Abstract
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 > 3t bound proved in [4] when the processes do not know the distribution of identifiers.
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Delporte-Gallet, C., Fauconnier, H., Tran-The, H. (2012). Byzantine Agreement with Homonyms in Synchronous Systems. In: Bononi, L., Datta, A.K., Devismes, S., Misra, A. (eds) Distributed Computing and Networking. ICDCN 2012. Lecture Notes in Computer Science, vol 7129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25959-3_6
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DOI: https://doi.org/10.1007/978-3-642-25959-3_6
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