Determining Regions of Linear Contribution Vectors of Small Access Structures

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Bahariyan, Sorush | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52256 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Khazaei, Shahram
Abstract:
Objective of Secret Sharing is assigning some random variable which will be called shares, generated based on a random variable called secret, to some participant such that only specific subsets of participants could reconstruct the secret by polling their shares together. Constructing shares as small as possible is desired, hence notions like information ratio and average information ratio have been studied and considered to be a measure of efficiency of secret sharing schemes. In this research contribution vectors of access structures with five participants and graph based access structures with six participants have been studied. Small access structures have been considered shortly after introduction of secret sharing which made it possible to detect advantages and shortcomings of proposed methods for constructing and finding bounds on optimal secret sharing schemes. In this research different methods for finding bounds on information ratio of access structures have been reviewed. Afterwards extension of this methods have been used to determine linear contribution vectors of small access structures
Keywords:
Secret Sharing Scheme ; Contribution Vector ; Decomposition ; Common Information ; Multiobjective Optimization ; Benson's Algorithm