The concept of secret sharing has been introduced independently by Shamir and Blakley, as a tool to protect a secret from getting exposed or from being lost. It allows a so-called dealer to share a secret among the members of a set P , which are usually called players or participants, in such a way that only certain specified subsets of players are able to reconstruct the secret while smaller s...

In this paper we introduce the class of composite access structures for secret sharing. We also provide secret sharing schemes realizing these structures and study their information rates. As a particular case of this construction, we present the subclass of iterated threshold schemes, a large class of ideal secret sharing schemes.

Cellular automata have been used for design of cryptosystems. Recently some secret sharing schemes based on linear memory cellular automata have been introduced which are used for both text and image. In this paper, we illustrate that these secret sharing schemes are vulnerable to dishonest participants’ collusion. We propose a cheating model for the secret sharing schemes based on linear memor...

Secret sharing schemes are one of the most important primi-tives in distributed systems. Cumulative secret sharing schemes provide a method to share a secret among a number of participants with arbitrary access structures. This paper presents two diierent methods for constructing cumulative secret sharing schemes. The rst method produces a simple and eecient cumulative scheme. The second method...

Secret-sharing schemes are an important tool in cryptography that is used in the construction of many secure protocols. However, the shares’ size in the best known secret-sharing schemes realizing general access structures is exponential in the number of parties in the access structure, making them impractical. On the other hand, the best lower bound known for sharing of an `-bit secret with re...

Nascimento et al. [19] introduced a quantum information theoretical model for Quantum Secret Sharing (QSS) schemes. In this thesis, we describe existing schemes, such as the construction using Monotone Span Programs (MSPs) [16], according to this model. Moreover, the correctness of these schemes is proved in an information theoretical way. In particular, we consider the so-called pure state QSS...

A secret-sharing scheme is a method by which a dealer distributes shares to parties such that only authorized subsets of parties can reconstruct the secret. Secret-sharing schemes are important tools in cryptography and they are used as a building box in many secure protocols, e.g., general protocol for multiparty computation, Byzantine agreement, threshold cryptography, access control, attribu...

Preface A secret sharing scheme starts with a secret and then derives from it certain shares (or shadows) which are distributed to users. The secret may be recovered only by certain predetermined groups which belong to the access structure. Secret sharing schemes have been independently introduced by Blakley [12] and Shamir [134] as a solution for safeguarding cryptographic keys. Secret sharing...

Secret Sharing from the perspective of threshold schemes has been wellstudied over the past decade. Threshold schemes, however, can only handle a small fraction of the secret sharing functions which we may wish to form. For example, if it is desirable to divide a secret among four participants A , B: C, and D in such a way that either A together with B can reconstruct the secret or C together w...