  11. Gabriel Bracha. Asynchronous byzantine agreement protocols. Inf. Comput., 75(2):130-143, 1987. URL: https://doi.org/10.1016/0890-5401(87)90054-X.
  12. Christian Cachin and Stefano Tessaro. Asynchronous veri.able information dispersal. In 24th IEEE Symposium on Reliable Distributed Systems (SRDS 2005), 2005, pages 191-202. IEEE Computer Society, 2005. URL: https://doi.org/10.1109/RELDIS.2005.9.
  13. Jinyuan Chen. Optimal error-free multi-valued byzantine agreement. In DISC 2021, volume 209 of LIPIcs, pages 17:1-17:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPICS.DISC.2021.17.
  14. Sourav Das, Zhuolun Xiang, and Ling Ren. Asynchronous data dissemination and its applications. In CCS '21: 2021 ACM SIGSAC Conference on Computer and Communications Security, pages 2705-2721. ACM, 2021. URL: https://doi.org/10.1145/3460120.3484808.
  15. Sourav Das, Zhuolun Xiang, and Ling Ren. Balanced quadratic reliable broadcast and improved asynchronous verifiable information dispersal. IACR Cryptol. ePrint Arch., page 52, 2022. URL: https://eprint.iacr.org/2022/052.
  16. Danny Dolev and Rüdiger Reischuk. Bounds on information exchange for byzantine agreement. In ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, 1982, pages 132-140. ACM, 1982. URL: https://doi.org/10.1145/800220.806690.
  17. Paul Feldman and Silvio Micali. Optimal algorithms for byzantine agreement. In Proceedings of the 20th Annual ACM Symposium on Theory of Computing, pages 148-161. ACM, 1988. URL: https://doi.org/10.1145/62212.62225.
  18. Michael J. Fischer and Nancy A. Lynch. A lower bound for the time to assure interactive consistency. Information Processing Letters, 1982. Google Scholar
  19. Chaya Ganesh and Arpita Patra. Optimal extension protocols for byzantine broadcast and agreement. Distributed Comput., 34(1):59-77, 2021. URL: https://doi.org/10.1007/S00446-020-00384-1.
  20. Jonathan Katz and Chiu-Yuen Koo. On expected constant-round protocols for byzantine agreement. In Annual International Cryptology Conference, 2006. Google Scholar
  21. Jonathan Katz and Chiu-Yuen Koo. On expected constant-round protocols for byzantine agreement. J. Comput. Syst. Sci., 75(2):91-112, 2009. URL: https://doi.org/10.1016/J.JCSS.2008.08.001.
  22. Leslie Lamport, Robert E. Shostak, and Marshall C. Pease. The byzantine generals problem. ACM Trans. Program. Lang. Syst., 4(3):382-401, 1982. URL: https://doi.org/10.1145/357172.357176.
  23. Guanfeng Liang and Nitin H. Vaidya. Error-free multi-valued consensus with byzantine failures. In Proceedings of the 30th Annual ACM Symposium on Principles of Distributed Computing, PODC 2011, pages 11-20. ACM, 2011. URL: https://doi.org/10.1145/1993806.1993809.
  24. Andrew D. Loveless, Ronald G. Dreslinski, and Baris Kasikci. Optimal and error-free multi-valued byzantine consensus through parallel execution. IACR Cryptol. ePrint Arch., page 322, 2020. URL: https://eprint.iacr.org/2020/322.
  25. Kartik Nayak, Ling Ren, Elaine Shi, Nitin H. Vaidya, and Zhuolun Xiang. Improved extension protocols for byzantine broadcast and agreement. In 34th International Symposium on Distributed Computing, DISC 2020, volume 179 of LIPIcs, pages 28:1-28:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPICS.DISC.2020.28.
  26. Arpita Patra. Error-free multi-valued broadcast and byzantine agreement with optimal communication complexity. In Principles of Distributed Systems - 15th International Conference, OPODIS 2011, volume 7109 of Lecture Notes in Computer Science, pages 34-49. Springer, 2011. URL: https://doi.org/10.1007/978-3-642-25873-2_4.
  27. Marshall C. Pease, Robert E. Shostak, and Leslie Lamport. Reaching agreement in the presence of faults. J. ACM, 27(2):228-234, 1980. URL: https://doi.org/10.1145/322186.322188.
  28. M. O. Rabin. Randomized byzantine generals. In 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 1983. Google Scholar
  29. Jacob T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities. J. ACM, 27(4):701-717, 1980. URL: https://doi.org/10.1145/322217.322225.
  30. Jianjun Zhu, Fan Li, and Jinyuan Chen. Communication-efficient and error-free gradecast with optimal resilience. In 2023 IEEE International Symposium on Information Theory (ISIT), pages 108-113, 2023. URL: https://doi.org/10.1109/ISIT54713.2023.10206579.
  31. Richard Zippel. Probabilistic algorithms for sparse polynomials. In Symbolic and Algebraic Computation, EUROSAM '79, An International Symposiumon Symbolic and Algebraic Computation, volume 72 of Lecture Notes in Computer Science, pages 216-226. Springer, 1979. URL: https://doi.org/10.1007/3-540-09519-5_73.
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