Compartmented Access Structures Research Articles

Efficient Explicit Constructions of Multipartite Secret Sharing Schemes

Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. Secret sharing schemes for multipartite access structures have received considerable attention due to the fact that multipartite secret sharing can be seen as a natural and useful generalization of threshold secret sharing. This work deals with efficient and explicit constructions of ideal multipartite secret sharing schemes. Most ideal multipartite secret sharing schemes in the literature can be classified as either hierarchical or compartmented. The main results are the constructions for ideal hierarchical access structures, a family that contains every ideal hierarchical access structure as a particular case such as the disjunctive hierarchical threshold access structure and the conjunctive hierarchical threshold access structure, the constructions for three families of compartmented access structures, and the constructions for two families compartmented access structures with compartments. We present an efficient method to construct ideal linear schemes realizing these access structures by linear algebraic techniques on the basis of the relationship between multipartite secret sharing schemes, polymatroids and matroids.

Asymptotically ideal Chinese remainder theorem ‐based secret sharing schemes for multilevel and compartmented access structures

Multilevel and compartmented access structures are two important classes of access structures where participants are grouped into levels/compartments with different degrees of trust and privileges. The construction of secret sharing schemes for such access structures has been the attention of researchers for a long time. Two main approaches have been taken so far, one of them is based on polynomial interpolation and the other one is based on the Chinese Remainder Theorem (CRT). In this article the first asymptotically ideal CRT-based secret sharing schemes for (disjunctive, conjunctive) multilevel and compartmented access structures are proposed. Our approach is compositional and it is based on a variant of the Asmuth-Bloom secret sharing scheme where some participants may have public shares. Based on this, the proposed secret sharing schemes for multilevel and compartmented access structures are asymptotically ideal if and only if they are based on 1-compact sequences of co-primes. Possible applications for secret image and multi-secret sharing are pointed-out.

Compartmented Secret Sharing Schemes and Locally Repairable Codes

Multipartite secret sharing is an important research object in the area of secret sharing schemes. Compartmented access structures are an interesting class of multipartite access structures. The constructions of ideal linear schemes realizing compartmented access structures are studied by codes in this paper. We find that compartmented secret sharing is related to a class of codes called locally repairable codes which are being used widely in distributed and cloud storage systems. We study secret sharing schemes for compartmented access structures with upper bounds, compartmented access structures with lowers bounds and compartmented access structures with upper and lower bounds. We establish the relationships between secret sharing schemes for these compartmented access structures and locally repairable codes. Based on the relationships and some locally repairable codes, we obtain ideal linear schemes realizing these compartmented access structures by efficient methods.

Efficient explicit constructions of compartmented secret sharing schemes

Multipartite secret sharing schemes have been an important object of study in the area of secret sharing schemes. Two interesting families of multipartite access structures are hierarchical access structures and compartmented access structures. This work deals with efficient and explicit constructions of ideal compartmented secret sharing schemes, while most of the known constructions are either inefficient or randomized. We construct ideal linear secret sharing schemes for three types of compartmented access structures, such as compartmented access structures with upper bounds, compartmented access structures with lower bounds, and compartmented access structures with upper and lower bounds. There exist some methods to construct ideal linear schemes realizing these compartmented access structures in the literature, but those methods are inefficient in general because non-singularity of many matrices has to be determined to check the correctness of the scheme. Our constructions do not need to do these computations. Our methods to construct ideal linear schemes realizing these access structures combine polymatroid-based techniques with Gabidulin codes. Gabidulin codes play a fundamental role in the constructions, and their properties imply that our methods are efficient.

Secret sharing schemes for compartmented access structures

In this paper, we devise ideal and probabilistic secret sharing schemes for two kinds of compartmented access structures. The first one is a compartmented access structures with hierarchical compartments. The second one is the compartmented access structures with strictly lower bounds. We propose ideal and probabilistic schemes for these two compartmented access structures by using the idea of bivariate interpolation.

Threshold Secret Sharing Scheme for Compartmented Access Structures

In the realm of visual cryptography, secret sharing is the predominant method of transmission and reception of secure data. Most of the (n, n) secret sharing schemes suffer from one common flaw — locking of information when the all- n number of receivers are not available for some reason. This paper proposes a new method of compartmented secret sharing scheme where some threshold number of equally privileged from each compartment can retrieve data. This scheme rules out regeneration of secret image at the single compartment thereby eliminating the danger of misusing secret image. The key features of this scheme are: better visual quality of the recovered image with no pixel expansion; non-requirement of half toning of color images; less computational complexity by reconstructing secret through XORing and simple addition of all share images. This scheme is highly beneficial in applications where data has to be stored securely in a database and in cloud computing to synchronize information passed to different groups or clusters from a single host.

Further ideal multipartite access structures from integer polymatroids

Ideal access structures admit ideal secret sharing schemes where the shares have the minimal size.As multipartite access structures can well mirror the real social organizations, of which the participants arepartitioned into disjoint groups according to their properties, it is desirable to find expressive ideal multipartiteaccess structures. Integer polymatroids, due to their close relationship with ideal multipartite access structures,have been shown as a powerful tool to study the ideality of some multipartite access structures. In this paper, tocater for flexible applications, we consider several ideal multipartite access structures that further extend someknown results. We first explore a type of compartmented access structures with strictly lower bounds, whichprovide fairness among all the participant groups when recovering the secret. Then, we investigate ideal benchaccess structures where the participant set is divided into two parts, that is, line-up section and bench section.The participants in line-up section can delegate their capabilities to the participants in bench section in such away that the participants in bench section can take over the role of their delegators in line-up section, which isapplicable to emergency situations when there are no enough participants in line-up section for recovering thesecret. Finally, we propose two types of ideal partially hierarchical access structures which are suitable to morerealistic hierarchical social organizations than existing results.

Natural Generalizations of Threshold Secret Sharing

We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit ideal linear secret sharing schemes over every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure the proofs for the existence of ideal secret sharing schemes for them.

Multipartite Secret Sharing by Bivariate Interpolation

Given a set of participants that is partitioned into distinct compartments, a multipartite access structure is an access structure that does not distinguish between participants belonging to the same compartment. We examine here three types of such access structures: two that were studied before, compartmented access structures and hierarchical threshold access structures, and a new type of compartmented access structures that we present herein. We design ideal perfect secret sharing schemes for these types of access structures that are based on bivariate interpolation. The secret sharing schemes for the two types of compartmented access structures are based on bivariate Lagrange interpolation with data on parallel lines. The secret sharing scheme for the hierarchical threshold access structures is based on bivariate Lagrange interpolation with data on lines in general position. The main novelty of this paper is the introduction of bivariate Lagrange interpolation and its potential power in designing schemes for multipartite settings, as different compartments may be associated with different lines or curves in the plane. In particular, we show that the introduction of a second dimension may create the same hierarchical effect as polynomial derivatives and Birkhoff interpolation were shown to do in Tassa (J. Cryptol. 20:237–264, 2007).