Some Basic Properties of General Nonperfect Secret Sharing Schemes
Kaoru Kurosawa, Wakaha Ogata · PubMed · 2020
: 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. Key Words: secret sharing scheme, nonperfect Category: E3. Data encryption 1 Introduction Secret sharing schemes permit a secret to be shared by participants in such a way that only qualified subsets of participants (access subset) can recover the secret. Secret sharing schemes are useful in the management of cryptographic keys, in multiparty p...