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 ...

We propose cryptographic rational secret sharing protocols over general networks. In a network, the dealer may not have direct connections to each player, and players of other players. present conditions on network topology for which our proposed are computational strict Nash equilibria (k−1)-resilient, along with analysis their round communication complexity. also new notions such as Φ-resilie...

Secret sharing schemes (SSS) are very important, because they are used in critical applications such as e-voting, cryptographic key distribution and sharing, secure online auctions, information hiding, and secure multiparty computation. We explained some popular algorithms of secret sharing such as threshold, graph, and visual schemes and their access structures. Besides, we discussed the limit...

2-level shared secret schemes are defined by Simmons in 1989. In this paper, we describe a survey of 2-level secret sharing schemes using finite geometry.

THRESHOLD CRYPTOGRAPHY WITH CHINESE REMAINDER THEOREM Kamer Kaya Ph.D. in Computer Engineering Supervisor: Asst. Prof. Dr. Ali Aydın Selçuk August, 2009 Information security has become much more important since electronic communication is started to be used in our daily life. The content of the term information security varies according to the type and the requirements of the area. However, no ...

The information ratio of a secret sharing scheme Σ measures the size of the largest share of the scheme, and is denoted by σ(Σ). The optimal information ratio of an access structure Γ is the infimum of σ(Σ) among all schemes Σ for Γ, and is denoted by σ(Γ). The main result of this work is that for every two access structures Γ and Γ′, |σ(Γ)− σ(Γ′)| ≤ |Γ∪ Γ′| − |Γ∩ Γ′|. We prove it constructivel...

Monotone span programs are a linear-algebraic model of computation. They are equivalent to linear secret sharing schemes and have various applications in cryptography and complexity. A fundamental question is how the choice of the field in which the algebraic operations are performed effects the power of the span program. In this paper we prove that the power of monotone span programs over fini...

A secret sharing scheme allows to share a secret among several participants such that only certain groups of them can recover it. Veri able secret sharing has been proposed to achieve security against cheating participants. Its rst realization had the special property that everybody, not only the participants, can verify that the shares are correctly distributed. We will call such schemes publi...