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

Comprehensive evaluation of deconvolution methods for human brain gene expression

Transcriptome deconvolution aims to estimate the cellular composition of an RNA sample from its gene expression data, which in turn can be used to correct for composition differences across samples. The human brain is unique in its transcriptomic diversity, and comprises a complex mixture of cell-types, including transcriptionally similar subtypes of neurons. Here, we carry out a comprehensive evaluation of deconvolution methods for human brain transcriptome data, and assess the tissue-specificity of our key observations by comparison with human pancreas and heart. We evaluate eight transcriptome deconvolution approaches and nine cell-type signatures, testing the accuracy of deconvolution using in silico mixtures of single-cell RNA-seq data, RNA mixtures, as well as nearly 2000 human brain samples. Our results identify the main factors that drive deconvolution accuracy for brain data, and highlight the importance of biological factors influencing cell-type signatures, such as brain region and in vitro cell culturing.Gavin J. Sutton, Daniel Poppe, Rebecca K. Simmons, Kieran Walsh, Urwah Nawaz, Ryan Lister, Johann A. Gagnon-Bartsch, Irina Voineag

Correlated evolution of multivariate traits: detecting co-divergence across multiple dimensions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75039/1/j.1420-9101.2007.01415.x.pd

Perfect Secrecy Systems Immune to Spoofing Attacks

We present novel perfect secrecy systems that provide immunity to spoofing attacks under equiprobable source probability distributions. On the theoretical side, relying on an existence result for $t$-designs by Teirlinck, our construction method constructively generates systems that can reach an arbitrary high level of security. On the practical side, we obtain, via cyclic difference families, very efficient constructions of new optimal systems that are onefold secure against spoofing. Moreover, we construct, by means of $t$-designs for large values of $t$, the first near-optimal systems that are 5- and 6-fold secure as well as further systems with a feasible number of keys that are 7-fold secure against spoofing. We apply our results furthermore to a recently extended authentication model, where the opponent has access to a verification oracle. We obtain this way novel perfect secrecy systems with immunity to spoofing in the verification oracle model.Comment: 10 pages (double-column); to appear in "International Journal of Information Security

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