Chapter

Advances in Cryptology – ASIACRYPT 2011

Volume 7073 of the series Lecture Notes in Computer Science pp 610-627

Natural Generalizations of Threshold Secret Sharing

  • Oriol FarràsAffiliated withUniversitat Rovira i VirgiliBen Gurion University
  • , Carles PadróAffiliated withNanyang Technological University
  • , Chaoping XingAffiliated withNanyang Technological University
  • , An YangAffiliated withNanyang Technological University

Abstract

We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit an ideal linear secret sharing schemes over every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure the proofs for the existence of ideal secret sharing schemes for them.

Keywords

Cryptography secret sharing ideal secret sharing schemes multipartite secret sharing integer polymatroids