Abstract
A threshold scheme is a system that protects a secret (key) among a group of participants in such a way that it can only be reconstructed from the joint information held by some predetermined number of these participants. In this paper we extend this problem to one where there is more than one secret that participants can reconstruct using the information that they hold. In particular we consider the situation where there is a secret s K associated with each k-subset K of participants and s K can be reconstructed by any group of t participants in K (t ≤ k). We establish bounds on the minimum amount of information that participants must hold in order to ensure that up to w participants (0 ≤ w ≤ n − k + t − 1) cannot obtain any information about a secret with which they are not associated. We also discuss examples of systems that satisfy this bound.
This work was supported by the Australian Research Council
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© 1994 Springer-Verlag Berlin Heidelberg
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Jackson, WA., Martin, K.M., O’Keefe, C.M. (1994). Multisecret Threshold Schemes. In: Stinson, D.R. (eds) Advances in Cryptology — CRYPTO’ 93. CRYPTO 1993. Lecture Notes in Computer Science, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48329-2_11
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