Nearly optimal robust secret sharing

Abstract: We prove that a known approach to improve Shamir's celebrated secret sharing scheme; i.e., adding an information-theoretic authentication tag to the secret, can make it robust for n parties against any collusion of size δn, for any constant δ ∈ (0; 1/2). This result holds in the so-called “nonrushing” model in which the n shares are submitted simultaneously for reconstruction. We thus finally obtain a simple, fully explicit, and robust secret sharing scheme in this model that is essentially optimal in all parameters including the share size which is k(1+o(1))+O(κ), where k is the secret length and κ is the security parameter. Like Shamir's scheme, in this modified scheme any set of more than δn honest parties can efficiently recover the secret. Using algebraic geometry codes instead of Reed-Solomon codes, the share length can be decreased to a constant (only depending on δ) while the number of shares n can grow independently. In this case, when n is large enough, the scheme satisfies the “threshold” requirement in an approximate sense; i.e., any set of δn(1 + ρ) honest parties, for arbitrarily small ρ > 0, can efficiently reconstruct the secret

Holographic Entanglement Entropy for 4D Conformal Gravity

Using the proposal for holographic entanglement entropy in higher derivative gravities, we compute holographic entanglement entropy for the conformal gravity in four dimensions which turns out to be finite. However, if one subtracts the contribution of the four dimensional Gauss-Bonnet term, the corresponding entanglement entropy has a divergent term and indeed restricted to an Einstein solution of the conformal gravity, the resultant entanglement entropy is exactly the same as that in the Einstein gravity. We will also make a comment on the first law of the entanglement thermodynamics for the conformal gravity in four dimensions.Comment: 16 pages, Published Versio

On Complexity for Higher Derivative Gravities

Using "complexity=action" proposal we study complexity growth of certain gravitational theories containing higher derivative terms. These include critical gravity in diverse dimensions. One observes that the complexity growth for neutral black holes saturates the proposed bound when the results are written in terms of physical quantities of the model. We will also study effects of shock wave to the complexity growth where we find that the presence of massive spin-2 mode slows down the rate of growth.Comment: 18 pages, 3 figures, journal versio

Complexity Growth with Lifshitz Scaling and Hyperscaling Violation

Using complexity=action proposal we study the growth rate of holographic complexity for Lifshitz and hyperscaling violating geometries. We will consider both one and two sided black branes in an Einstein-Maxwell-Dilaton gravitational theory. We find that in either case Lloyd's bound is violated and the rate of growth of complexity saturates to a value which is greater than twice the mass of the corresponding black brane. This value reduces to the mass of the black brane in the isotropic case. We show that in two sided black brane the saturation happens from above while for one sided black brane it happens from below.Comment: 17 pages, 4 figures, v2: typos corrected, references added, v3: Minor corrections, New counter terms added that also contribute to the rate of complexity growth. The conclusion is not changed, now 19 pages, v4: matches published versio

ENHANCED SENSOR NETWORK : A SPECIALIZED INFRASTRUCTURE FOR CONTEXT-AWARE APPLICATIONS

Respecting the mobile world, it is about the time to demand for systems to fully take advantage of their environment. In this way, Enhanced Sensor Network is another step toward developing realistic context-aware applications, which is based on the basic infrastructures provided by wireless sensor networks (WSN) and context-aware application development paradigms. In this paper we introduce a framework for integrating WSNs with context-aware application requirements to enhance wireless sensor network as an infrastructure which can provide necessary contextual information for context-aware applications

Comparative structural response of two steel bridges constructed 100 years apart

This paper presents a comparative numerical analysis of the structural behaviour and seismic performance of two existing steel bridges, the Infiernillo II Bridge and the Pinhao Bridge, one located in Mexico and the other in Portugal. The two bridges have similar general geometrical characteristics, but were constructed 100 years apart. Three-dimensional structural models of both bridges are developed and analysed for various load cases and several seismic conditions. The results of the comparative analysis between the two bridges are presented in terms of natural frequencies and corresponding vibration modes, maximum stresses in the structural elements and maximum displacements. The study is aimed at determining the influence of a 1 century period in material properties, transverse sections and expected behaviour of two quite similar bridges. In addition, the influence of the bearing conditions in the global response of the Pinhao Bridge was evaluated

Corner contributions to holographic entanglement entropy in AdS4/BCFT3

We study the holographic entanglement entropy of spatial regions with corners in the AdS4/BCFT3correspondence by considering three dimensional boundary conformal field theories whose boundary is a timelike plane. We compute analytically the corner function corresponding to an infinite wedge having one edge on the boundary. A relation between this corner function and the holographic one point function of the stress tensor is observed. An analytic expression for the corner function of an infinite wedge having only its tip on the boundary is also provided. This formula requires to find the global minimum among two extrema of the area functional. The corresponding critical configurations of corners are studied. The results have been checked against a numerical analysis performed by computing the area of the minimal surfaces anchored to some finite domains containing corners

Holographic entanglement entropy in AdS4/BCFT3 and the Willmore functional

We study the holographic entanglement entropy of spatial regions having arbitrary shapes in the AdS4/BCFT3 correspondence with static gravitational backgrounds, focusing on the subleading term with respect to the area law term in its expansion as the UV cutoff vanishes. An analytic expression depending on the unit vector normal to the minimal area surface anchored to the entangling curve is obtained. When the bulk spacetime is a part of AdS4, this formula becomes the Willmore functional with a proper boundary term evaluated on the minimal surface viewed as a submanifold of a three dimensional flat Euclidean space with boundary. For some smooth domains, the analytic expressions of the finite term are reproduced, including the case of a disk disjoint from a boundary which is either flat or circular. When the spatial region contains corners adjacent to the boundary, the subleading term is a logarithmic divergence whose coefficient is determined by a corner function that is known analytically, and this result is also recovered. A numerical approach is employed to construct extremal surfaces anchored to entangling curves with arbitrary shapes. This analysis is used both to check some analytic results and to find numerically the finite term of the holographic entanglement entropy for some ellipses at finite distance from a flat boundary