On the optimization of bipartite secret sharing schemes

Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the tripartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.Peer ReviewedPostprint (author's final draft

Ideal hierarchical secret sharing schemes

Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention from the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization deals with the properties of the hierarchically minimal sets of the access structure, which are the minimal qualified sets whose participants are in the lowest possible levels in the hierarchy. By using our characterization, it can be efficiently checked whether any given hierarchical access structure that is defined by its hierarchically minimal sets is ideal. We use the well known connection between ideal secret sharing and matroids and, in particular, the fact that every ideal access structure is a matroid port. In addition, we use recent results on ideal multipartite access structures and the connection between multipartite matroids and integer polymatroids. We prove that every ideal hierarchical access structure is the port of a representable matroid and, more specifically, we prove that every ideal structure in this family admits ideal linear secret sharing schemes over fields of all characteristics. In addition, methods to construct such ideal schemes can be derived from the results in this paper and the aforementioned ones on ideal multipartite secret sharing. Finally, we use our results to find a new proof for the characterization of the ideal weighted threshold access structures that is simpler than the existing one.Peer ReviewedPostprint (author's final draft

On the representability of the biuniform matroid

Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields. © 2013, Society for Industrial and Applied MathematicsPeer ReviewedPostprint (published version

On the representability of the biuniform matroid

Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields. © 2013, Society for Industrial and Applied MathematicsPeer ReviewedPostprint (published version

E–Voting System based on Secret Sharing Scheme

The electoral process is considered as one of the important and sensitive operations that take place from time to time in all countries of the world and need to be protected. The importance of the electronic voting came because, it provides a maintaining for the secrecy of the vote, as well as, the speed, accuracy and credibility of the vote counts. This is due to the growing of the technology that always needs for electronic process and for new approaches to achieve high security. In this paper, a new E-voting system is designed based on secret sharing scheme. The new protocol is implemented to show its efficiency in terms of computational time and cost

Unified Ciphertext-Policy weighted attribute-based encryption for sharing data in cloud computing

© 2018 by the authors. With the rapid development of cloud computing, it is playing an increasingly important role in data sharing. Meanwhile, attribute-based encryption (ABE) has been an effective way to share data securely in cloud computing. In real circumstances, there is often a mutual access sub-policy in different providers' access policies, and the significance of each attribute is usual diverse. In this paper, a secure and efficient data-sharing scheme in cloud computing, which is called unified ciphertext-policy weighted attribute-based encryption (UCP-WABE), is proposed. The weighted attribute authority assigns weights to attributes depending on their importance. The mutual information extractor extracts the mutual access sub-policy and generates the mutual information. Thus, UCP-WABE lowers the total encryption time cost of multiple providers. We prove that UCP-WABE is selectively secure on the basis of the security of ciphertext-policy weighted attribute-based encryption (CP-WABE). Additionally, the results of the implementation shows that UCP-WABE is efficient in terms of time