A secret sharing scheme is a method of distributing a secret value among members of a group such that only certain coalitions of these participants can find the secret. A subset of users that can recover the secret is called a qualified coalition, and the set of all qualified coalitions is called the access structure. An access structure is called monotone if every coalition containing a qualif...

One of the recent generalizations of (t, n) secret sharing for hierarchical threshold access structures is given by Tassa, where he answers the natural question of sharing a secret among a set of participants, say military officers, so that the secret can be constructed by a group of participants, some of whom are hierarchically superior to others. Both recent schemes proposed by Tassa for addr...

Beimel, Tassa and Weinreb (2008) and Farras and Padro (2010) partially characterized access structures of ideal weighted threshold secret sharing schemes in terms of the operation of composition. They classified indecomposable ideal weighted threshold access structures, and proved that any other ideal weighted threshold access structure is a composition of indecomposable ones. It remained uncle...

The concept of quasi-threshold multipartite access structures for secret sharing schemes is introduced. These access structures allow one distinguished class of participants to retain control over the reconstruction of the secret, while allowing flexibility over the quorum of participants from other classes. While ideal bipartite access structures have been classified, the case for multipartite...

Weighted threshold secret sharing was introduced by Shamir in his seminal work on secret sharing. In such settings, there is a set of users where each user is assigned a positive weight. A dealer wishes to distribute a secret among those users so that a subset of users may reconstruct the secret if and only if the sum of weights of its users exceeds a certain threshold. A secret sharing scheme ...

In this paper we consider graph access structures and we show that such an access structure can be realized by a (strongly) multiplicative monotone span program if and only if the privacy structure contains at least three (resp. four) maximal sets. Thus, we obtain a new family of access structures with an explicit construction that is both ideal and strongly multiplicative. Until now only three...

We propose efficient secret sharing schemes realizing general access structures. Our proposed schemes are perfect secret sharing schemes and include Shamir’s (k, n)-threshold schemes as a special case. Furthermore, we show that a verifiable secret sharing scheme for general access structures is realized by one of the proposed schemes. key words: (k, n)-threshold scheme, general access structure...

A multi-secret sharing scheme allows several secrets to be shared amongst a group of participants. In 2005, Shao and Cao developed a verifiable multi-secret sharing scheme where each participant’s share can be used several times which reduces the number of interactions between the dealer and the group members. In addition, some secrets may require a higher security level than others involving t...

It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m,m)-threshold scheme by using the so-called cumulative map or from a (t,m)threshold SSS by a modified cumulative map. However, such constructed SSSs are not efficient generally. In this paper, we propose a new method to construct a SSS from a (t,m)-threshold scheme for any given general...

Secure communication has become more and more important for system security. Since avoiding the use of encryption one by one can introduce less computation complexity, secret sharing scheme (SSS) has been used to design many security protocols. In SSSs, several authors have studied multipartite access structures, in which the set of participants is divided into several parts and all participant...