Bounds on information exchange for Byzantine agreement

  • Authors:

  • Danny Dolev;Rüdiger Reischuk

  • Affiliations:

  • Institute of Mathematics and Computer Science, Hebrew University, Givat Ram, 91904 Jerusalem, Israel and IBM Research Laboratory, San Jose, California;Fakultät Mathematik, Universiät Bielefeld, 4800 Bielefeld 1, West Germany and IBM Research Laboratory, San Jose, California

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1985

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Abstract

Byzantine Agreement has become increasingly important in establishing distributed properties when errors may exist in the systems. Recent polynomial algorithms for reaching Byzantine Agreement provide us with feasible solutions for obtaining coordination and synchronization in distributed systems. In this paper the amount of information exchange necessary to ensure Byzantine Agreement is studied. This is measured by the total number of messages the participating processors have to send in the worst case. In algorithms that use a signature scheme, the number of signatures appended to messages are also counted.First it is shown that &OHgr;(nt) is a lower bound for the number of signatures for any algorithm using authentication, where n denotes the number of processors and t the upper bound on the number of faults the algorithm is supposed to handle. For algorithms that reach Byzantine Agreement without using authentication this is even a lower bound for the total number of messages. If n is large compared to t, these bounds match the upper bounds from previously known algorithms. For the number of messages in the authenticated case we prove the lower bound &OHgr;(n + t2). Finally algorithms that achieve this bound are presented.