Browsing by Author "Kaşkaloğlu, Kerem"

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Citation - Scopus: 0
Nested multipartite secret sharing
(2011) Kaskaloglu,K.; Özbudak,F.; Mathematics
Quite recently, Tassa introduced an ideal and perfect secret sharing scheme realizing conjunctive hierarchical threshold access structures motivated by the problem of sharing a private key among three employees of a bank, at least one of whom must be a department manager, for the purpose of signing an electronic funds transfer. We ask the natural question concerning What if there are two branches of banks that are needed to be involved in the signing process? In such a case, one might encounter the presence of two distinct hierarchies involved in the same access structure. In this paper, being motivated by such a sample scenario, we describe a new generalization, what we name nested multipartite access structures, which may involve the well-known compartmented or hierarchical access structures as substructures. The corresponding generic scheme we describe employs multivariate interpolation and is ideal, linear and perfect with probability 1 O(q1) on a finite field Fq. We describe the scheme in particular for the trivariate case as an example. Such an approach is hopefully useful not only for the initial motivating example, but also for a variety of interesting scenarios. In particular, we propose a non-nested generalization for the conventional compartmented access structures, which depicts a stronger way of controlling the additional t (t1 + + t m) participants. © 2011 IEEE.
Citation - WoS: 2
Citation - Scopus: 2
On the q-bernstein Polynomials of Piecewise Linear Functions in the Case q > 1
(Pergamon-elsevier Science Ltd, 2013) Kaskaloglu, Kerem; Ostrovska, Sofiya; Mathematics
The aim of this paper is to present new results related to the approximation of continuous functions by their q-Bernstein polynomials in the case q > 1. The first part of the paper is devoted to the behavior of the q-Bernstein polynomials of piecewise linear functions. This study naturally leads to the notion of truncated q-Bernstein polynomials introduced in the paper. The second part deals with the asymptotic estimates for the norms of the m-truncated q-Bernstein polynomials, in the case where both n and q vary. The results of the paper are illustrated by numerical examples. (C) 2012 Elsevier Ltd. All rights reserved.