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Synchronous Byzantine Agreement with Expected O(1) Rounds, Expected \(O(n^2)\) Communication, and Optimal Resilience

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Financial Cryptography and Data Security (FC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11598))

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Abstract

We present new protocols for Byzantine agreement in the synchronous and authenticated setting, tolerating the optimal number of f faults among \(n=2f+1\) parties. Our protocols achieve an expected O(1) round complexity and an expected \(O(n^2)\) communication complexity. The exact round complexity in expectation is 10 for a static adversary and 16 for a strongly rushing adaptive adversary. For comparison, previous protocols in the same setting require expected 29 rounds.

A preliminary draft of the paper appeard on ePrint in 2017 [2]. The current version improves and subsumes the Byzantine agreement part of the preliminary draft.

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Notes

  1. 1.

    Katz and Koo [19] did not analyze communication complexity in their paper. Based on our understanding, their unrolled protocol in the appendix can achieve \(O(n^2)\) communication complexity by similarly incorporating threshold signatures and a quadratic common-coin protocol.

References

  1. Abraham, I., et al.: Communication complexity of byzantine agreement, revisited. arXiv preprint, arXiv:1805.03391 (2018)

  2. Abraham, I., Devadas, S., Dolev, D., Nayak, K., Ren, L.: Synchronous byzantine agreement with expected \({O}(1)\) rounds, expected \({O}(n^2)\) communication, and optimal resilience. Cryptology ePrint Archive, Report 2018/1028 (2018). https://eprint.iacr.org/2018/1028

  3. Abraham, I., Gueta, G., Malkhi, D.: Hot-stuff the linear, optimal-resilience, one-message BFT devil. arXiv preprint arXiv:1803.05069 (2018)

  4. Abraham, I., Malkhi, D., Nayak, K., Ren, L., Spiegelman, A.: A blockchain protocol based on reconfigurable byzantine consensus. In: OPODIS, Solida (2017)

    Google Scholar 

  5. Adya, A., et al.: FARSITE: federated, available, and reliable storage for an incompletely trusted environment. ACM SIGOPS Oper. Syst. Rev. 36(SI), 1–14 (2002)

    Article  Google Scholar 

  6. Ben-Or, M.: Another advantage of free choice (extended abstract): completely asynchronous agreement protocols. In: Proceedings of the Second Annual ACM Symposium on Principles of Distributed Computing, pp. 27–30. ACM (1983)

    Google Scholar 

  7. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, pp. 1–10. ACM (1988)

    Google Scholar 

  8. Cachin, C., Kursawe, K., Shoup, V.: Random oracles in constantinople: practical asynchronous byzantine agreement using cryptography. J. Cryptol. 18(3), 219–246 (2005)

    Article  MathSciNet  Google Scholar 

  9. Castro, M., Liskov, B.: Practical byzantine fault tolerance. In: OSDI, vol. 99, pp. 173–186 (1999)

    Google Scholar 

  10. Dolev, D., Halpern, J., Simons, B., Strong, R.: Dynamic fault-tolerant clock synchronization. J. ACM 42(1), 143–185 (1995)

    Article  Google Scholar 

  11. Dolev, D., Reischuk, R.: Bounds on information exchange for Byzantine agreement. J. ACM (JACM) 32(1), 191–204 (1985)

    Article  MathSciNet  Google Scholar 

  12. Dolev, D., Raymond Strong, H.: Authenticated algorithms for Byzantine agreement. SIAM J. Comput. 12(4), 656–666 (1983)

    Article  MathSciNet  Google Scholar 

  13. Dwork, C., Lynch, N., Stockmeyer, L.: Consensus in the presence of partial synchrony. J. ACM 35(2), 288–323 (1988)

    Article  MathSciNet  Google Scholar 

  14. Feldman, P., Micali, S.: An optimal probabilistic protocol for synchronous byzantine agreement. SIAM J. Comput. 26(4), 873–933 (1997)

    Article  MathSciNet  Google Scholar 

  15. Fischer, M.J., Lynch, N.A.: A lower bound for the time to assure interactive consistency. Inf. Process. Lett. 14(4), 183–186 (1982)

    Article  MathSciNet  Google Scholar 

  16. Fitzi, M., Garay, J.A.: Efficient player-optimal protocols for strong and differential consensus. In: Proceedings of the Twenty-Second Annual Symposium on Principles of Distributed Computing, pp. 211–220. ACM (2003)

    Google Scholar 

  17. Goldwasser, S., Micali, S., Wigderson, A.: How to play any mental game, or a completeness theorem for protocols with an honest majority. In: Proceedings of the 19th Annual ACM STOC, vol. 87, pp. 218–229 (1987)

    Google Scholar 

  18. Gueta, G.G., et al.: SBFT: a scalable decentralized trust infrastructure for blockchains. arXiv preprint arXiv:1804.01626 (2018)

  19. Katz, J., Koo, C.-Y.: On expected constant-round protocols for Byzantine agreement. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 445–462. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_27

    Chapter  Google Scholar 

  20. King, V., Saia, J.: Breaking the \(O(n^2)\) bit barrier: scalable Byzantine agreement with an adaptive adversary. J. ACM 58(4), 18 (2011)

    Article  MathSciNet  Google Scholar 

  21. Kogias, E.K., Jovanovic, P., Gailly, N., Khoffi, I., Gasser, L., Ford, B.: Enhancing bitcoin security and performance with strong consistency via collective signing. In: 25th USENIX Security Symposium, pp. 279–296. USENIX Association (2016)

    Google Scholar 

  22. Kubiatowicz, J., et al.: OceanStore: an architecture for global-scale persistent storage. ACM Sigplan Not. 35(11), 190–201 (2000)

    Article  Google Scholar 

  23. Lamport, L.: The part-time parliament. ACM Trans. Comput. Syst. 16(2), 133–169 (1998)

    Article  Google Scholar 

  24. Lamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382–401 (1982)

    Article  Google Scholar 

  25. Libert, B., Joye, M., Yung, M.: Born and raised distributively: fully distributed non-interactive adaptively-secure threshold signatures with short shares. Theoret. Comput. Sci. 645, 1–24 (2016)

    Article  MathSciNet  Google Scholar 

  26. Liu, S., Cachin, C., Quéma, V., Vukolic, M.: XFT: practical fault tolerance beyond crashes. In: 12th USENIX Symposium on Operating Systems Design and Implementation, pp. 485–500. USENIX Association (2016)

    Google Scholar 

  27. Loss, J., Moran, T.: Combining asynchronous and synchronous Byzantine agreement: the best of both worlds. Cryptology ePrint Archive 2018/235 (2018)

    Google Scholar 

  28. Micali, S.: ALGORAND: the efficient and democratic ledger. arXiv:1607.01341 (2016)

  29. Pass, R., Shi, E.: Feasibilities and infeasibilities for achieving responsiveness in permissionless consensus. In: International Symposium on Distributed Computing. Springer (2017)

    Google Scholar 

  30. Pass, R., Shi, E.: Thunderella: blockchains with optimistic instant confirmation. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 3–33. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_1

    Chapter  Google Scholar 

  31. Rabin, M.O.: Randomized Byzantine generals. In: Proceedings of the 24th Annual Symposium on Foundations of Computer Science, pp. 403–409. IEEE (1983)

    Google Scholar 

  32. Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45539-6_15

    Chapter  Google Scholar 

  33. Zhou, L., Schneider, F., van Renesse, R.: COCA: a secure distributed online certification authority. ACM Trans. Comput. Syst. 20(4), 329–368 (2002)

    Article  Google Scholar 

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Acknowledgments

We thank Dahlia Malkhi and Benjamin Chan for many useful discussions.

Author information

Authors and Affiliations

  1. VMware Research, Palo Alto, USA

    Ittai Abraham, Kartik Nayak & Ling Ren

  2. MIT, Cambridge, USA

    Srinivas Devadas

  3. Hebrew University of Jerusalem, Jerusalem, Israel

    Danny Dolev

  4. Duke University, Durham, USA

    Kartik Nayak

  5. University of Illinois at Urbana-Champaign, Urbana, USA

    Ling Ren

Authors
  1. Ittai Abraham
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  2. Srinivas Devadas
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  3. Danny Dolev
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  4. Kartik Nayak
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  5. Ling Ren
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Corresponding author

Correspondence to Ling Ren .

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Editors and Affiliations

  1. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada

    Ian Goldberg

  2. Tandy School of Computer Science, University of Tulsa, Tulsa, USA

    Tyler Moore

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Abraham, I., Devadas, S., Dolev, D., Nayak, K., Ren, L. (2019). Synchronous Byzantine Agreement with Expected O(1) Rounds, Expected \(O(n^2)\) Communication, and Optimal Resilience. In: Goldberg, I., Moore, T. (eds) Financial Cryptography and Data Security. FC 2019. Lecture Notes in Computer Science(), vol 11598. Springer, Cham. https://doi.org/10.1007/978-3-030-32101-7_20

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  • DOI: https://doi.org/10.1007/978-3-030-32101-7_20

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