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Linear Secret Sharing from the Optimality Point of View

Norouzi Bezmin Abadi, Hassan | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53738 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Khazaei, Shahram
  7. Abstract:
  8. A secret sharing scheme is a way to share a secret between a group of people so that only authorized subsets can retrieve the original secret. Secret sharing schemes were first introduced by Shamir and Blakley for threshold access structures. In a threshold access structure, a subset of individuals is allowed if the number of members exceeds a predetermined threshold. After Shamir, the study of general access structures was considered, and Ito, Saito, and Nishizeki proposed a way to construct a secret sharing scheme for these structures. Reducing the length of party's share in secret-sharing schemes and finding the optimal scheme for access structures has long been the focus of researchers in this field, and four decades after the introduction of secret-sharing schemes, there is still a big gap between the minimum and maximum information ratio of access structures. The information ratio of an access structure is an indicator for examining the optimality of the scheme of that structure in order to minimize the length of paty's share. In this dissertation, in addition to examining these issues and related outcomes, we specifically study linear secret sharing schemes and examine their minimum and maximum boundaries
  9. Keywords:
  10. Secret Sharing Scheme ; Information Ratio ; Lower Bound ; Linear Secret Sharing Scheme ; Monotone Scheme ; Rank Inequality ; Monotone Span Program

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