Improving the Linear Programming Technique in the Search for Lower Bounds in Secret Sharing

  • Oriol Farràs
  • Tarik Kaced
  • Sebastià Martín
  • Carles Padró
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10820)

Abstract

We present a new improvement in the linear programming technique to derive lower bounds on the information ratio of secret sharing schemes. We obtain non-Shannon-type bounds without using information inequalities explicitly. Our new technique makes it possible to determine the optimal information ratio of linear secret sharing schemes for all access structures on 5 participants and all graph-based access structures on 6 participants. In addition, new lower bounds are presented also for some small matroid ports and, in particular, the optimal information ratios of the linear secret sharing schemes for the ports of the Vamos matroid are determined.

Keywords

Secret sharing Information inequalities Rank inequalities Common information Linear programming 

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Oriol Farràs
    • 1
  • Tarik Kaced
    • 2
  • Sebastià Martín
    • 3
  • Carles Padró
    • 3
  1. 1.Universitat Rovira i VirgiliTarragonaSpain
  2. 2.Sorbonne Université, LIP6ParisFrance
  3. 3.Universitat Politècnica de CatalunyaBarcelonaSpain

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