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Every Bit Counts in Consensus

Authors Pierre Civit, Seth Gilbert, Rachid Guerraoui, Jovan Komatovic, Matteo Monti, Manuel Vidigueira

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Author Details

Pierre Civit
  • Sorbonne University, Paris, France
Seth Gilbert
  • National University of Singapore, Singapore
Rachid Guerraoui
  • Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Jovan Komatovic
  • Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Matteo Monti
  • Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Manuel Vidigueira
  • Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland

Funding

  • Gilbert, Seth: Supported in part by the Singapore MOE Tier 2 grant MOE-T2EP20122-0014.
  • Vidigueira, Manuel: Supported in part by the FNS (#200021_215383).

Cite As Get BibTex

Pierre Civit, Seth Gilbert, Rachid Guerraoui, Jovan Komatovic, Matteo Monti, and Manuel Vidigueira. Every Bit Counts in Consensus. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 13:1-13:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.DISC.2023.13

Abstract

Consensus enables n processes to agree on a common valid L-bit value, despite t < n/3 processes being faulty and acting arbitrarily. A long line of work has been dedicated to improving the worst-case communication complexity of consensus in partial synchrony. This has recently culminated in the worst-case word complexity of O(n²). However, the worst-case bit complexity of the best solution is still O(n²L + n²κ) (where κ is the security parameter), far from the Ω(nL + n²) lower bound. The gap is significant given the practical use of consensus primitives, where values typically consist of batches of large size (L > n).
This paper shows how to narrow the aforementioned gap. Namely, we present a new algorithm, DARE (Disperse, Agree, REtrieve), that improves upon the O(n²L) term via a novel dispersal primitive. DARE achieves O(n^{1.5}L + n^{2.5}κ) bit complexity, an effective √n-factor improvement over the state-of-the-art (when L > nκ). Moreover, we show that employing heavier cryptographic primitives, namely STARK proofs, allows us to devise DARE-Stark, a version of DARE which achieves the near-optimal bit complexity of O(nL + n²poly(κ)). Both DARE and DARE-Stark achieve optimal O(n) worst-case latency.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Byzantine consensus
  • Bit complexity
  • Latency

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References

  1. Michael Abd-El-Malek, Gregory R Ganger, Garth R Goodson, Michael K Reiter, and Jay J Wylie. Fault-scalable byzantine fault-tolerant services. ACM SIGOPS Operating Systems Review, 39(5):59-74, 2005. Google Scholar
  2. Ittai Abraham and Gilad Asharov. Gradecast in synchrony and reliable broadcast in asynchrony with optimal resilience, efficiency, and unconditional security. In Alessia Milani and Philipp Woelfel, editors, PODC '22: ACM Symposium on Principles of Distributed Computing, Salerno, Italy, July 25 - 29, 2022, pages 392-398. ACM, 2022. URL: https://doi.org/10.1145/3519270.3538451.
  3. Ittai Abraham, T-H. Hubert Chan, Danny Dolev, Kartik Nayak, Rafael Pass, Ling Ren, and Elaine Shi. Communication Complexity of Byzantine Agreement, Revisited. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, PODC '19, pages 317-326, New York, NY, USA, 2019. Association for Computing Machinery. URL: https://doi.org/10.1145/3293611.3331629.
  4. Ittai Abraham, Dahlia Malkhi, Kartik Nayak, Ling Ren, and Alexander Spiegelman. Solida: A blockchain protocol based on reconfigurable byzantine consensus. arXiv preprint arXiv:1612.02916, 2016. Google Scholar
  5. Ittai Abraham, Dahlia Malkhi, Kartik Nayak, Ling Ren, and Alexander Spiegelman. Solidus: An incentive-compatible cryptocurrency based on permissionless byzantine consensus. CoRR, abs/1612.02916, 2016. Google Scholar
  6. Ittai Abraham, Dahlia Malkhi, and Alexander Spiegelman. Asymptotically Optimal Validated Asynchronous Byzantine Agreement. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing (PODC), pages 337-346, 2019. Google Scholar
  7. Ittai Abraham, Dahlia Malkhi, and Alexander Spiegelman. Asymptotically Optimal Validated Asynchronous Byzantine Agreement. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, pages 337-346, 2019. Google Scholar
  8. Atul Adya, William J Bolosky, Miguel Castro, Gerald Cermak, Ronnie Chaiken, John R Douceur, Jon Howell, Jacob R Lorch, Marvin Theimer, and Roger P Wattenhofer. Farsite: Federated, available, and reliable storage for an incompletely trusted environment. ACM SIGOPS Operating Systems Review, 36(SI):1-14, 2002. Google Scholar
  9. Nicolas Alhaddad, Sourav Das, Sisi Duan, Ling Ren, Mayank Varia, Zhuolun Xiang, and Haibin Zhang. Brief announcement: Asynchronous verifiable information dispersal with near-optimal communication. In Alessia Milani and Philipp Woelfel, editors, PODC '22: ACM Symposium on Principles of Distributed Computing, Salerno, Italy, July 25 - 29, 2022, pages 418-420. ACM, 2022. URL: https://doi.org/10.1145/3519270.3538476.
  10. Nicolas Alhaddad, Sisi Duan, Mayank Varia, and Haibin Zhang. Succinct Erasure Coding Proof Systems. Cryptology ePrint Archive, 2021. Google Scholar
  11. Yair Amir, Claudiu Danilov, Jonathan Kirsch, John Lane, Danny Dolev, Cristina Nita-Rotaru, Josh Olsen, and David Zage. Scaling byzantine fault-tolerant replication towide area networks. In International Conference on Dependable Systems and Networks (DSN'06), pages 105-114. IEEE, 2006. Google Scholar
  12. Elli Androulaki, Christian Cachin, Dan Dobre, and Marko Vukolic. Erasure-coded byzantine storage with separate metadata. In Marcos K. Aguilera, Leonardo Querzoni, and Marc Shapiro, editors, Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Cortina d'Ampezzo, Italy, December 16-19, 2014. Proceedings, volume 8878 of Lecture Notes in Computer Science, pages 76-90. Springer, 2014. URL: https://doi.org/10.1007/978-3-319-14472-6_6.
  13. Mihir Bellare and Phillip Rogaway. Random oracles are practical: A paradigm for designing efficient protocols. In Proceedings of the 1st ACM Conference on Computer and Communications Security, pages 62-73, 1993. Google Scholar
  14. Michael Ben-Or, Ran Canetti, and Oded Goldreich. Asynchronous Secure Computation. In Proceedings of the twenty-fifth annual ACM symposium on Theory of computing, pages 52-61, 1993. Google Scholar
  15. Michael Ben-Or, Boaz Kelmer, and Tal Rabin. Asynchronous Secure Computations with Optimal Resilience. In Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing, pages 183-192, 1994. Google Scholar
  16. Eli Ben-Sasson, Iddo Bentov, Yinon Horesh, and Michael Riabzev. Scalable, transparent, and post-quantum secure computational integrity. Cryptology ePrint Archive, 2018. Google Scholar
  17. Alysson Bessani, João Sousa, and Eduardo EP Alchieri. State Machine Replication for the Masses with BFT-SMART. In 2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, pages 355-362. IEEE, 2014. Google Scholar
  18. Amey Bhangale, Chen-Da Liu-Zhang, Julian Loss, and Kartik Nayak. Efficient adaptively-secure byzantine agreement for long messages. In Shweta Agrawal and Dongdai Lin, editors, 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, volume 13791 of Lecture Notes in Computer Science, pages 504-525. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-22963-3_17.
  19. Richard E Blahut. Theory and practice of error control codes, volume 126. Addison-Wesley Reading, 1983. Google Scholar
  20. Manuel Bravo, Gregory Chockler, and Alexey Gotsman. Making Byzantine Consensus Live. In 34th International Symposium on Distributed Computing (DISC), volume 179, pages 1-17, 2020. Google Scholar
  21. Manuel Bravo, Gregory V. Chockler, and Alexey Gotsman. Making byzantine consensus live. Distributed Comput., 35(6):503-532, 2022. URL: https://doi.org/10.1007/s00446-022-00432-y.
  22. Ethan Buchman. Tendermint: Byzantine fault tolerance in the age of blockchains. PhD thesis, University of Guelph, 2016. Google Scholar
  23. Ethan Buchman, Jae Kwon, and Zarko Milosevic. The latest gossip on BFT consensus. arXiv preprint arXiv:1807.04938, pages 1-14, 2018. URL: https://arxiv.org/abs/1807.04938.
  24. Christian Cachin, Rachid Guerraoui, and Luís E. T. Rodrigues. Introduction to Reliable and Secure Distributed Programming (2. ed.). Springer, 2011. URL: https://doi.org/10.1007/978-3-642-15260-3.
  25. Christian Cachin, Klaus Kursawe, Frank Petzold, and Victor Shoup. Secure and Efficient Asynchronous Broadcast Protocols. In Joe Kilian, editor, Advances in Cryptology - CRYPTO 2001, 21st Annual International Cryptology Conference, Santa Barbara, California, USA, August 19-23, 2001, Proceedings, volume 2139 of Lecture Notes in Computer Science, pages 524-541. Springer, 2001. URL: https://doi.org/10.1007/3-540-44647-8_31.
  26. Christian Cachin and Stefano Tessaro. Asynchronous Verifiable Information Dispersal. In 24th IEEE Symposium on Reliable Distributed Systems (SRDS'05), pages 191-201. IEEE, 2005. Google Scholar
  27. Martina Camaioni, Rachid Guerraoui, Matteo Monti, Pierre-Louis Roman, Manuel Vidigueira, and Gauthier Voron. Chop chop: Byzantine atomic broadcast to the network limit. arXiv preprint arXiv:2304.07081, 2023. Google Scholar
  28. Jan Camenisch, Manu Drijvers, Timo Hanke, Yvonne Anne Pignolet, Victor Shoup, and Dominic Williams. Internet Computer Consensus. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, 2021:81-91, 2022. URL: https://doi.org/10.1145/3519270.3538430.
  29. Miguel Castro and Barbara Liskov. Practical byzantine fault tolerance and proactive recovery. ACM Transactions on Computer Systems (TOCS), 20(4):398-461, 2002. Google Scholar
  30. Miguel Castro and Barbara Liskov. Practical byzantine fault tolerance and proactive recovery. ACM Transactions on Computer Systems (TOCS), 20(4):398-461, 2002. Google Scholar
  31. Dario Catalano and Dario Fiore. Vector Commitments and Their Applications. In Public-Key Cryptography-PKC 2013: 16th International Conference on Practice and Theory in Public-Key Cryptography, Nara, Japan, February 26-March 1, 2013. Proceedings 16, pages 55-72. Springer, 2013. Google Scholar
  32. Jing Chen and Silvio Micali. Algorand. arXiv preprint arXiv:1607.01341, 2016. Google Scholar
  33. Jinyuan Chen. Fundamental limits of byzantine agreement. CoRR, abs/2009.10965, 2020. URL: https://arxiv.org/abs/2009.10965.
  34. Jinyuan Chen. Optimal error-free multi-valued byzantine agreement. In Seth Gilbert, editor, 35th International Symposium on Distributed Computing, DISC 2021, October 4-8, 2021, Freiburg, Germany (Virtual Conference), 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.
  35. Ashish Choudhury and Arpita Patra. On the communication efficiency of statistically secure asynchronous MPC with optimal resilience. J. Cryptol., 36(2):13, 2023. URL: https://doi.org/10.1007/s00145-023-09451-9.
  36. Pierre Civit, Muhammad Ayaz Dzulfikar, Seth Gilbert, Vincent Gramoli, Rachid Guerraoui, Jovan Komatovic, and Manuel Vidigueira. Byzantine Consensus Is Θ(n²): The Dolev-Reischuk Bound Is Tight Even in Partial Synchrony! In Christian Scheideler, editor, 36th International Symposium on Distributed Computing, DISC 2022, October 25-27, 2022, Augusta, Georgia, USA, volume 246 of LIPIcs, pages 14:1-14:21. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.DISC.2022.14.
  37. Pierre Civit, Seth Gilbert, Rachid Guerraoui, Jovan Komatovic, Matteo Monti, and Manuel Vidigueira. Every Bit Counts in Consensus. arXiv preprint arXiv:2306.00431, 2023. Google Scholar
  38. Pierre Civit, Seth Gilbert, Rachid Guerraoui, Jovan Komatovic, and Manuel Vidigueira. On the Validity of Consensus. To appear in PODC 2023, abs/2301.04920, 2023. URL: https://doi.org/10.48550/arXiv.2301.04920.
  39. Miguel Correia. From byzantine consensus to blockchain consensus. In Essentials of Blockchain Technology, pages 41-80. Chapman and Hall/CRC, 2019. Google Scholar
  40. Miguel Correia, Nuno Ferreira Neves, and Paulo Veríssimo. From Consensus to Atomic Broadcast: Time-Free Byzantine-Resistant Protocols without Signatures. The Computer Journal, 49(1):82-96, 2006. Google Scholar
  41. Tyler Crain, Vincent Gramoli, Mikel Larrea, and Michel Raynal. Dbft: Efficient leaderless byzantine consensus and its application to blockchains. In 2018 IEEE 17th International Symposium on Network Computing and Applications (NCA), pages 1-8. IEEE, 2018. Google Scholar
  42. George Danezis, Lefteris Kokoris-Kogias, Alberto Sonnino, and Alexander Spiegelman. Narwhal and tusk: a dag-based mempool and efficient bft consensus. In Proceedings of the Seventeenth European Conference on Computer Systems, pages 34-50, 2022. Google Scholar
  43. Sourav Das, Vinith Krishnan, Irene Miriam Isaac, and Ling Ren. Spurt: Scalable distributed randomness beacon with transparent setup. In 43rd IEEE Symposium on Security and Privacy, SP 2022, San Francisco, CA, USA, May 22-26, 2022, pages 2502-2517. IEEE, 2022. URL: https://doi.org/10.1109/SP46214.2022.9833580.
  44. Sourav Das, Zhuolun Xiang, and Ling Ren. Asynchronous Data Dissemination and its Applications. In Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, pages 2705-2721, 2021. Google Scholar
  45. Sourav Das, Thomas Yurek, Zhuolun Xiang, Andrew Miller, Lefteris Kokoris-Kogias, and Ling Ren. Practical asynchronous distributed key generation. In 43rd IEEE Symposium on Security and Privacy, SP 2022, San Francisco, CA, USA, May 22-26, 2022, pages 2518-2534. IEEE, 2022. URL: https://doi.org/10.1109/SP46214.2022.9833584.
  46. Christian Decker, Jochen Seidel, and Roger Wattenhofer. Bitcoin Meets Strong Consistency. In Proceedings of the 17th International Conference on Distributed Computing and Networking, pages 1-10, 2016. Google Scholar
  47. Dan Dobre, Ghassan O. Karame, Wenting Li, Matthias Majuntke, Neeraj Suri, and Marko Vukolic. Proofs of writing for robust storage. IEEE Trans. Parallel Distributed Syst., 30(11):2547-2566, 2019. URL: https://doi.org/10.1109/TPDS.2019.2919285.
  48. Danny Dolev and Rüdiger Reischuk. Bounds on information exchange for Byzantine agreement. Journal of the ACM (JACM), 1985. Google Scholar
  49. Assia Doudou and André Schiper. Muteness Detectors for Consensus with Byzantine Processes. In Brian A. Coan and Yehuda Afek, editors, Proceedings of the Seventeenth Annual ACM Symposium on Principles of Distributed Computing, PODC '98, Puerto Vallarta, Mexico, June 28 - July 2, 1998, page 315. ACM, 1998. URL: https://doi.org/10.1145/277697.277772.
  50. Sisi Duan, Xin Wang, and Haibin Zhang. Practical Signature-Free Asynchronous Common Subset in Constant Time. Cryptology ePrint Archive, 2023. Google Scholar
  51. Sisi Duan, Haibin Zhang, and Boxin Zhao. Waterbear: Information-theoretic asynchronous BFT made practical. IACR Cryptol. ePrint Arch., page 21, 2022. URL: https://eprint.iacr.org/2022/021.
  52. Cynthia Dwork, Lynch Nancy, and Larry Stockmeyer. Consensus in the Presence of Partial Synchrony. Journal of the ACM (JACM), 35(2):288-323, 1988. Google Scholar
  53. Facebook. Winterfell: A STARK prover and verifier for arbitrary computations. URL: https://github.com/facebook/winterfell#Performance.
  54. Michael J. Fischer, Nancy A. Lynch, and Michael S. Paterson. Impossibility of Distributed Consensus with One Faulty Process. Journal of the Association for Computing Machinery,, 32(2):374-382, 1985. Google Scholar
  55. Adam Ga̧gol, Damian Leśniak, Damian Straszak, and Michał Świȩtek. ALEPH: Efficient atomic broadcast in asynchronous networks with Byzantine nodes. AFT 2019 - Proceedings of the 1st ACM Conference on Advances in Financial Technologies, pages 214-228, 2019. URL: https://doi.org/10.1145/3318041.3355467.
  56. Chaya Ganesh and Arpita Patra. Broadcast extensions with optimal communication and round complexity. In George Giakkoupis, editor, Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC 2016, Chicago, IL, USA, July 25-28, 2016, pages 371-380. ACM, 2016. URL: https://doi.org/10.1145/2933057.2933082.
  57. Chaya Ganesh and Arpita Patra. Optimal extension protocols for byzantine broadcast and agreement. IACR Cryptol. ePrint Arch., page 63, 2017. URL: http://eprint.iacr.org/2017/063.
  58. 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.
  59. James Hendricks, Gregory R. Ganger, and Michael K. Reiter. Low-overhead byzantine fault-tolerant storage. In Thomas C. Bressoud and M. Frans Kaashoek, editors, Proceedings of the 21st ACM Symposium on Operating Systems Principles 2007, SOSP 2007, Stevenson, Washington, USA, October 14-17, 2007, pages 73-86. ACM, 2007. URL: https://doi.org/10.1145/1294261.1294269.
  60. James Hendricks, Gregory R. Ganger, and Michael K. Reiter. Verifying distributed erasure-coded data. In Indranil Gupta and Roger Wattenhofer, editors, Proceedings of the Twenty-Sixth Annual ACM Symposium on Principles of Distributed Computing, PODC 2007, Portland, Oregon, USA, August 12-15, 2007, pages 139-146. ACM, 2007. URL: https://doi.org/10.1145/1281100.1281122.
  61. Ioannis Kaklamanis, Lei Yang, and Mohammad Alizadeh. Poster: Coded broadcast for scalable leader-based bft consensus. In Proceedings of the 2022 ACM SIGSAC Conference on Computer and Communications Security, pages 3375-3377, 2022. Google Scholar
  62. Idit Keidar, Eleftherios Kokoris-Kogias, Oded Naor, and Alexander Spiegelman. All you need is DAG. In Avery Miller, Keren Censor-Hillel, and Janne H. Korhonen, editors, PODC '21: ACM Symposium on Principles of Distributed Computing, Virtual Event, Italy, July 26-30, 2021, pages 165-175. ACM, 2021. URL: https://doi.org/10.1145/3465084.3467905.
  63. Ramakrishna Kotla, Lorenzo Alvisi, Mike Dahlin, Allen Clement, and Edmund Wong. Zyzzyva: speculative byzantine fault tolerance. In Proceedings of twenty-first ACM SIGOPS symposium on Operating systems principles, pages 45-58, 2007. Google Scholar
  64. Ramakrishna Kotla and Michael Dahlin. High throughput byzantine fault tolerance. In International Conference on Dependable Systems and Networks, 2004, pages 575-584. IEEE, 2004. Google Scholar
  65. Leslie Lamport, Robert Shostak, and Marshall Pease. The Byzantine Generals Problem. ACM Trans. Program. Lang. Syst., 4(3):382-401, 1982. Google Scholar
  66. Andrew Lewis-Pye. Quadratic worst-case message complexity for State Machine Replication in the partial synchrony model, 2022. URL: https://doi.org/10.48550/ARXIV.2201.01107.
  67. Fan Li and Jinyuan Chen. Communication-efficient signature-free asynchronous byzantine agreement. In IEEE International Symposium on Information Theory, ISIT 2021, Melbourne, Australia, July 12-20, 2021, pages 2864-2869. IEEE, 2021. URL: https://doi.org/10.1109/ISIT45174.2021.9518010.
  68. Benoît Libert, Marc Joye, and Moti Yung. Born and Raised Distributively: Fully Distributed Non-Interactive Adaptively-Secure Threshold Signatures with Short Shares. Theoretical Computer Science, 645:1-24, 2016. Google Scholar
  69. Yuan Lu, Zhenliang Lu, Qiang Tang, and Guiling Wang. Dumbo-MVBA: Optimal Multi-Valued Validated Asynchronous Byzantine Agreement, Revisited. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, pages 129-138, 2020. Google Scholar
  70. Loi Luu, Viswesh Narayanan, Kunal Baweja, Chaodong Zheng, Seth Gilbert, and Prateek Saxena. Scp: A computationally-scalable byzantine consensus protocol for blockchains. Cryptology ePrint Archive, 2015. Google Scholar
  71. Dahlia Malkhi, Kartik Nayak, and Ling Ren. Flexible byzantine fault tolerance. In Proceedings of the 2019 ACM SIGSAC conference on computer and communications security, pages 1041-1053, 2019. Google Scholar
  72. Ralph C. Merkle. A Digital Signature Based on a Conventional Encryption Function. In Advances in Cryptology - CRYPTO, 1987. Google Scholar
  73. Andrew Miller, Yu Xia, Kyle Croman, Elaine Shi, and Dawn Song. The honey badger of bft protocols. In Proceedings of the 2016 ACM SIGSAC conference on computer and communications security, pages 31-42, 2016. Google Scholar
  74. Atsuki Momose and Ling Ren. Multi-threshold byzantine fault tolerance. In Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, pages 1686-1699, 2021. Google Scholar
  75. Atsuki Momose and Ling Ren. Optimal Communication Complexity of Authenticated Byzantine Agreement. In 35th International Symposium on Distributed Computing (DISC), volume 209, pages 32:1-32:0. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany, 2021. Google Scholar
  76. Achour Mostéfaoui, Hamouma Moumen, and Michel Raynal. Signature-Free Asynchronous Binary Byzantine Consensus with t less n/3, O(n2) Messages, and O(1) Expected Time. J. ACM, 62(4):31:1-31:21, 2015. URL: https://doi.org/10.1145/2785953.
  77. Satoshi Nakamoto. Bitcoin: A peer-to-peer electronic cash system. Decentralized business review, page 21260, 2008. Google Scholar
  78. Oded Naor and Idit Keidar. Expected Linear Round Synchronization: The Missing Link for Linear Byzantine SMR. 34th International Symposium on Distributed Computing (DISC), 179, 2020. Google Scholar
  79. Kartik Nayak, Ling Ren, Elaine Shi, Nitin H. Vaidya, and Zhuolun Xiang. Improved extension protocols for byzantine broadcast and agreement. In Hagit Attiya, editor, 34th International Symposium on Distributed Computing, DISC 2020, October 12-16, 2020, Virtual Conference, 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.
  80. Nuno Ferreira Neves, Miguel Correia, and Paulo Verissimo. Solving Vector Consensus with a Wormhole. IEEE Transactions on Parallel and Distributed Systems, 16(12):1120-1131, 2005. Google Scholar
  81. Irving S Reed and Gustave Solomon. Polynomial codes over certain finite fields. Journal of the society for industrial and applied mathematics, 8(2):300-304, 1960. Google Scholar
  82. Irving S Reed and Gustave Solomon. Polynomial odes over certain finite fields. Journal of the society for industrial and applied mathematics, 8(2):300-304, 1960. Google Scholar
  83. Victor Shoup. Practical Threshold Signatures. In Bart Preneel, editor, Advances in Cryptology - EUROCRYPT 2000, International Conference on the Theory and Application of Cryptographic Techniques, Bruges, Belgium, May 14-18, 2000, Proceeding, volume 1807 of Lecture Notes in Computer Science, pages 207-220. Springer, 2000. URL: https://doi.org/10.1007/3-540-45539-6_15.
  84. Victor Shoup and Nigel P Smart. Lightweight asynchronous verifiable secret sharing with optimal resilience. Cryptology ePrint Archive, 2023. Google Scholar
  85. Alexander Spiegelman. In Search for an Optimal Authenticated Byzantine Agreement. In Seth Gilbert, editor, 35th International Symposium on Distributed Computing (DISC 2021), volume 209 of Leibniz International Proceedings in Informatics (LIPIcs), pages 38:1-38:19, Dagstuhl, Germany, 2021. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.DISC.2021.38.
  86. Alexander Spiegelman, Neil Giridharan, Alberto Sonnino, and Lefteris Kokoris-Kogias. Bullshark: Dag bft protocols made practical. In Proceedings of the 2022 ACM SIGSAC Conference on Computer and Communications Security, pages 2705-2718, 2022. Google Scholar
  87. Giuliana Santos Veronese, Miguel Correia, Alysson Neves Bessani, Lau Cheuk Lung, and Paulo Verissimo. Efficient byzantine fault-tolerance. IEEE Transactions on Computers, 62(1):16-30, 2011. Google Scholar
  88. Gavin Wood et al. Ethereum: A secure decentralised generalised transaction ledger. Ethereum project yellow paper, 151(2014):1-32, 2014. Google Scholar
  89. Maofan Yin, Dahlia Malkhi, Michael K. Reiter, Guy Golan Gueta, and Ittai Abraham. HotStuff: BFT Consensus with Linearity and Responsiveness. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, pages 347-356, 2019. Google Scholar
  90. Thomas Yurek, Licheng Luo, Jaiden Fairoze, Aniket Kate, and Andrew Miller. hbacss: How to robustly share many secrets. In 29th Annual Network and Distributed System Security Symposium, NDSS 2022, San Diego, California, USA, April 24-28, 2022. The Internet Society, 2022. URL: https://www.ndss-symposium.org/ndss-paper/auto-draft-245/.
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