Access Structure Hiding Secret Sharing from Novel Set Systems and Vector Families

Secret sharing provides a means to distribute shares of a secret such that any authorized subset of shares, specified by an access structure, can be pooled together to recompute the secret. The standard secret sharing model requires public access structures, which violates privacy and facilitates the adversary by revealing high-value targets. In this paper, we address this shortcoming by introducing \emph{hidden access structures}, which remain secret until some authorized subset of parties collaborate. The central piece of this work is the construction of a set-system $\mathcal{H}$ with strictly greater than $\exp\left(c \dfrac{1.5 (\log h)^2}{\log \log h}\right)$ subsets of a set of $h$ elements. Our set-system $\mathcal{H}$ is defined over $\mathbb{Z}_m$, where $m$ is a non-prime-power, such that the size of each set in $\mathcal{H}$ is divisible by $m$ but the sizes of their pairwise intersections are not divisible by $m$, unless one set is a subset of another. We derive a vector family $\mathcal{V}$ from $\mathcal{H}$ such that superset-subset relationships in $\mathcal{H}$ are represented by inner products in $\mathcal{V}$. We use $\mathcal{V}$ to "encode" the access structures and thereby develop the first \emph{access structure hiding} secret sharing scheme. For a setting with $\ell$ parties, our scheme supports $2^{2^{\ell/2 - O(\log \ell) + 1}}$ out of the $2^{2^{\ell - O(\log \ell)}}$ total monotone access structures, and its maximum share size for any access structures is $(1+ o(1)) \dfrac{2^{\ell+1}}{\sqrt{\pi \ell/2}}$. The scheme assumes semi-honest polynomial-time parties, and its security relies on the Generalized Diffie-Hellman assumption.Comment: This is the full version of the paper that appears in D. Kim et al. (Eds.): COCOON 2020 (The 26th International Computing and Combinatorics Conference), LNCS 12273, pp. 246-261. This version contains tighter bounds on the maximum share size, and the total number of access structures supporte

The Erd\H{o}s-Ko-Rado theorem for twisted Grassmann graphs

We present a "modern" approach to the Erd\H{o}s-Ko-Rado theorem for Q-polynomial distance-regular graphs and apply it to the twisted Grassmann graphs discovered in 2005 by van Dam and Koolen.Comment: 5 page

Diagonally Neighbour Transitive Codes and Frequency Permutation Arrays

Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication. In particular, a certain class of constant composition codes called frequency permutation arrays have been suggested as ideal, in some sense, for these purposes. In this paper we characterise a family of neighbour transitive codes in Hamming graphs in which frequency permutation arrays play a central rode. We also classify all the permutation codes generated by groups in this family

Incremental dimension reduction of tensors with random index

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low and predictable. Component encoding and decoding are performed on-line without computationally expensive re-analysis of the data set. The range of tensor indices can be extended dynamically without modifying the component representation. This idea originates from a mathematical model of semantic memory and a method known as random indexing in natural language processing. We generalize the random-indexing algorithm to tensors and present signal-to-noise-ratio simulations for representations of vectors and matrices. We present also a mathematical analysis of the approximate orthogonality of high-dimensional ternary vectors, which is a property that underpins this and other similar random-coding approaches to dimension reduction. To further demonstrate the properties of random indexing we present results of a synonym identification task. The method presented here has some similarities with random projection and Tucker decomposition, but it performs well at high dimensionality only (n>10^3). Random indexing is useful for a range of complex practical problems, e.g., in natural language processing, data mining, pattern recognition, event detection, graph searching and search engines. Prototype software is provided. It supports encoding and decoding of tensors of order >= 1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure

The Tourist Experience of Heritage Urban Spaces: Valletta as a Case Study

This article provides an understanding of how tourists experience heritage urban spaces by investigating features that influence tourist experiences most. It is framed within urban design literature which refers to three elements of urban space namely physical setting (or form), activity, and meaning. These elements are used to explore how urban spaces are experienced by tourists. Its findings are derived from an in-depth qualitative analysis of interviews with tourists to Valletta, Malta. The research suggests that the intrinsic qualities of the space are relevant to the tourist experience but what is even more relevant are the interactions of the tourist with different elements within that space, namely interactions with surroundings, interactions with others, and interactions with self/meaning. Within this broad conceptual model, the research identifies important sub-themes. Some of these reinforce the findings of existing work on tourist experiences, but others are often under-estimated or neglected

Understanding Face and Shame: A Servant-Leadership and Face Management Model

Clergy can have a negative impact on churches and other individuals when they knowingly or unknowingly attempt to save face, that is, try to protect their standing or reputation. The desire to gain face and the fear of losing face and feeling ashamed will likely permeate clergy’s decision-making processes without even being noticed. This study explores the essence of face and face management and the relationship between face management and two characteristics of servant-leadership—awareness and healing—in both Chinese and American churches through the methodology of hermeneutic phenomenology. Prior to this study, to my knowledge, no hermeneutic phenomenological research of face management has been conducted in a church setting. Through a review of the literature, four areas are explored: face and shame, face management, servant-leadership, and face, shame, and face management within the church. This study obtained approval from the Institutional Review Board and informed consent from the participants. Three Chinese and three American Christian ministers were chosen to complete a question sheet and participate in two semi-structured interview sessions. A first cycle of open coding and second cycle of pattern coding were used during data analysis. Face experiences are discussed in light of eight major themes: body, triggers, becoming, face concepts, strategies, emotions, servant-leadership, and the church. Findings from the study help build a servant-leadership and face management model, which can offer an anchored approach for clergy and pastoral counselors to address face and shame and to develop therapeutic interventions

A person-centered perspective on working with people who have experienced psychological trauma and helping them move forward to posttraumatic growth

Over the past decade posttraumatic growth (PTG) has become a major topic for theory, research and practice in mainstream trauma psychology. The aim of this paper is to discuss the implications of PTG for the person-centered approach. It is argued that PTG provides a new non-medical language for understanding psychological trauma that is consistent with the person-centered approach. Person-centered personality theory provides an explanation for how PTG arises and leads to new testable predictions for research into how person-centered therapy may be able to facilitate PTG