Abstract
In this paper we present first ever error-free, asynchronous broadcast (called as A-cast) and Byzantine Agreement (called as ABA) protocols with optimal communication complexity and fault tolerance. Our protocols are multi-valued, meaning that they deal with ℓ bit input and achieve communication complexity of \({\mathcal O}(n\ell)\) bits for large enough ℓ for a set of n ≥ 3t + 1 parties in which at most t can be Byzantine corrupted. Previously, Patra and Rangan (Latincrypt’10, ICITS’11) reported multi-valued, communication optimal A-cast and ABA protocols that are only probabilistically correct.
Following all the previous works on multi-valued protocols, we too follow reduction-based approach for our protocols, meaning that our protocols are designed given existing A-cast and ABA protocols for small message (possibly for single bit). Our reductions invoke less or equal number of instances of protocols for single bit in comparison to the reductions of Patra and Rangan. Furthermore, our reductions run in constant expected time, in contrast to \({\mathcal O}(n)\) of Patra and Rangan (ICITS’11). Also our reductions are much simpler and more elegant than their reductions.
By adapting our techniques from asynchronous settings, we present new error-free, communication optimal reduction-based protocols for broadcast (BC) and Byzantine Agreement (BA) in synchronous settings that are constant-round and call for only \(\mathcal O(n^2)\) instances of protocols for single bit. Prior to this, communication optimality has been achieved by Fitzi and Hirt (PODC’06) who proposed probabilistically correct multi-valued BC and BA protocols with constant-round and \({\mathcal O}(n(n+\kappa))\) (κ is the error parameter) invocations to the single bit protocols. Recently, Liang and Vaidya (PODC’11) achieved the same without error probability. However, their reduction calls for round complexity and number of instances that are function of the message size, \({\mathcal O}(\sqrt{\ell} + n^2)\) and \({\mathcal O}(n^2\sqrt{\ell} + n^4)\), respectively where ℓ = Ω(n 6).
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References
Abraham, I., Dolev, D., Halpern, J.Y.: An almost-surely terminating polynomial protocol for asynchronous Byzantine Agreement with optimal resilience. In: PODC, pp. 405–414. ACM Press (2008)
Berman, P., Garay, G.A., Perry, K.J.: Bit optimal distributed consensus. Computer Science Research (2009)
BenOr, M., Kelmer, B., Rabin, T.: Asynchronous secure computations with optimal resilience. In: PODC, pp. 183–192. ACM Press (1994)
Ben-Or, M.: Another advantage of free choice: Completely asynchronous agreement protocols. In: PODC, pp. 27–30. ACM Press (1983)
Ben-Or, M., Canetti, R., Goldreich, O.: Asynchronous Secure Computation. In: STOC, pp. 52–61. ACM Press (1993)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: STOC, pp. 1–10. ACM Press (1988)
Bracha, G.: An asynchronous \(\lfloor (n - 1) / 3 \rfloor\)-resilient consensus protocol. In: PODC, pp. 154–162. ACM Press (1984)
Beerliová-Trubíniová, Z., Hirt, M.: Efficient Multi-Party Computation with Dispute Control. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 305–328. Springer, Heidelberg (2006)
Canetti, R.: Studies in Secure Multiparty Computation and Applications. PhD thesis, Weizmann Institute, Israel (1995)
Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults (extended abstract). In: STOC, pp. 383–395. ACM Press (1985)
Canetti, R., Rabin, T.: Fast asynchronous Byzantine Agreement with optimal resilience. In: STOC, pp. 42–51. ACM Press (1993)
Coan, B.A., Welch, J.L.: Modular construction of a Byzantine Agreement protocol with optimal message bit complexity. Information and Computation 97(1), 61–85 (1992)
Dolev, D., Reischuk, R.: Bounds on information exchange for Byzantine Agreement. JACM 32(1), 191–204 (1985)
Fitzi, M., Hirt, M.: Optimally Efficient Multi-valued Byzantine Agreement. In: PODC, pp. 163–168 (2006)
Fischer, M.J., Lynch, N.A., Paterson, M.: Impossibility of distributed consensus with one faulty process. JACM 32(2), 374–382 (1985)
Feldman, P., Micali, S.: An Optimal Algorithm for Synchronous Byzantine Agreemet. In: STOC, pp. 639–648. ACM Press (1988)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman (1979)
Hirt, M., Maurer, U., Przydatek, B.: Efficient Secure Multi-party Computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000)
Liang, G., Vaidya, N.H.: Error-Free Multi-Valued Consensus with Byzantine Failures. In: PODC, pp. 11–20. ACM Press (2011)
Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann (1996)
Patra, A., Rangan, C.P.: Communication Optimal Multi-Valued Asynchronous Broadcast Protocol. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol. 6212, pp. 162–177. Springer, Heidelberg (2010)
Patra, A., Rangan, C.P.: Communication Optimal Multi-Valued Asynchronous Byzantine Agreement with Optimal Resilience. In: Fehr, S. (ed.) ICITS 2011. LNCS, vol. 6673, pp. 206–226. Springer, Heidelberg (2011)
Pease, M., Shostak, R.E., Lamport, L.: Reaching agreement in the presence of faults. JACM 27(2), 228–234 (1980)
Pfitzmann, B., Waidner, M.: Unconditional Byzantine Agreement for Any Number of Faulty Processors. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 339–350. Springer, Heidelberg (1992)
Rabin, M.O.: Randomized Byzantine generals. In: FOCS, pp. 403–409. IEEE Computer Society (1983)
Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority (extended abstract). In: STOC, pp. 73–85. ACM Press (1989)
Turpin, R., Coan, B.A.: Extending binary Byzantine Agreement to multivalued Byzantine Agreement. IPL 18(2), 73–76 (1984)
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Patra, A. (2011). Error-free Multi-valued Broadcast and Byzantine Agreement with Optimal Communication Complexity. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_4
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