Proceedings of CRYPTO 84 on Advances in cryptology
Nonperfect secret sharing schemes and matroids
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Communications of the ACM
Lower Bound on the Size of Shares of Nonperfect Secret Sharing Schemes
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
A Strong Ramp Secret Sharing Scheme Using Matrix Projection
WOWMOM '06 Proceedings of the 2006 International Symposium on on World of Wireless, Mobile and Multimedia Networks
Strongly secure ramp secret sharing schemes for general access structures
Information Processing Letters
Secret-sharing schemes: a survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
IEEE Transactions on Information Theory
Secret Sharing and Non-Shannon Information Inequalities
IEEE Transactions on Information Theory
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An important issue of threshold secret sharing (TSS) schemes is to minimize the size of shares. This issue is resolved for the simpler classes called (k,n)-TSS and (k,L,n)-threshold ramp secret sharing (TRSS). That is, for each of these two classes, an optimum construction which minimizes the share size was presented. The goal of this paper is to develop an optimum construction for a more general threshold class where the mutual information between the secret and a set of shares is defined by a discrete function which monotonically increases from zero to one with the number of shares. A tight lower bound of the entropy of shares is first derived and then an optimum construction is presented. The derived lower bound is larger than the previous one except for special functions such as convex and concave functions. The optimum construction encodes the secret by using one or more optimum TRSS schemes independently. The optimality is shown by devising a combination of TRSS schemes which achieves the new lower bound.