Chaya Ganesh
ABSTRACT
The problem of broadcast and Byzantine Agreement are of interest to both distributed computing and cryptography community. Often these primitives require prohibitive communication and round complexity. Broadcast extensions have been introduced to broadcast long messages at the cost of small number of broadcasts for bit. The latter are referred to as seed broadcasts.
In a setting with n parties and an adversary controlling at most t parties in Byzantine fashion such that t < n, we present a broadcast extension that is simultaneously optimal in terms of communication complexity and round complexity. Specifically, we achieve O(l n) bits of communication complexity for a message of length l bits and O(n) round complexity. The known broadcast extension protocol in the same setting was only communication optimal.
A concrete broadcast extension protocol is obtained when the seed broadcasts are instantiated with broadcast protocols for bit. Our optimal broadcast extension protocol in t < n setting leads to concrete extension protocols that improve the round complexity of existing concrete extension protocols by a factor of Ω(n). We also improve the state-of-the-art round complexity of the communication optimal concrete broadcast extension protocol in t < n/2 setting. The result comes as a corollary of a new extension protocol that improves both the round complexity as well as the seed round complexity of the existing extension protocols for t < n/2. The seed round complexity is defined as the number of rounds in which a broadcast for bit is invoked.
- Piotr Berman, Juan A Garay, and Kenneth J Perry. Bit optimal distributed consensus. In Computer science, pages 313--321. Springer, 1992. Google Scholar
Cross Ref
- Zuzana Beerliová-Trubíıniová and Martin Hirt. Efficient multi-party computation with dispute control. In Theory of Cryptography, pages 305--328. Springer, 2006. Google ScholarDigital Library
- Ronald Cramer, Rosario Gennaro, and Berry Schoenmakers. A secure and optimally efficient multi-authority election scheme. In Advances in Cryptology - EUROCRYPT 1997, pages 103--118. Springer, 1997. Google ScholarCross Ref
- Brian A Coan and Jennifer L Welch. Modular construction of a byzantine agreement protocol with optimal message bit complexity. Information and Computation, 97(1):61--85, 1992.Google ScholarDigital Library
- Danny Dolev and Rüdiger Reischuk. Bounds on information exchange for byzantine agreement. J. ACM, 32(1):191--204, 1985. Google ScholarDigital Library
- Danny Dolev and H. Raymond Strong. Authenticated algorithms for byzantine agreement. SIAM Journal on Computing, 12(4):656--666, 1983.Google ScholarDigital Library
- Shimon Even, Oded Goldreich, and Abraham Lempel. A randomized protocol for signing contracts. Communications of the ACM, 28(6):637--647, 1985. Google ScholarDigital Library
- Matthias Fitzi and Martin Hirt. Optimally efficient multi-valued byzantine agreement. In Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing, pages 163--168. ACM, 2006. Google ScholarDigital Library
- Pesech Feldman and Silvio Micali. An optimal probabilistic protocol for synchronous byzantine agreement. SIAM Journal on Computing, 26(4):873--933, 1997. Google ScholarDigital Library
- Juan Garay, Jonathan Katz, Chiu-Yuen Koo, and Rafail Ostrovsky. Round complexity of authenticated broadcast with a dishonest majority. In Foundations of Computer Science, 2007. FOCS'07, pages 658--668. IEEE, 2007. Google ScholarDigital Library
- Oded Goldreich, Silvio Micali, and Avi Wigderson. How to play any mental game. In Proceedings of the nineteenth annual ACM symposium on Theory of computing, pages 218--229. ACM, 1987. Google ScholarDigital Library
- Martin Hirt and Pavel Raykov. Multi-valued byzantine broadcast: The( t<n) case. In Advances in Cryptology--ASIACRYPT 2014, pages 448--465. Springer, 2014.Google ScholarCross Ref
- Yuval Ishai, Joe Kilian, Kobbi Nissim, and Erez Petrank. Extending oblivious transfers efficiently. In Advances in Cryptology-CRYPTO 2003, pages 145--161. Springer, 2003.Google ScholarCross Ref
- Jonathan Katz and Chiu-Yuen Koo. On expected constant-round protocols for byzantine agreement. In Advances in Cryptology - CRYPTO 2006, pages 445--462, 2006. Google ScholarDigital Library
- Leslie Lamport and Michael Fischer. Byzantine generals and transaction commit protocols. Technical report, Technical Report 62, SRI International, 1982.Google Scholar
- Guanfeng Liang and Nitin Vaidya. Error-free multi-valued consensus with byzantine failures. In Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pages 11--20. ACM, 2011. Google ScholarDigital Library
- Arpita Patra. Error-free multi-valued broadcast and byzantine agreement with optimal communication complexity. In Proceedings of Principles of Distributed Systems - 15th International Conference, OPODIS 2011, pages 34--49, 2011. Google ScholarDigital Library
- Marshall Pease, Robert Shostak, and Leslie Lamport. Reaching agreement in the presence of faults. Journal of the ACM (JACM), 27(2):228--234, 1980. Google ScholarDigital Library
- Birgit Pfitzmann and Michael Waidner. Information-theoretic pseudosignatures and byzantine agreement for t ≥ n/3. Technical Report RZ 2882, IBM Research, 1996.Google Scholar
- R. Turpin and B. A. Coan. Extending binary Byzantine Agreement to multivalued Byzantine Agreement. Information Processing Letters, 18(2):73--76, 1984.Google ScholarCross Ref
- Andrew Chi-Chih Yao. Some complexity questions related to distributive computing(preliminary report). In Proceedings of the Eleventh Annual ACM Symposium on Theory of Computing, STOC '79, pages 209--213. ACM, 1979. Google ScholarDigital Library
Index Terms
- Broadcast Extensions with Optimal Communication and Round Complexity
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