Brief Announcement: Communication-Optimal Convex Agreement
Pages 492 - 495
Abstract
Byzantine Agreement (BA) allows a set of n parties to agree on a value even when up to t of the parties involved are corrupted. While previous works have shown that, for ℓ-bit inputs, BA can be achieved with the optimal communication complexity Õ(ℓn) for sufficiently large ℓ, BA only ensures that honest parties agree on a meaningful output when they hold the same input, rendering the primitive inadequate for many real-world applications.
This gave rise to the notion of Convex Agreement (CA), introduced by Vaidya and Garg [PODC'13], which requires the honest parties' outputs to be in the convex hull of the honest inputs. Unfortunately, all existing CA protocols incur a communication complexity of at least Ω(ℓn2). In this work, we introduce the first CA protocol with the optimal communication of O(ℓn) bits for inputs in ℤ of size ℓ = Ω(κ · n2 log n), where κ is the security parameter.
References
[1]
Ittai Abraham, Yonatan Amit, and Danny Dolev. 2005. Optimal Resilience Asynchronous Approximate Agreement. In Principles of Distributed Systems, Teruo Higashino (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 229--239.
[2]
Dan Alistarh, Faith Ellen, and Joel Rybicki. 2021. Wait-Free Approximate Agreement on Graphs. In Structural Information and Communication Complexity, Tomasz Jurdziński and Stefan Schmid (Eds.). Springer International Publishing, Cham, 87--105.
[3]
Michael Ben-Or, Danny Dolev, and Ezra N. Hoch. 2010. Brief Announcement: Simple Gradecast Based Algorithms. In Distributed Computing, Nancy A. Lynch and Alexander A. Shvartsman (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 194--197.
[4]
Amey Bhangale, Chen-Da Liu-Zhang, Julian Loss, and Kartik Nayak. 2023. Efficient adaptively-secure byzantine agreement for long messages. In Advances in Cryptology-ASIACRYPT 2022: 28th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, December 5--9, 2022, Proceedings, Part I. Springer, Springer-Verlag, Berlin, Heidelberg, 504--525.
[5]
Christian Cachin and Stefano Tessaro. 2005. Asynchronous verifiable information dispersal. In 24th IEEE Symposium on Reliable Distributed Systems (SRDS'05). IEEE, IEEE Computer Society, Orlando, FL, USA, 191--201.
[6]
Wutichai Chongchitmate and Rafail Ostrovsky. 2018. Information-Theoretic Broadcast with Dishonest Majority for Long Messages. In TCC 2018, Part I (LNCS, Vol. 11239), Amos Beimel and Stefan Dziembowski (Eds.). Springer, Heidelberg, Cham, 370--388.
[7]
Andrei Constantinescu, Diana Ghinea, Lioba Heimbach, Zilin Wang, and Roger Wattenhofer. 2024. A Fair and Resilient Decentralized Clock Network for Transaction Ordering. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023) (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 286), Alysson Bessani, Xavier Défago, Junya Nakamura, Koichi Wada, and Yukiko Yamauchi (Eds.). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 8:1--8:20.
[8]
Andrei Constantinescu, Diana Ghinea, Roger Wattenhofer, and Floris Westermann. 2023. Meeting in a Convex World: Convex Consensus with Asynchronous Fallback. Cryptology ePrint Archive, Paper 2023/1364. https://eprint.iacr.org/2023/1364
[9]
Danny Dolev, Nancy A. Lynch, Shlomit S. Pinter, Eugene W. Stark, and William E. Weihl. 1986. Reaching Approximate Agreement in the Presence of Faults. J. ACM 33, 3 (May 1986), 499--516.
[10]
Danny Dolev and H. Raymond Strong. 1983. Authenticated algorithms for Byzantine agreement. SIAM J. Comput. 12, 4 (1983), 656--666.
[11]
A. D. Fekete. 1987. Asynchronous approximate agreement. In Proceedings of the Sixth Annual ACM Symposium on Principles of Distributed Computing (Vancouver, British Columbia, Canada) (PODC '87). Association for Computing Machinery, New York, NY, USA, 64--76.
[12]
Alan David Fekete. 1990. Asymptotically optimal algorithms for approximate agreement. Distributed Computing 4, 1 (1990), 9--29.
[13]
Michael J Fischer, Nancy A Lynch, and Michael S Paterson. 1985. Impossibility of distributed consensus with one faulty process. Journal of the ACM (JACM) 32, 2 (1985), 374--382.
[14]
Matthias Fitzi and Martin Hirt. 2006. Optimally efficient multi-valued Byzantine agreement. In 25th ACM PODC, Eric Ruppert and Dahlia Malkhi (Eds.). ACM, New York, NY, USA, 163--168.
[15]
Chaya Ganesh and Arpita Patra. 2016. Broadcast Extensions with Optimal Communication and Round Complexity. In 35th ACM PODC, George Giakkoupis (Ed.). ACM, New York, NY, USA, 371--380.
[16]
Diana Ghinea, Chen-Da Liu-Zhang, and Roger Wattenhofer. 2022. Optimal Synchronous Approximate Agreement with Asynchronous Fallback. In Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing (Salerno, Italy) (PODC'22). Association for Computing Machinery, New York, NY, USA, 70--80.
[17]
Diana Ghinea, Chen-Da Liu-Zhang, and Roger Wattenhofer. 2023. Multidimensional Approximate Agreement with Asynchronous Fallback. In Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures (Orlando, FL, USA) (SPAA '23). Association for Computing Machinery, New York, NY, USA, 141--151.
[18]
Diana Ghinea, Chen-Da Liu-Zhang, and Roger Wattenhofer. 2024. Communication-Optimal Convex Agreement. Cryptology ePrint Archive, Paper 2024/251. https://eprint.iacr.org/2024/251
[19]
Martin Hirt and Pavel Raykov. 2014. Multi-valued Byzantine Broadcast: The t < n Case. In ASIACRYPT 2014, Part II (LNCS, Vol. 8874), Palash Sarkar and Tetsu Iwata (Eds.). Springer, Heidelberg, Berlin, Heidelberg, 448--465.
[20]
Jérémy Ledent. 2021. Brief Announcement: Variants of Approximate Agreement on Graphs and Simplicial Complexes. In Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing (Virtual Event, Italy) (PODC'21). Association for Computing Machinery, New York, NY, USA, 427--430.
[21]
Christoph Lenzen and Julian Loss. 2022. Optimal Clock Synchronization with Signatures. In Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing (Salerno, Italy) (PODC'22). Association for Computing Machinery, New York, NY, USA, 440--449.
[22]
Guanfeng Liang and Nitin Vaidya. 2011. Error-free multi-valued consensus with Byzantine failures. In Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing. Association for Computing Machinery, New York, NY, USA, 11--20.
[23]
Darya Melnyk and Roger Wattenhofer. 2018. Byzantine Agreement with Interval Validity. In 2018 IEEE 37th Symposium on Reliable Distributed Systems (SRDS). IEEE Computer Society, Salvador, Brazil, 251--260.
[24]
Hammurabi Mendes and Maurice Herlihy. 2013. Multidimensional approximate agreement in Byzantine asynchronous systems. In 45th ACM STOC, Dan Boneh, Tim Roughgarden, and Joan Feigenbaum (Eds.). ACM Press, Palo Alto, CA, USA, 391--400.
[25]
Hammurabi Mendes, Maurice Herlihy, Nitin Vaidya, and Vijay K Garg. 2015. Multidimensional agreement in Byzantine systems. Distributed Computing 28, 6 (2015), 423--441.
[26]
Kartik Nayak, Ling Ren, Elaine Shi, Nitin H. Vaidya, and Zhuolun Xiang. 2020. Improved Extension Protocols for Byzantine Broadcast and Agreement. In 34th International Symposium on Distributed Computing (DISC 2020) (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 179), Hagit Attiya (Ed.). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 28:1--28:17.
[27]
Thomas Nowak and Joel Rybicki. 2019. Byzantine Approximate Agreement on Graphs. In 33rd International Symposium on Distributed Computing (DISC 2019) (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 146), Jukka Suomela (Ed.). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 29:1--29:17.
[28]
David Stolz and Roger Wattenhofer. 2016. Byzantine Agreement with Median Validity. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015) (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 46), Emmanuelle Anceaume, Christian Cachin, and Maria Potop-Butucaru (Eds.). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 1--14.
[29]
Russell Turpin and Brian A Coan. 1984. Extending binary Byzantine agreement to multivalued Byzantine agreement. Inform. Process. Lett. 18, 2 (1984), 73--76.
[30]
Nitin H. Vaidya and Vijay K. Garg. 2013. Byzantine vector consensus in complete graphs. In 32nd ACM PODC, Panagiota Fatourou and Gadi Taubenfeld (Eds.). ACM, Montreal, QC, 65--73.
Index Terms
- Brief Announcement: Communication-Optimal Convex Agreement
Recommendations
Brief Announcement: Asynchronous Secure Distributed Computing with Transferrable Non-equivocation Revisited
PODC '18: Proceedings of the 2018 ACM Symposium on Principles of Distributed ComputingIn this paper, we consider two fundamental problems in secure distributed computing, namely Asynchronous Byzantine Agreement (ABA) and Asynchronous Secure Multi-party Computation (ASMPC). Our focus is on the honest majority setting, involving a set of n ...
Brief announcement: impossibility results for optimistic fair exchange with multiple autonomous arbiters
PODC '09: Proceedings of the 28th ACM symposium on Principles of distributed computingFair exchange is one of the most fundamental problems in secure distributed computation. Alice has something that Bob wants, and Bob has something that Alice wants. A fair exchange protocol would guarantee that, even if one of them maliciously deviates ...
Brief announcement: communication efficient asynchronous byzantine agreement
PODC '10: Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computingIn [7], the authors presented a novel perfect (i.e error-free Asynchronous Verifiable Secret Sharing (AVSS) protocol and using the AVSS, they designed a perfect Asynchronous Multiparty Computation (AMPC) protocol that provides the best known ...
Comments
Information & Contributors
Information
Published In
June 2024
570 pages
ISBN:9798400706684
DOI:10.1145/3662158
- Chair:
- Ran Gelles,
- Proceedings Chair:
- Dennis Olivetti,
- Program Chair:
- Petr Kuznetsov
Copyright © 2024 Copyright is held by the owner/author(s). Publication rights licensed to ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
Sponsors
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 17 June 2024
Check for updates
Author Tags
Qualifiers
- Short-paper
Conference
Acceptance Rates
Overall Acceptance Rate 740 of 2,477 submissions, 30%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 28Total Downloads
- Downloads (Last 12 months)28
- Downloads (Last 6 weeks)6
Reflects downloads up to 30 Aug 2024
Other Metrics
Citations
View Options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in