Nested multipartite secret sharing

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2011

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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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.

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IEEE Beijing Section; Pudong New Area Association for Computer; Pudong New Area Science and Technology Development Fund; Tongji University; Xiamen University

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Proceedings - 2011 IEEE International Conference on Computer Science and Automation Engineering, CSAE 2011 -- 2011 IEEE International Conference on Computer Science and Automation Engineering, CSAE 2011 -- 10 June 2011 through 12 June 2011 -- Shanghai -- 86066

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4

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66

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73

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