Discovering network topology in the presence of byzantine faults

  • Authors:
  • Mikhail Nesterenko;Sébastien Tixeuil

  • Affiliations:
  • Computer Science Department, Kent State University, Kent, OH;LRI-CNRS UMR 8623 & INRIA Grand Large, Universitéé Paris Sud, France

  • Venue:
  • SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
  • Year:
  • 2006

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Abstract

We study the problem of Byzantine-robust topology discovery in an arbitrary asynchronous network. We formally state the weak and strong versions of the problem. The weak version requires that either each node discovers the topology of the network or at least one node detects the presence of a faulty node. The strong version requires that each node discovers the topology regardless of faults We focus on non-cryptographic solutions to these problems. We explore their bounds. We prove that the weak topology discovery problem is solvable only if the connectivity of the network exceeds the number of faults in the system. Similarly, we show that the strong version of the problem is solvable only if the network connectivity is more than twice the number of faults We present solutions to both versions of the problem. Our solutions match the established graph connectivity bounds. The programs are terminating, they do not require the individual nodes to know either the diameter or the size of the network. The message complexity of both programs is low polynomial with respect to the network size