# Information Security and Cryptography Research Group

## Multi-Valued Byzantine Broadcast: the $t < n$ Case

### Martin Hirt and Pavel Raykov

Advances in Cryptology — ASIACRYPT 2014, Lecture Notes in Computer Science, Springer, vol. 8874, pp. 448–465, Dec 2014.

All known protocols implementing broadcast from synchronous point-to-point channels tolerating any $t < n$ Byzantine corruptions have communication complexity at least $\Omega(\ell n^2)$. We give cryptographically secure and information-theoretically secure protocols for $t < n$ that communicate $O(\ell n)$ bits in order to broadcast sufficiently long $\ell$ bit messages. This matches the optimal communication complexity bound for any protocol allowing to broadcast $\ell$ bit messages. While broadcast protocols with the optimal communication complexity exist in cases where $t < n/3$ (by Liang and Vaidya in PODC '11) or $t < n/2$ (by Fitzi and Hirt in PODC '06), this paper is the first to present such protocols for $t < n$.

## BibTeX Citation

@inproceedings{HirRay14,
author       = {Martin Hirt and Pavel Raykov},
title        = {Multi-Valued Byzantine Broadcast: the $t < n$ Case},
booktitle    = {Advances in Cryptology --- ASIACRYPT 2014},
pages        = {448--465},
series       = {Lecture Notes in Computer Science},
volume       = {8874},
year         = {2014},
month        = {12},
publisher    = {Springer},
}