## Cryptology ePrint Archive: Report 2015/352

Pavel Raykov

Abstract: Byzantine broadcast is a distributed primitive that allows a specific party to consistently distribute a message among $n$ parties in the presence of potential misbehavior of up to $t$ of the parties. The celebrated result of \cite{PSL80} shows that broadcast is achievable from point-to-point channels if and only if $t < n/3$.

The following two generalizations have been proposed to the original broadcast problem. In~\cite{FM98} the authors considered a \emph{general adversary} characterized by the sets of parties that can be corrupted. It was shown that broadcast is achievable from point-to-point channels if and only if no three possible corrupted sets can cover the whole party set. In~\cite{CFFLMM05} the notion of point-to-point channels has been extended to the $b$-minicast channels allowing to locally broadcast among any subset of $b$ parties. It has been shown that broadcast secure against adversaries corrupting up to $t$ parties is achievable from $b$-minicast if and only if $t < \frac{b-1}{b+1}n$.

In this paper we combine both generalizations by considering the problem of achieving broadcast from $b$-minicast channels secure against general adversaries. Our main result is a condition on the possible corrupted sets such that broadcast is achievable from $b$-minicast if and only if this condition holds.

Category / Keywords: cryptographic protocols / Byzantine broadcast

Original Publication (with major differences): ICALP 2015 (Track C)

Date: received 20 Apr 2015, last revised 20 Apr 2015

Contact author: pavelraykov at post tau ac il

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2015/352

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