Abstract
This paper presents a new algorithm that reduces multivalued consensus to binary consensus in an asynchronous message-passing system made up of n processes where up to t may commit Byzantine failures. This algorithm has the following noteworthy properties: it assumes t < n/3 (and is consequently optimal from a resilience point of view), uses O(n 2) messages, has a constant time complexity, and does not use signatures. The design of this reduction algorithm relies on two new all-to-all communication abstractions. The first one allows the non-faulty processes to reduce the number of proposed values to c, where c is a small constant. The second communication abstraction allows each non-faulty process to compute a set of (proposed) values such that, if the set of a non-faulty process contains a single value, then this value belongs to the set of any non-faulty process. Both communication abstractions have an O(n 2) message complexity and a constant time complexity. The reduction of multivalued Byzantine consensus to binary Byzantine consensus is then a simple sequential use of these communication abstractions. To the best of our knowledge, this is the first asynchronous message-passing algorithm that reduces multivalued consensus to binary consensus with O(n 2) messages and constant time complexity (measured with the longest causal chain of messages) in the presence of up to t < n/3 Byzantine processes, and without using cryptography techniques. Moreover, this reduction algorithm uses a single instance of the underlying binary consensus, and tolerates message re-ordering by Byzantine processes.
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References
Aguilera, M.K., Frolund, S., Hadzilacos, V., Horn, S., Toueg, S.: Abortable and query-abortable objects and their efficient implementation. In: Proc. 26th Annual ACM Symposium on Principles of Distributed Computing (PODC 2007), pp. 23–32 (2007)
Attiya, H., Welch, J.: Distributed computing: fundamentals, simulations and advanced topics, 2nd edn., p. 414 pages. Wiley Interscience (2004)
Ben-Or, M.: Another advantage of free choice: completely asynchronous agreement protocols. In: Proc. 2nd ACM Symposium on Principles of Distributed Computing (PODC 1983), pp. 27–30. ACM Press (1983)
Bracha, G.: Asynchronous Byzantine agreement protocols. Information & Computation 75(2), 130–143 (1987)
Bracha, G., Toueg, S.: Asynchronous consensus and broadcast protocols. Journal of the ACM 32(4), 824–840 (1985)
Cachin, C., Kursawe, K., Petzold, F., Shoup, V.: Secure and efficient asynchronous broadcast protocols. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 524–541. Springer, Heidelberg (2001)
Correia, M., Ferreira Neves, N., Verissimo, P.: From consensus to atomic broadcast: time-free Byzantine-resistant protocols without signatures. Computer Journal 49(1), 82–96 (2006)
De Prisco, R., Malkhi, D., Reiter, M.: On k-set consensus problems in asynchronous systems. Transactions on Parallel and Distributed Systems 12(1), 7–21 (2001)
Dwork, C., Lynch, N., Stockmeyer, L.: Consensus in the presence of partial synchrony. Journal of the ACM 35(2), 288–323 (1988)
Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. Journal of the ACM 32(2), 374–382 (1985)
Friedman, R., Mostéfaoui, A., Rajsbaum, S., Raynal, M.: Distributed agreement problems and their connection with error-correcting codes. IEEE Transactions on Computers 56(7), 865–875 (2007)
Friedman, R., Mostéfaoui, A., Raynal, M.: \(\Diamond{\cal P}_{mute}\)-based consensus for asynchronous Byzantine systems. Parallel Processing Letters 15(1-2), 162–182 (2005)
Friedman, R., Mostéfaoui, A., Raynal, M.: Simple and efficient oracle-based consensus protocols for asynchronous Byzantine systems. IEEE Transactions on Dependable and Secure Computing 2(1), 46–56 (2005)
Hadzilacos, V., Toueg, S.: On deterministic abortable objects. In: Proc. 32th Annual ACM Symposium on Principles of Distributed Computing (PODC 2013), pp. 4–12 (2013)
Kihlstrom, K.P., Moser, L.E., Melliar-Smith, P.M.: Byzantine fault detectors for solving consensus. The Computer Journal 46(1), 16–35 (2003)
King, V., Saia, J.: Breaking the O(n 2) bit barrier: scalable Byzantine agreement with an adaptive adversary. In: Proc. 30th ACM Symposium on Principles of Distributed Computing (PODC 2011), pp. 420–429. ACM Press (2011)
Lamport, L., Shostack, R., Pease, M.: The Byzantine generals problem. ACM Transactions on Programming Languages and Systems 4(3), 382–401 (1982)
Liang, G., Vaidya, N.: Error-free multi-valued consensus with Byzantine failures. In: Proc. 30th ACM Symposium on Principles of Distributed Computing (PODC 2011), pp. 11–20. ACM Press (2011)
Lynch, N.A.: Distributed algorithms, 872 pages. Morgan Kaufmann Pub., San Francisco (1996)
Martin, J.-P., Alvisi, L.: Fast Byzantine consensus. IEEE Transactions on Dependable and Secure Computing 3(3), 202–215 (2006)
Milosevic, Z., Hutle, M., Schiper, A.: On the reduction of atomic broadcast to consensus with Byzantine faults. In: Proc. 30th IEEE Int’l Symposium on Reliable Distributed Systems (SRDS 2011), pp. 235–244. IEEE Computer Press (2011)
Mostéfaoui, A., Moumen, H., Raynal, M.: Signature-free asynchronous Byzantine consensus with t < n/3 and O(n 2) messages. In: Proc. 33rd Annual ACM Symposium on Principles of Distributed Computing (PODC 2014), pp. 2–9. ACM Press (2014)
Mostéfaoui, A., Rajsbaum, S., Raynal, M.: Conditions on input vectors for consensus solvability in asynchronous distributed systems. Journal of the ACM 50(6), 922–954 (2003)
Mostéfaoui, A., Raynal, M.: Signature-free broadcast-based intrusion tolerance: never decide a Byzantine value. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 143–158. Springer, Heidelberg (2010)
Mostéfaoui, A., Raynal, M.: Asynchronous Byzantine systems: from multivalued to binary consensus with t < n/3, O(n 2) messages, O(1) time, and no signature. Tech Report 2014, 17 pages, IRISA, Université de Rennes (F) (2015), https://hal.inria.fr/hal-01102496
Mostéfaoui, A., Raynal, M., Tronel, F.: From binary consensus to multivalued consensus in asynchronous message-passing systems. Information Processing Letters 73, 207–213 (2000)
Patra, A.: Error-free multi-valued broadcast and Byzantine agreement with optimal communication complexity. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 34–49. Springer, Heidelberg (2011)
Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. Journal of the ACM 27, 228–234 (1980)
Rabin, M.: Randomized Byzantine generals. In: Proc. 24th IEEE Symposium on Foundations of Computer Science (FOCS 1983), pp. 116–124. IEEE Computer Society Press (1983)
Raynal, M.: Communication and agreement abstractions for fault-tolerant asynchronous distributed systems. Morgan & Claypool, 251 pages (2010) ISBN 978-1-60845-293-4
Raynal, M.: Fault-tolerant agreement in synchronous message-passing systems, 165 pages. Morgan & Claypool Publishers (2010) ISBN 978-1-60845-525-6
Raynal, M.: Concurrent programming: algorithms, principles and foundations, 515 pages. Springer (2013)
Toueg, S.: Randomized Byzantine agreement. In: Proc. 3rd Annual ACM Symposium on Principles of Distributed Computing (PODC 1984), pp. 163–178. ACM Press (1984)
Turpin, R., Coan, B.A.: Extending binary Byzantine agreement to multivalued Byzantine agreement. Information Processing Letters 18, 73–76 (1984)
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Mostéfaoui, A., Raynal, M. (2015). Signature-Free Asynchronous Byzantine Systems: From Multivalued to Binary Consensus with t < n/3, O(n 2) Messages, and Constant Time. In: Scheideler, C. (eds) Structural Information and Communication Complexity. SIROCCO 2015. Lecture Notes in Computer Science(), vol 9439. Springer, Cham. https://doi.org/10.1007/978-3-319-25258-2_14
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