Abstract
Classical distributed protocols like broadcast or multi-party 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.
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Broadcast withExtendedValidity: 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.
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Broadcast withExtendedConsistency: 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.
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DetectableMulti-PartyComputation: 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.
Partially supported by the Packard Foundation.
Supported by the Swiss National Science Foundation, project no. 2000-066716.01/1.
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Fitzi, M., Hirt, M., Holenstein, T., Wullschleger, J. (2003). Two-Threshold Broadcast and Detectable Multi-party Computation. In: Biham, E. (eds) Advances in Cryptology — EUROCRYPT 2003. EUROCRYPT 2003. Lecture Notes in Computer Science, vol 2656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39200-9_4
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