Nonperfect Secret Sharing Schemes and Matroids
نویسندگان
چکیده
This paper shows that nonperfect secret sharing schemes (NSS) have matroid structures and presents a direct link between the secret sharing matroids and entropy for both perfect and nonperfect schemes. We deene natural classes of NSS and derive a lower bound of jVij for those classes. \Ideal" nonperfect schemes are deened based on this lower bound. We prove that every such ideal secret sharing scheme has a matroid structure. The rank function of the matroid is given by the entropy divided by some constant. It satisses a simple equation which represents the access level of each subset of participants.
منابع مشابه
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 su cient 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...
متن کاملSome New Results on Nonperfect Secret Sharing Schemes
In secret sharing schemes, jV i j should be as small as possible, where V i denotes the set of share of player P i. It is known that the scheme must be nonperfect if jV i j < jSj, where S denotes the set of s. A secret sharing scheme is called nonperfect if there exists a subset of players who have some information on the sectret s but cannot recover s. For nonperfect secret sharing schemes, th...
متن کاملSecurity Analysis of a Hash-Based Secret Sharing Scheme
Secret sharing schemes perform an important role in protecting se-cret by sharing it among multiple participants. In 1979, (t; n) threshold secret sharing schemes were proposed by Shamir and Blakley independently. In a (t; n) threshold secret sharing scheme a secret can be shared among n partic-ipants such that t or more participants can reconstruct the secret, but it can not be reconstructed b...
متن کاملLower Bound on the Size of Shares of Nonperfect Secret Sharing Schemes
In a secret sharing scheme (SS), a dealer D distributes a piece of information Vi of a secret S to each participant Pi. If we desire that jVij < jSj, 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 rst presents a general lower bound on jVij which includes the previous lower bounds for perfect SSs and nonperf...
متن کاملMatroids and Quantum Secret Sharing Schemes
A secret sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such...
متن کامل