Some Basic Properties of General Nonperfect Secret Sharing Schemes

Nonperfect secret sharing schemes (NSSs) have an advantage such that the size of shares can be shorter than that of perfect secret sharing schemes. This paper shows some basic properties of general NSS. First, we present a necessary and sufficient condition on the existence of an NSS. Next, we show two bounds of the size of shares, a combinatorial type bound and an entropy type bound. Further, we define a compact NSS as an NSS which meets the equalities of both our bounds. Then we show that a compact NSS has some special access hierarchy and it is closely related to a matroid. Verifiable nonperfect secret sharing schemes are also presented.