Efficient Asynchronous Byzantine Agreement with Optimal Resilience

Byzantine agreement (BA) is considered as one of the most fundamental primitives for fault-tolerant distributed computing and cryptographic protocols. BA among a set of n parties each having an input value, allows them to reach agreement on a common value even if some of the parties are faulty and try to prevent agreement among the non-faulty parties. A preliminary version of this paper appeared in PODC 2009. The work of Arpita Patra is supported by Microsoft Research India PhD fellowship. Arpita Patra would also like to thank ACM and IARCS for financial support to attend PODC 2009 and present a preliminary version of this paper. The work of Ashish Choudhary is supported by Infosys Technology India PhD fellowship. Ashish Choudhary would also like to acknowledge financial support from Project No CSE/O5-06/076/DITX/CPAN on Protocols for Secure Communication and Computation, sponsored by Department of Information Technology, Govt. of India to attend PODC 2009, where a preliminary version of this paper is presented. The work of C. Pandu Rangan is supported by project grants of Project No CSE/O5-06/076/DITX/CPAN on Protocols for Secure Communication and Computation, sponsored by Department of Information Technology, Govt. of India. Arpita Patra Dept. of Computer Science and Engineering IIT Madras, Chennai India 600036 Tel.: +91-44-22575370 E-mail: arpitapatra 10@yahoo.co.in, arpitapatra10@gmail.com Ashish Choudhary Dept. of Computer Science and Engineering IIT Madras, Chennai India 600036 Tel.: +91-44-22575370 E-mail: partho 31@yahoo.co.in, partho31@gmail.com C. Pandu Rangan Dept. of Computer Science and Engineering IIT Madras, Chennai India 600036 Tel.: +91-44-22574358 E-mail: prangan55@yahoo.com, prangan55@gmail.com An important variant of BA is Asynchronous Byzantine Agreement (ABA). An ABA protocol is carried out among n parties in a completely asynchronous network, where every two parties are directly connected by a private channel and t out of the n parties are under the control of a computationally unbounded Byzantine (active) adversary At. The communication complexity of ABA is one of its most important complexity measures. In this paper, we present a simple and efficient ABA protocol whose communication complexity is significantly better than the communication complexity of the existing ABA protocols in the literature. Our protocol is optimally resilient and thus requires n = 3t + 1 parties for its execution. Specifically, the amortized communication complexity of our ABA protocol is O(Cn log 1 ǫ ) bits for attaining agreement on a single bit, where ǫ denotes the probability of non-termination and C denotes the expected running time of our protocol. Conditioned on the event that our ABA protocol terminates, it does so in constant expected time; i.e., C = O(1). We compare our result with most recent optimally resilient, ABA protocols proposed in [17] and [1] and show that our protocol gains by a factor of O(n(log 1 ǫ )) over the ABA of [17] and by a factor of O(n log n log 1 ǫ ) over the ABA of [1]. Towards the designing of our efficient ABA protocol, we first present a novel and simple asynchronous verifiable secret sharing (AVSS) protocol with n = 3t + 1, which significantly improves the communication complexity of the only known AVSS protocol of [17] with n = 3t + 1. Our AVSS shares multiple secrets concurrently and is far better than multiple parallel executions of AVSS sharing single secret. Thus our AVSS brings forth several advantages of concurrently sharing multiple secrets. We believe that our AVSS can be used in