Abstract
Byzantine Agreement (BA) and Broadcast (BC) are considered to be the most fundamental primitives for fault-tolerant distributed computing and cryptographic protocols. An important variant of BA and BC is Asynchronous Byzantine Agreement (ABA) and Asynchronous Broadcast (called as A-cast) respectively. Most often in the literature, protocols for ABA and A-cast were designed for a single bit message. But in many applications, these protocols may be invoked on long message rather than on single bit. Therefore, it is important to design efficient multi-valued protocols (i.e. protocols with long message) which extract advantage of directly dealing with long messages and are far better than multiple invocations to existing protocols for single bit. In synchronous network settings, this line of research was initiated by Turpin and Coan [27] and later it is culminated in the result of Fitzi et al. [15] who presented the first ever communication optimal (i.e. the communication complexity is minimal in asymptotic sense) multi-valued BA and BC protocols with the help of BA and BC protocols for short message. It was left open in [15] to achieve the same in asynchronous settings.
In [21], the authors presented a communication optimal multi-valued A-cast using existing A-cast [6] for small message. Here we achieve the same for ABA which is known to be harder problem than A-cast. Specifically, we design a communication optimal, optimally resilient (allows maximum fault tolerance) multi-valued ABA protocol, based on the existing ABA protocol for short message.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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 (2008)
Beerliová-Trubíniová, Z., Hirt, M.: Perfectly-secure MPC with linear communication complexity. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 213–230. Springer, Heidelberg (2008)
Ben-Or, M.: Another advantage of free choice: Completely asynchronous agreement protocols. In: PODC, pp. 27–30 (1983)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: STOC, pp. 1–10 (1988)
Ben-Or, M., Kelmer, B., Rabin, T.: Asynchronous secure computations with optimal resilience. In: PODC, pp. 183–192 (1994)
Bracha, G.: An asynchronous \(\lfloor (n - 1) / 3 \rfloor\)-resilient consensus protocol. In: PODC, pp. 154–162 (1984)
Canetti, R.: Studies in Secure Multiparty Computation and Applications. PhD thesis, Weizmann Institute, Israel (1995)
Canetti, R., Rabin, T.: Fast asynchronous Byzantine Agreement with optimal resilience. In: STOC, pp. 42–51 (1993)
Carter, L., Wegman, M.N.: Universal classes of hash functions. Journal of Computer and System Sciences 18(4), 143–154 (1979)
Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults. In: STOC, pp. 383–395 (1985)
Feldman, P., Micali, S.: An optimal algorithm for synchronous Byzantine Agreemet. In: STOC, pp. 639–648 (1988)
Feldman, P., Micali, S.: An optimal probabilistic protocol for synchronous Byzantine Agreement. SIAM Journal of Computing 26(4), 873–933 (1997)
Fischer, M.J., Lynch, N.A., Paterson, M.: Impossibility of distributed consensus with one faulty process. JACM 32(2), 374–382 (1985)
Fitzi, M.: Generalized Communication and Security Models in Byzantine Agreement. PhD thesis, ETH Zurich (2002)
Fitzi, M., Hirt, M.: Optimally efficient multi-valued Byzantine Agreement. In: PODC, pp. 163–168 (2006)
Hirt, M., Maurer, U.M., Przydatek, B.: Efficient secure multi-party computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000)
Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)
Patra, A., Choudhary, A., Rabin, T., Rangan, C.P.: The round complexity of verifiable secret sharing revisited. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 487–504. Springer, Heidelberg (2009)
Patra, A., Choudhary, A., Rangan, C.P.: Efficient statistical asynchronous verifiable secret sharing with optimal resilience. In: Kurosawa, K. (ed.) Information Theoretic Security. LNCS, vol. 5973, pp. 74–92. Springer, Heidelberg (2010)
Patra, A., Choudhary, A., Pandu Rangan, C.: Efficient asynchronous Byzantine Agreement with optimal resilience. In: PODC, pp. 92–101 (2009)
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)
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)
Prabhu, B.S., Srinathan, K., Pandu Rangan, C.: Trading players for efficiency in unconditional multiparty computation. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 342–353. Springer, Heidelberg (2003)
Rabin, M.O.: Randomized Byzantine generals. In: FOCS, pp. 403–409 (1983)
Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: STOC, pp. 73–85 (1989)
Turpin, R., Coan, B.A.: Extending binary Byzantine Agreement to multivalued Byzantine Agreement. Information Processing Letters 18(2), 73–76 (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Patra, A., Rangan, C.P. (2011). Communication Optimal Multi-valued Asynchronous Byzantine Agreement with Optimal Resilience. In: Fehr, S. (eds) Information Theoretic Security. ICITS 2011. Lecture Notes in Computer Science, vol 6673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20728-0_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-20728-0_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20727-3
Online ISBN: 978-3-642-20728-0
eBook Packages: Computer ScienceComputer Science (R0)