Abstract
A multisecret threshold scheme is a system that protects a number of secrets (or keys) among a group of participants, as follows. Given a set of n participants, there is a secret s K associated with each k–subset K of these participants. The scheme ensures that s K can be reconstructed by any group of t participants in K (\(1 < t < k\)). A lower bound has been established on the amount of information that participants must hold in order to ensure that any set of up to w participants \((0 \leqslant w \leqslant n - k + t - 1)\) cannot obtain any information about a secret with which they are not associated. In this paper, for parameters t=2 and w=n-k+t-1, we give a construction for multisecret threshold schemes that satisfy this bound.
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Jackson, WA., Martin, K.M. & O'Keefe, C.M. A Construction for Multisecret Threshold Schemes. Designs, Codes and Cryptography 9, 287–303 (1996). https://doi.org/10.1023/A:1027380522085
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DOI: https://doi.org/10.1023/A:1027380522085