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The optimal information rate for graph access structures of nine participants

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Abstract

The information rate is an important metric of the performance of a secret-sharing scheme. In this paper we consider 272 non-isomorphic connected graph access structures with nine vertices and eight or nine edges, and either determine or bound the optimal information rate in each case. We obtain exact values for the optimal information rate for 231 cases and present a method that is able to derive information-theoretical upper bounds on the optimal information rate. Moreover, we apply some of the constructions to determine lower bounds on the information rate. Regarding information rate, we conclude with a full listing of the known optimal information rate (or bounds on the optimal information rate) for all 272 graphs access structures of nine participants.

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Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Yun Song & Zhihui Li

  2. College of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Yongming Li

  3. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Ren Xin

Authors
  1. Yun Song
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  2. Zhihui Li
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  3. Yongming Li
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  4. Ren Xin
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Corresponding author

Correspondence to Zhihui Li.

Additional information

Yun Song received her MS in cryptography from Shaanxi Normal University, China in 2012. She is currently a PhD candidate in cryptography at Shaanxi Normal University. Her research interests lie in information security and quantum secret sharing.

Zhihui Li received her PhD in computer software and theory from Northwestern Polytechnical University, China. She is currently a professor in the College of Mathematics and Information Science at Shaanxi Normal University in China. She has published more than 60 academic papers in international conferences and journals. Her research interests are in the areas of information security, coding theory and quantum information.

Yongming Li received his PhD from Sichuan University. He is currently a professor in the College of Computer Science at Shaanxi Normal University, China. His research interests are in the areas of computational intelligence, quantum logic, quantum computation and quantum information. Dr. Li has published over 200 technical papers in international journals and conference proceedings. He has served as a reviewer to numerous international journals, and as a committee member to many conferences and review panels.

Ren Xin received his PhD from Xi’an University of Architecture and Technology, China in 2012. He got a postdoctoral position in Beijing University of Technology in 2014. He is currently a lecturer in the School of Civil Engineering at Xi’an University of Architecture and Technology in China. His research interests are in the areas of computer graphics, numerical analysis of finite elements and engineering structure reliability theory.

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Song, Y., Li, Z., Li, Y. et al. The optimal information rate for graph access structures of nine participants. Front. Comput. Sci. 9, 778–787 (2015). https://doi.org/10.1007/s11704-015-3255-6

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  • DOI: https://doi.org/10.1007/s11704-015-3255-6

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