Two-threshold broadcast and detectable multi-party computation

  • Authors:

  • Matthias Fitzi;Martin Hirt;Thomas Holenstein;Jürg Wullschleger

  • Affiliations:

  • University of California, Davis;ETH Zurich, Switzerland;ETH Zurich, Switzerland;ETH Zurich, Switzerland

  • Venue:
  • EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
  • Year:
  • 2003

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Abstract

Classical distributed protocols like broadcast or multiparty computation provide security as long as the number of malicious players f is bounded by some given threshold t, i.e., f ≤ t. If f exceeds t then these protocols are completely insecure. We relax this binary concept to the notion of two-threshold security: Such protocols guarantee full security as long as f ≤ t for some small threshold t, and still provide some degraded security when t f ≤ T for a larger threshold T. In particular, we propose the following problems. • Broadcast with Extended Validity: Standard broadcast is achieved when f ≤ t. When t f ≤ T, then either broadcast is achieved, or every player learns that there are too many faults. Furthermore, when the sender is honest, then broadcast is always achieved. • Broadcast with Extended Consistency: Standard broadcast is achieved when f ≤ t. When t f ≤ T, then either broadcast is achieved, or every player learns that there are too many faults. Furthermore, the players agree on whether or not broadcast is achieved. • Detectable Multi-Party Computation: Secure computation is achieved when f ≤ t. When t f ≤ T, then either the computation is secure, or all players detect that there are too many faults and abort. The above protocols for n players exist if and only if t = 0 or t+2T n.