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Studying Ideal Access Structures in Secret Sharing Schemes

Haji Aghajanpour, Niloufar | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54324 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Khazaei, Shahram
  7. Abstract:
  8. A secret sharing scheme involves a dealer who has a secret and distribute that among a set of participants, in such a way that only authorized subsets can recover the secret value. The collection of authorized subsets called the access structure and a secret sharing scheme in which unauthorized subset cannot reveal any partial information about the secret is called a perfect secret sharing scheme. One of the problems in secret sharing schemes is finding the appropriate lower bound for a parameter called the information ratio and optimizing it. A perfect secret sharing scheme is ideal when it has an optimal information ratio. In other words, if all shares have the same length as the secret, which is the best possible situation, then both the scheme and its access structure are said to be ideal. Classifying and identifying ideal access structures is an important open problem in secret sharing. In this thesis, we review of studies on ideal access structures and their categorized in general. These studies cover a wide range of access structures such as threshold access structures, bipartite and multipartite structures, hierarchical access structures, access structures with ideal multi-linear schemes, access structure with ideal homomorphic schemes, access structures with intersection number equal to one, universally ideal access structures, etc
  9. Keywords:
  10. Secret Sharing Scheme ; Information Ratio ; Access Structure ; Ideal Access Structure ; Ideal Secret Sharing Scheme

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