Advances in Cryptology – CRYPTO 2013

Volume 8043 of the series Lecture Notes in Computer Science pp 277-288

Secret Sharing, Rank Inequalities and Information Inequalities

  • Sebastià MartínAffiliated withLancaster UniversityUniversitat Politècnica de Catalunya
  • , Carles PadróAffiliated withLancaster UniversityNanyang Technological University
  • , An YangAffiliated withLancaster UniversityNanyang Technological University

* Final gross prices may vary according to local VAT.

Get Access


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.


Secret sharing Information inequalities Rank inequalities Polymatroids