Abstract
In a secret sharing scheme (SS), a dealer D distributes a piece of information V i of a secret S to each participant P i . If we desire that ¦V i ¦ < ¦S¦, a nonperfct SS must be used, in which there exists a semi-access set C that has some information on S, but cannot recover S. This paper first presents a general lower bound on ¦V i ¦ which includes the previous lower bounds for perfect SSs and nonperfect SSs as special cases. There exist, however, access hierarchies in which ¦V i ¦ must be larger than the general lower bound, of course. As our second contribution, we determine the optimum size of V i for such a certain access hierarchy.
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© 1995 Springer-Verlag Berlin Heidelberg
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Okada, K., Kurosawa, K. (1995). Lower bound on the size of shares of nonperfect secret sharing schemes. In: Pieprzyk, J., Safavi-Naini, R. (eds) Advances in Cryptology — ASIACRYPT'94. ASIACRYPT 1994. Lecture Notes in Computer Science, vol 917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000422
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DOI: https://doi.org/10.1007/BFb0000422
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