New Construction Methods of Secret Sharing Schemes Based on Authorized Subsets

Abstract

We propose new construction methods of secret sharing schemes realizing general access structures. Our proposed construction methods are perfect secret sharing schemes and include Shamir's (k, n)-threshold schemes as a special case. Furthermore, except for some access structures for which the efficiency is the same as the previous ones, the proposed construction methods are more efficient than Benaloh and Leichter's scheme and the scheme I of TUM05.