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Validity in Responsive Byzantine Agreement

Authors Diana Ghinea , Simon Holmgaard Kamp , Chen-Da Liu-Zhang

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LIPIcs.DISC.2026.51.pdf
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ACM Subject Classification
  • Theory of computation → Cryptographic protocols
Keywords
  • byzantine agreement
  • validity
  • responsive protocols
  • responsive termination

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Abstract

Byzantine Agreement (BA) protocols must ensure not only agreement and termination, but also validity: the value agreed upon should meaningfully reflect the honest parties' inputs. The choice of validity condition can change the exact resilience threshold at which BA is solvable. Tight characterizations for BA with general validity conditions are known in the partially synchronous model (PODC'23), in the synchronous model (PODC'24), and in the network-agnostic model (DISC'25). Our work focuses on general validity for synchronous BA with responsive termination: such protocols remain secure against up to t_s byzantine corruptions, but incur a running time that depends on the actual network delay δ, rather than the conservative delay bound Δ ≫ δ, whenever at most t_r ≤ t_s parties are corrupted. 
We present a tight characterization of the validity properties solvable in this setting. We prove that every non-trivial validity property requires n > 2 t_r+t_s even in authenticated settings (where a public-key infrastructure and digital signatures are available) and n > 3 t_s in unauthenticated settings. These threshold conditions are accompanied by a validity-dependent requirement, the responsive similarity condition: roughly, for any concrete configuration of honest inputs, there is a value that is valid for any view that a protocol could obtain from this initial configuration. We then present matching protocols in both settings, showing that these conditions are sufficient.
The main technical contribution is an authenticated responsive Core-Set Agreement protocol requiring n > 2 t_r+t_s. This threshold may place the protocol in an honest-minority regime, where prior constructions for general validity do not apply and where standard Synchronous Broadcast is not responsive.
Finally, we instantiate the characterization for several standard validity notions - Weak Validity, Strong Unanimity, Convex Validity, and Honest-Input Validity.

Cite As Get BibTex

Diana Ghinea, Simon Holmgaard Kamp, and Chen-Da Liu-Zhang. Validity in Responsive Byzantine Agreement. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 51:1-51:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.DISC.2026.51

Author Details

Diana Ghinea
  • Lucerne University of Applied Sciences and Arts, Switzerland
Simon Holmgaard Kamp
  • Ruhr University Bochum, Germany
Chen-Da Liu-Zhang
  • Lucerne University of Applied Sciences and Arts, Switzerland

Funding

C. Liu-Zhang and D. Ghinea were supported in part by the SNSF grant number 2000-1-243069. S. H. Kamp was funded by the European Union, ERC2023-StG-101116713. Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union. Neither the European Union nor the granting authority can be held responsible for them.

Acknowledgements

We thank the anonymous DISC 2026 reviewers for their pointers to deterministic responsive BA protocols.

References

  1. Ittai Abraham and Danny Dolev. Byzantine agreement with optimal early stopping, optimal resilience and polynomial complexity. In Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, STOC '15, pages 605-614, New York, NY, USA, 2015. Association for Computing Machinery. URL: https://doi.org/10.1145/2746539.2746581.
  2. Hagit Attiya and Jennifer L. Welch. Bounds on Worst-Case Responsiveness for Agreement Algorithms. In Alysson Bessani, Xavier Défago, Junya Nakamura, Koichi Wada, and Yukiko Yamauchi, editors, 27th International Conference on Principles of Distributed Systems (OPODIS 2023), volume 286 of Leibniz International Proceedings in Informatics (LIPIcs), pages 32:1-32:22, Dagstuhl, Germany, 2024. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2023.32.
  3. Michael Ben-Or, Ran Canetti, and Oded Goldreich. Asynchronous secure computation. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, STOC '93, pages 52-61, New York, NY, USA, 1993. Association for Computing Machinery. URL: https://doi.org/10.1145/167088.167109.
  4. Michael Ben-Or, Boaz Kelmer, and Tal Rabin. Asynchronous secure computations with optimal resilience (extended abstract). In Proceedings of the Thirteenth Annual ACM Symposium on Principles of Distributed Computing, PODC '94, pages 183-192, New York, NY, USA, 1994. Association for Computing Machinery. URL: https://doi.org/10.1145/197917.198088.
  5. Piotr Berman, Juan A Garay, and Kenneth J Perry. Optimal early stopping in distributed consensus. In Distributed Algorithms: 6th International Workshop, WDAG'92 Haifa, Israel, November 2-4, 1992 Proceedings 6, pages 221-237. Springer, 1992. Google Scholar
  6. Erica Blum, Jonathan Katz, Chen-Da Liu-Zhang, and Julian Loss. Asynchronous byzantine agreement with subquadratic communication. In Rafael Pass and Krzysztof Pietrzak, editors, TCC 2020, Part I, volume 12550 of LNCS, pages 353-380. Springer, Heidelberg, November 2020. URL: https://doi.org/10.1007/978-3-030-64375-1_13.
  7. Erica Blum, Chen-Da Liu Zhang, and Julian Loss. Always have a backup plan: Fully secure synchronous MPC with asynchronous fallback. In Daniele Micciancio and Thomas Ristenpart, editors, CRYPTO 2020, Part II, volume 12171 of LNCS, pages 707-731. Springer, Heidelberg, August 2020. URL: https://doi.org/10.1007/978-3-030-56880-1_25.
  8. Ran Canetti and Tal Rabin. Fast asynchronous byzantine agreement with optimal resilience. In 25th ACM STOC, pages 42-51. ACM Press, May 1993. URL: https://doi.org/10.1145/167088.167105.
  9. Pierre Civit, Seth Gilbert, Rachid Guerraoui, Jovan Komatovic, Anton Paramonov, and Manuel Vidigueira. All byzantine agreement problems are expensive. In Proceedings of the 43rd ACM Symposium on Principles of Distributed Computing, PODC '24, pages 157-169, New York, NY, USA, 2024. Association for Computing Machinery. URL: https://doi.org/10.1145/3662158.3662780.
  10. Pierre Civit, Seth Gilbert, Rachid Guerraoui, Jovan Komatovic, and Manuel Vidigueira. On the validity of consensus. In Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing, pages 332-343, 2023. URL: https://doi.org/10.1145/3583668.3594567.
  11. Andrei Constantinescu, Marc Dufay, Diana Ghinea, and Roger Wattenhofer. Validity in Network-Agnostic Byzantine Agreement. In Dariusz R. Kowalski, editor, 39th International Symposium on Distributed Computing (DISC 2025), volume 356 of Leibniz International Proceedings in Informatics (LIPIcs), pages 24:1-24:23, Dagstuhl, Germany, 2025. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.DISC.2025.24.
  12. Andrei Constantinescu, Marc Dufay, Anton Paramonov, and Roger Wattenhofer. From few to many faults: Optimal adaptive byzantine agreement, 2026. URL: https://arxiv.org/abs/2505.19989.
  13. Andrei Constantinescu, Diana Ghinea, Lioba Heimbach, Zilin Wang, and Roger Wattenhofer. A Fair and Resilient Decentralized Clock Network for Transaction Ordering. In Alysson Bessani, Xavier Défago, Junya Nakamura, Koichi Wada, and Yukiko Yamauchi, editors, 27th International Conference on Principles of Distributed Systems (OPODIS 2023), volume 286 of Leibniz International Proceedings in Informatics (LIPIcs), pages 8:1-8:20, Dagstuhl, Germany, 2024. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2023.8.
  14. Andrei Constantinescu, Diana Ghinea, Roger Wattenhofer, and Floris Westermann. Convex Consensus with Asynchronous Fallback. In Dan Alistarh, editor, 38th International Symposium on Distributed Computing (DISC 2024), volume 319 of Leibniz International Proceedings in Informatics (LIPIcs), pages 15:1-15:23, Dagstuhl, Germany, 2024. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.DISC.2024.15.
  15. Giovanni Deligios, Ivana Klasovita, and Chen-Da Liu-Zhang. Asymptotically optimal early termination for dishonest majority broadcast. In Serge Fehr and Pierre-Alain Fouque, editors, Advances in Cryptology - EUROCRYPT 2025, pages 116-144, Cham, 2025. Springer Nature Switzerland. URL: https://doi.org/10.1007/978-3-031-91092-0_5.
  16. Giovanni Deligios and Mose Mizrahi Erbes. Closing the efficiency gap between synchronous and network-agnostic consensus. In Marc Joye and Gregor Leander, editors, Advances in Cryptology - EUROCRYPT 2024, pages 432-461, Cham, 2024. Springer Nature Switzerland. URL: https://doi.org/10.1007/978-3-031-58740-5_15.
  17. Danny Dolev and Rüdiger Reischuk. Bounds on information exchange for byzantine agreement. J. ACM, 32(1):191-204, January 1985. URL: https://doi.org/10.1145/2455.214112.
  18. Danny Dolev and H. Raymond Strong. Authenticated algorithms for byzantine agreement. SIAM Journal on Computing, 12(4):656-666, 1983. URL: https://doi.org/10.1137/0212045.
  19. Marc Dufay, Diana Ghinea, and Anton Paramonov. General convex agreement with near-optimal communication, 2026. URL: https://doi.org/10.48550/arXiv.2602.21411.
  20. Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Consensus in the presence of partial synchrony. J. ACM, 35(2):288-323, April 1988. URL: https://doi.org/10.1145/42282.42283.
  21. Fatima Elsheimy, Simon Holmgaard Kamp, Julian Loss, and Jesper Buus Nielsen. Optimal best-of-both-worlds consensus. In Annual International Cryptology Conference, pages 3-34. Springer, 2026. URL: https://doi.org/10.1007/978-3-032-35428-0_1.
  22. Michael J Fischer, Nancy A Lynch, and Michael S Paterson. Impossibility of distributed consensus with one faulty process. Journal of the ACM (JACM), 32(2):374-382, 1985. URL: https://doi.org/10.1145/3149.214121.
  23. Diana Ghinea, Simon Holmgaard Kamp, and Chen-Da Liu-Zhang. Validity in responsive byzantine agreement. Cryptology ePrint Archive, Paper 2026/1183, 2026. URL: https://eprint.iacr.org/2026/1183.
  24. Diana Ghinea, Chen-Da Liu-Zhang, and Roger Wattenhofer. Brief Announcement: Communication-Optimal Convex Agreement. In The 43rd ACM Symposium on Principles of Distributed Computing (PODC), Nantes, France, June 2024. Google Scholar
  25. Diana Ghinea, Chen-Da Liu-Zhang, and Roger Wattenhofer. Communication-optimal convex agreement. In Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC '25, pages 39-49, New York, NY, USA, 2025. Association for Computing Machinery. URL: https://doi.org/10.1145/3732772.3733551.
  26. Guy Goren, Yoram Moses, and Alexander Spiegelman. Probabilistic indistinguishability and the quality of validity in byzantine agreement. In Proceedings of the 4th ACM Conference on Advances in Financial Technologies, AFT '22, pages 111-125, New York, NY, USA, 2023. Association for Computing Machinery. URL: https://doi.org/10.1145/3558535.3559789.
  27. Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang. Multi-threshold asynchronous reliable broadcast and consensus. In 24th International Conference on Principles of Distributed Systems, page 1, 2021. Google Scholar
  28. Chen-Da Liu-Zhang, Julian Loss, Ueli Maurer, Tal Moran, and Daniel Tschudi. MPC with synchronous security and asynchronous responsiveness. In Shiho Moriai and Huaxiong Wang, editors, ASIACRYPT 2020, Part III, volume 12493 of LNCS, pages 92-119. Springer, Heidelberg, December 2020. URL: https://doi.org/10.1007/978-3-030-64840-4_4.
  29. Julian Loss and Tal Moran. Combining asynchronous and synchronous byzantine agreement: The best of both worlds. Cryptology ePrint Archive, Paper 2018/235, 2018. URL: https://eprint.iacr.org/2018/235.
  30. Julian Loss and Jesper Buus Nielsen. Early stopping for any number of corruptions. In Marc Joye and Gregor Leander, editors, Advances in Cryptology - EUROCRYPT 2024, pages 457-488, Cham, 2024. Springer Nature Switzerland. URL: https://doi.org/10.1007/978-3-031-58734-4_16.
  31. Darya Melnyk, Yuyi Wang, and Roger Wattenhofer. Byzantine Preferential Voting. In 14th Conference on Web and Internet Economics (WINE), Oxford, United Kingdom, December 2018. Google Scholar
  32. Darya Melnyk and Roger Wattenhofer. Byzantine agreement with interval validity. In 2018 IEEE 37th Symposium on Reliable Distributed Systems (SRDS), pages 251-260, 2018. URL: https://doi.org/10.1109/SRDS.2018.00036.
  33. Hammurabi Mendes, Maurice Herlihy, Nitin Vaidya, and Vijay K Garg. Multidimensional agreement in byzantine systems. Distributed Computing, 28(6):423-441, 2015. URL: https://doi.org/10.1007/S00446-014-0240-5.
  34. Andrew Miller, Yu Xia, Kyle Croman, Elaine Shi, and Dawn Song. The honey badger of BFT protocols. In Edgar R. Weippl, Stefan Katzenbeisser, Christopher Kruegel, Andrew C. Myers, and Shai Halevi, editors, ACM CCS 2016, pages 31-42. ACM Press, October 2016. URL: https://doi.org/10.1145/2976749.2978399.
  35. Gil Neiger. Distributed consensus revisited. Information Processing Letters, 49(4):195-201, 1994. URL: https://doi.org/10.1016/0020-0190(94)90011-6.
  36. Thomas Nowak and Joel Rybicki. Byzantine Approximate Agreement on Graphs. In Jukka Suomela, editor, 33rd International Symposium on Distributed Computing (DISC 2019), volume 146 of Leibniz International Proceedings in Informatics (LIPIcs), pages 29:1-29:17, Dagstuhl, Germany, 2019. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.DISC.2019.29.
  37. Rafael Pass and Elaine Shi. Hybrid consensus: Efficient consensus in the permissionless model. In LIPIcs-Leibniz International Proceedings in Informatics, volume 91. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.DISC.2017.39.
  38. Rafael Pass and Elaine Shi. Thunderella: Blockchains with optimistic instant confirmation. In Jesper Buus Nielsen and Vincent Rijmen, editors, EUROCRYPT 2018, Part II, volume 10821 of LNCS, pages 3-33. Springer, Heidelberg, April / May 2018. URL: https://doi.org/10.1007/978-3-319-78375-8_1.
  39. Kenneth J Perry and Sam Toueg. An authenticated byzantine generals algorithm with early stopping. Technical report, Cornell University, 1984. Google Scholar
  40. David Stolz and Roger Wattenhofer. Byzantine Agreement with Median Validity. In Emmanuelle Anceaume, Christian Cachin, and Maria Potop-Butucaru, editors, 19th International Conference on Principles of Distributed Systems (OPODIS 2015), volume 46 of Leibniz International Proceedings in Informatics (LIPIcs), pages 1-14, Dagstuhl, Germany, 2016. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2015.22.
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