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On group-characterizability of homomorphic secret sharing schemes

Kaboli, R ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1016/j.tcs.2021.08.032
  3. Publisher: Elsevier B. V , 2021
  4. Abstract:
  5. A group-characterizable (GC) random variable is induced by a finite group, called main group, and a collection of its subgroups. The notion extends directly to secret sharing schemes (SSSs). It is known that linear and abelian SSSs can be equivalently described in terms of GC SSSs. In this paper, we present a necessary and sufficient condition for a SSS to be equivalent to a GC one. Using this result, we show that homomorphic SSSs (HSSSs) are equivalent to GC SSSs whose subgroups are normal in the main group. We also present two applications for this equivalent description of HSSSs. One concerns lower bounding the information ratio of access structures for the class of HSSSs, and the other is about the coincidence between statistical, almost-perfect and perfect security notions for the same class. © 2021 Elsevier B.V
  6. Keywords:
  7. Equivalence classes ; Group theory ; Information theory ; Access structure ; Condition ; Finite groups ; Group-characterizable random variable ; Homomorphic secret sharing ; Main group ; Perfect securities ; Secret sharing schemes ; Security notion ; Random variables
  8. Source: Theoretical Computer Science ; Volume 891 , 2021 , Pages 116-130 ; 03043975 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0304397521005090