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On ideal and weakly-ideal access structures

Kaboli, R ; Sharif University of Technology | 2023

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  1. Type of Document: Article
  2. DOI: 10.3934/amc.2021017
  3. Publisher: American Institute of Mathematical Sciences , 2023
  4. Abstract:
  5. For more than two decades, proving or refuting the following statement has remained a challenging open problem in the theory of secret sharing schemes (SSSs): every ideal access structure admits an ideal perfect multi-linear SSS. The class of group-characterizable (GC) SSSs include the multi-linear ones. Hence, if the above statement is true, then so is the following weaker statement: every ideal access structure admits an ideal perfect GC SSS. One contribution of this paper is to show that ideal SSSs are not nec-essarily GC. Our second contribution is to study the above two statements with respect to several variations of weakly-ideal access structures. Recently, Mejia and Montoya studied ideal access structures that admit ideal multi-linear schemes and provided a classification-like theorem for them. We additionally present some tools that are useful to extend their result. © 2023, American Institute of Mathematical Sciences. All rights reserved
  6. Keywords:
  7. Ideal access structure ; Ideal secret sharing scheme ; Latin square ; Linear and group-characterizable random variable ; Matroid
  8. Source: Advances in Mathematics of Communications ; Volume 17, Issue 3 , 2023 , Pages 697-713 ; 19305346 (ISSN)
  9. URL: https://www.aimsciences.org/article/doi/10.3934/amc.2021017