Joint Compartmented Threshold Access Structures

In this paper, we introduce the notion of a joint compartmented threshold access structure (JCTAS). We study the necessary conditions for the existence of an ideal and perfect secret sharing scheme and give a characterization of almost all ideal JCTASes. Then we give an ideal and almost surely perfect construction that realizes such access structures. We prove the asymptotic perfectness of this construction by the Schwartz-Zippel Lemma

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

An Ideal Compartmented Secret Sharing Scheme Based on Linear Homogeneous Recurrence Relations

Multipartite secret sharing schemes are those that have multipartite access structures. The set of the participants in those schemes is divided into several parts, and all the participants in the same part play the equivalent role. One type of such access structure is the compartmented access structure. We propose an ideal and efficient compartmented multi-secret sharing scheme based on the linear homogeneous recurrence (LHR) relations. In the construction phase, the shared secrets are hidden in some terms of the linear homogeneous recurrence sequence. In the recovery phase, the shared secrets are obtained by solving those terms in which the shared secrets are hidden. When the global threshold is $t$, our scheme can reduce the computational complexity from $O(n^{t-1})$ to $O(n^{\max(t_i-1)}\log n)$, where $t_i<t$. The security of the proposed scheme is based on Shamir\u27s threshold scheme. Moreover, it is efficient to share the multi-secret and to change the shared secrets in the proposed scheme. That is, the proposed scheme can improve the performances of the key management and the distributed system

Society-oriented cryptographic techniques for information protection

Groups play an important role in our modern world. They are more reliable and more trustworthy than individuals. This is the reason why, in an organisation, crucial decisions are left to a group of people rather than to an individual. Cryptography supports group activity by offering a wide range of cryptographic operations which can only be successfully executed if a well-defined group of people agrees to co-operate. This thesis looks at two fundamental cryptographic tools that are useful for the management of secret information. The first part looks in detail at secret sharing schemes. The second part focuses on society-oriented cryptographic systems, which are the application of secret sharing schemes in cryptography. The outline of thesis is as follows

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 an 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

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, while most of the known constructions are either inefficient or randomized. 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. On the basis of the relationship between multipartite secret sharing schemes, polymatroids, and matroids, the problem of how to construct a scheme realizing a multipartite access structure can be transformed to the problem of how to find a representation of a matroid from a presentation of its associated polymatroid. In this paper, we give efficient algorithms to find representations of the matroids associated to several families of multipartite access structures. More precisely, based on know results about integer polymatroids, for each of those families of access structures above, we give an efficient method to find a representation of the integer polymatroid over some finite field, and then over some finite extension of that field, we give an efficient method to find a presentation of the matroid associated to the integer polymatroid. Finally, we construct ideal linear schemes realizing those families of multipartite access structures by efficient methods

Targeted Technology Applications for Infield Reserve Growth: A Synopsis of the Secondary Natural Gas Recovery Project Research, Gulf Coast Basin

A diverse and vast resource base of 1,295 trillion cubic feet (Tcf) of technically recoverable natural gas resources (including proved reserves, conventional resources, and nonconventional resources) was estimated by the National Petroleum Council (1992) in a recent analysis of domestic petroleum supplies. Of this resource base, 216 Tcf is predicted to be recoverable by reserve appreciation in existing fields in the lower 48 states. The integrated application of concepts and cost-effective technologies from the disciplines of geology, engineering, geophysics, and petrophysics will be required for converting these resources into producible reserves. In the last decade, characterization of the internal geometry of reservoirs, mainly oil reservoirs, has demonstrated a higher degree of compartmentalization than previously recognized. This compartmentalization, other than structural compartmentalization, is primarily a function of the depositional system and, secondarily, of the diagenetic history of the reservoir after deposition. The objective of a current infield reserve growth analysis of nonassociated natural gas reservoirs is to define the potential for incremental gas recovery based on better understanding of depositional and diagenetic heterogeneity within these reservoirs. Natural gas reserve growth (reserve appreciation) in conventional reservoirs has multiple components. Historically, extensions and deeper pool drilling have been the standard approach used by industry to achieve infield reserve additions. Recompletions of existing wells were often made without the concepts of reservoir heterogeneity or compartmentalization as a tool in recompletion strategy. Where significant geologic variation occurs, untapped, incompletely drained, or bypassed reservoir compartments remain to be drained of natural gas by new infield drilling or by recompleting strategically placed development wells. Today infield reserve growth is beginning to be based on an understanding of vertical and lateral heterogeneity that leads to recompletions in bypassed and incompletely drained reservoirs that were not previously recognized. In addition to concepts of reservoir heterogeneity and compartmentalization, new surface and downhole tools are being developed that will enhance the operator's ability to define these resource targets with greater precision and reliability. Examples of these tools now being developed and selectively used include borehole gravity, through-casing resistivity, cross-well geophysics, and surface three-dimensional seismic in the onshore.Bureau of Economic Geolog

Congressional Oversight of Modern Warfare: History, Pathologies, and Proposals for Reform

Despite significant developments in the nature of twenty-first century warfare, Congress continues to employ a twentieth century oversight structure. Modern warfare tactics, including cyber operations, drone strikes, and special operations, do not neatly fall into congressional committee jurisdictions. Counterterrorism and cyber operations, which are inherently multi-jurisdictional and highly classified, illustrate the problem. In both contexts, over the past several years Congress has addressed oversight shortcomings by strengthening its reporting requirements, developing relatively robust oversight regimes. But in solving one problem, Congress has created another: deeply entrenched information silos that inhibit the sharing of information about modern warfare across committees. This has real consequences. The Senate Foreign Relations Committee and House Foreign Affairs Committee may have to vote on an authorization for the use of military force against a country without a full understanding of options for covert operations that might achieve the same purpose with less risk. The House and Senate Armed Services Committees may be asked to approve a train-and-equip program for a partner force in a nation without knowing that the CIA is already operating essentially the same program. And the House and Senate Intelligence Committees may support a proposed covert operation without understanding the broader foreign policy context, and therefore, the reaction that it might provoke if it were discovered. But there is good news with the bad. If Congress is to blame for this information siloing, Congress is also able to fix it. This Article’s discussion of solutions begins with a proposal made by the 9/11 Commission to address information sharing failures—the formation of a super committee to address national security matters. After explaining why this is not the right answer, this Article offers four concrete proposals to remedy the problem. First, Congress should promote inter-committee information sharing by expanding cross-committee membership. Second, Congress should require joint briefings to committees when matters cut across jurisdictional boundaries. Third, Congress should permit members to share classified information with other members under limited, clearly defined circumstances. And fourth, Congress should create a Congressional National Security Council to coordinate cross-cutting national security matters and share mutually relevant information

Report on the Fourth Excavation Season (2011) of the Madâ'in Sâlih Archaeological Project

This volume is the report on the results of the fourth excavation season of the Saudi-French Archaeological Project at Madâ'in Sâlih, ancient Hegra in the Nabataean kingdom, in north-west Saudi Arabia (MAEE, SCTA, CNRS, Univ Paris 1, IFPO). Apart from the results obtained in the different excavation areas (both in the residential area and in tomb IGN 117), the reader will find a study on the cairns/tumuli of the site (W. Abu-Azizeh) as well as intermediary reports on the geophysical detection (Chr. Benech), the fauna (J. Studer) and the pottery (C. Durand).Ce volume constitue le rapport sur les résultats de la quatrième campagne de fouilles de la mission archéologique franco-saoudienne de Madâ'in Sâlih, l'ancienne Hégra des Nabatéens, dans le nord-ouest de l'Arabie Saoudite (MAEE, SCTA, CNRS, Univ. Paris 1, IFPO). Outre les résultats obtenus dans les différents chantiers (dans la zone résidentielle et dans le tombeau IGN 117), le lecteur trouvera une étude synthétique sur les cairns/tumuli du site (W. Abu-Azizeh) ainsi que des rapports intermédiaires sur la détection géophysique (Chr. Benech), la faune (J. Studer) et la céramique (C. Durand)