Byzantine agreement with homonyms in synchronous systems

• Authors: Carole Delporte-Gallet;Hugues Fauconnier;Hung Tran-The
• Venue: ICDCN'12 Proceedings of the 13th international conference on Distributed Computing and Networking
• Year: 2012

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 n1 ,…, nl 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 l3t bound proved in [4] when the processes do not know the distribution of identifiers.