Sutdies in Ideal Access Structures

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Kaboli Nooshabadi, Reza | 2022

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Type of Document: Ph.D. Dissertation
Language: Farsi
Document No: 55293 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Khazaei, Shahram
Abstract:
In this thesis, in addition to reviewing the previous work done in the study of ideal access structures, we present the author's recent results in this field. As a first result, we introduce a new technique for reducing the size of the secret space in ideal homomorphic secret sharing schemes. The concept of decomposition of secret sharing schemes is formally introduced for the first time. In this regard, we show that ideal homomorphic and abelian secret sharing schemes are decomposable. We also examine the inherent group-characterizability of secret sharing schemes and show that an ideal secret sharing scheme is not necessarily inherently group-characterizable. Some weaker definitions of the ideal access structure are also explored. Finally, we discuss the classification of ideal access structures and suggest some ideas for generalizing the existing results.
Keywords:
Ideal Access Structure ; Decomposition ; Matroids Theory ; Linear Secret Sharing Scheme ; Ideal Secret Sharing Scheme ; Group-Characterizable Secret Sharing Scheme ; Homomorphic Secret Sharing Scheme