Secret Sharing, Rank Inequalities and Information Inequalities

  • Sebastià Martín
  • Carles Padró
  • An Yang
Conference paper

DOI: 10.1007/978-3-642-40084-1_16

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8043)
Cite this paper as:
Martín S., Padró C., Yang A. (2013) Secret Sharing, Rank Inequalities and Information Inequalities. In: Canetti R., Garay J.A. (eds) Advances in Cryptology – CRYPTO 2013. Lecture Notes in Computer Science, vol 8043. Springer, Berlin, Heidelberg

Abstract

Beimel and Orlov proved that all information inequalities on four or five variables, together with all information inequalities on more than five variables that are known to date, provide lower bounds on the size of the shares in secret sharing schemes that are at most linear on the number of participants. We present here another negative result about the power of information inequalities in the search for lower bounds in secret sharing. Namely, we prove that all information inequalities on a bounded number of variables only can provide lower bounds that are polynomial on the number of participants.

Keywords

Secret sharing Information inequalities Rank inequalities Polymatroids 

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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Sebastià Martín
    • 1
  • Carles Padró
    • 2
  • An Yang
    • 2
  1. 1.Universitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Nanyang Technological UniversitySingapore

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