**Almost-Surely Terminating Asynchronous Byzantine Agreement Revisited**

*Laasya Bangalore and Ashish Choudhury and Arpita Patra*

**Abstract: **The problem of Byzantine Agreement (BA) is of interest to both distributed computing and cryptography community. Following well-known results from the distributed computing literature, BA problem in the asynchronous network setting encounters inevitable non-termination issues. The impasse is overcome via randomization that allows construction of BA protocols in two flavours of termination guarantee -- with overwhelming probability and with probability one. The latter type termed as almost-surely terminating BAs are the focus of this paper. An eluding problem in the domain of almost-surely terminating BAs is achieving a constant expected running time. Our work makes progress in this direction.

In a setting with $n$ parties and an adversary with unbounded computing power controlling at most $t$ parties in Byzantine fashion, we present two almost-surely terminating BA protocols in the asynchronous setting:

1. With the optimal resilience of $t < \frac{n}{3}$, our first protocol runs for expected ${\cal O}(n)$ time. The existing protocols in the same setting either runs for expected ${\cal O}(n^2)$ time (Abraham et al, PODC 2008) or requires exponential computing power from the honest parties (Wang, CoRR 2015). In terms of communication complexity, our construction outperforms all the known constructions that offer almost-surely terminating feature.

2. With the resilience of $t < \frac{n}{3 + \epsilon}$ for any $\epsilon > 0$, our second protocol runs for expected ${\cal O}(\frac{1}{\epsilon})$ time. The expected running time of our protocol turns constant when $\epsilon$ is a constant fraction. The known constructions with constant expected running time either require $\epsilon$ to be at least $1$ (Feldman-Micali, STOC 1988), implying $t < n/4$, or calls for exponential computing power from the honest parties (Wang, CoRR 2015). We follow the traditional route of building BA via common coin protocol that in turn reduces to asynchronous verifiable secret-sharing (AVSS). Our constructions are built on a variant of AVSS that is termed as shunning. A shunning AVSS fails to offer the properties of AVSS when the corrupt parties strike, but allows the honest parties to locally detect and shun a set of corrupt parties for any future communication. Our shunning AVSS with $t < n/3$ and $t < \frac{n}{3 + \epsilon}$ guarantee $\Omega(n)$ and respectively $\Omega(\epsilon t^2)$ conflicts to be revealed when failure occurs. Turning this shunning AVSS to a common coin protocol efficiently constitutes yet another contribution of our paper.

**Category / Keywords: **

**Original Publication**** (with major differences): **PODC 2018

**Date: **received 30 Apr 2018, last revised 30 Apr 2018

**Contact author: **ashish choudhury at iiitb ac in

**Available format(s): **PDF | BibTeX Citation

**Version: **20180501:121939 (All versions of this report)

**Short URL: **ia.cr/2018/394

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