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Published in:
2012 | OriginalPaper | Chapter
Byzantine Agreement with Homonyms in Synchronous Systems
Authors : Carole Delporte-Gallet, Hugues Fauconnier, Hung Tran-The
Published in: Distributed Computing and Networking
Publisher: Springer Berlin Heidelberg
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We consider here the Byzantine agreement problem in synchronous systems with
homonyms
. In this model different processes may have the same authenticated identifier. In such a system of
n
processes sharing a set of
l
identifiers, we define a
distribution of the identifiers
as an integer partition of
n
into
l
parts
n
1
,…,
n
l
giving for each identifier
i
the number of processes having this identifier.
Assuming that the processes know the distribution of identifiers we give a necessary and sufficient condition on the integer partition of
n
to solve the Byzantine agreement with at most
t
Byzantine processes. Moreover we prove that there exists a distribution of
l
identifiers enabling to solve Byzantine agreement with at most
t
Byzantine processes if and only if
$l > \frac{(n-r)t}{n-t-min(t,r)}$
where
$r = n \bmod l $
.
This bound is to be compared with the
l
> 3
t
bound proved in [4] when the processes do not know the distribution of identifiers.