Matroids and Quantum Secret Sharing Schemes

A secret sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum secret sharing schemes. In addition to providing a new perspective on quantum secret sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum secret sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum secret sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure state quantum secret sharing scheme with information rate one

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

Optimal non-perfect uniform secret sharing schemes

A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this end, we extend the known connections between polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information that every subset of participants obtains about the secret value. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, the ones whose values depend only on the number of participants, generalize the threshold access structures. Our main result is to determine the optimal information ratio of the uniform access functions. Moreover, we present a construction of linear secret sharing schemes with optimal information ratio for the rational uniform access functions.Peer ReviewedPostprint (author's final draft

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 bipartite 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.Postprint (author’s final draft

Principles of 3D chromosome folding and evolutionary genome reshuffling in mammals.

Studying the similarities and differences in genomic interactions between species provides fertile grounds for determining the evolutionary dynamics underpinning genome function and speciation. Here, we describe the principles of 3D genome folding in vertebrates and show how lineage-specific patterns of genome reshuffling can result in different chromatin configurations. We (1) identified different patterns of chromosome folding in across vertebrate species (centromere clustering versus chromosomal territories); (2) reconstructed ancestral marsupial and afrotherian genomes analyzing whole-genome sequences of species representative of the major therian phylogroups; (3) detected lineage-specific chromosome rearrangements; and (4) identified the dynamics of the structural properties of genome reshuffling through therian evolution. We present evidence of chromatin configurational changes that result from ancestral inversions and fusions/fissions. We catalog the close interplay between chromatin higher-order organization and therian genome evolution and introduce an interpretative hypothesis that explains how chromatin folding influences evolutionary patterns of genome reshuffling. [Abstract copyright: Copyright © 2022 The Author(s). Published by Elsevier Inc. All rights reserved.

Hospital-acquired influenza infections detected by a surveillance system over six seasons, from 2010/2011 to 2015/2016

In addition to outbreaks of nosocomial influenza, sporadic nosocomial influenza infections also occur but are generally not reported in the literature. This study aimed to determine the epidemiologic characteristics of cases of nosocomial influenza compared with the remaining severe cases of severe influenza in acute hospitals in Catalonia (Spain) which were identified by surveillance. An observational case-case epidemiological study was carried out in patients aged ≥18 years from Catalan 12 hospitals between 2010 and 2016. For each laboratory-confirmed influenza case (nosocomial or not) we collected demographic, virological and clinical characteristics. We defined patients with nosocomial influenza as those admitted to a hospital for a reason other than acute respiratory infection in whom ILI symptoms developed ≥48 h after admission and influenza virus infection was confirmed using RT-PCR. Mixed-effects regression was used to estimate the crude and adjusted OR. One thousand seven hundred twenty-two hospitalized patients with severe laboratory-confirmed influenza virus infection were included: 96 (5.6%) were classified as nosocomial influenza and more frequently had > 14 days of hospital stay (42.7% vs. 27.7%, P <.001) and higher mortality (18.8% vs. 12.6%, P <.02). The variables associated with nosocomial influenza cases in acute-care hospital settings were chronic renal disease (aOR 2.44 95% CI 1.44-4.15) and immunodeficiency (aOR 1.79 95% CI 1.04-3.06). Nosocomial infections are a recurring problem associated with high rates of chronic diseases and death. These findings underline the need for adherence to infection control guidelines

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

A first update on mapping the human genetic architecture of COVID-19

peer reviewe

Secret sharing schemes for (k, n)-consecutive access structures

We consider access structures over a set P of n participants, defined by a parameter k with 1 = k = n in the following way: a subset is authorized if it contains participants i, i + 1,...,i + k - 1, for some i ¿ {1,...,n-k+1}. We call such access structures, which may naturally appear in real applications involving distributed cryptography, (k, n)- consecutive. We prove that these access structures are only ideal when k = 1, n - 1, n. Actually, we obtain the same result that has been obtained for other families of access structures: being ideal is equivalent to being a vector space access structure and is equivalent to having an optimal information rate strictly bigger than 2 3 . For the non-ideal cases, we give either the exact value of the optimal information rate, for k = n - 2 and k = n - 3, or some bounds on it.Postprint (author's final draft