Abstract
A multi-secret sharing scheme is a protocol to distribute n secrets s 1,..., s n among a set of participants \(\mathcal{P}\) in such a way that: 1) any non-qualified subset of participants \(A \subseteq \mathcal{P}\) has absolutely no information on the secrets; 2) any qualified subset can recover all the secrets, but 3) any non-qualified subset knowing the value of a number of secrets might have some information on other secrets.
In this paper we lay foundations for a general theory of multi-secret sharing schemes by using the entropy approach, as done in [4] and [6] to analyze singlesecret sharing schemes. We prove lower bounds on the size of information held by each participant in any multi-secret sharing scheme. We provide an optimal protocol for multi-secret sharing schemes on a particular access structure, where the access structure specifies the subsets of participants qualified to reconstruct the secret.
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Blundo, C., De Santis, A., Vaccaro, U. (1993). Efficient sharing of many secrets. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_68
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DOI: https://doi.org/10.1007/3-540-56503-5_68
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