Natural Generalizations of Threshold Secret Sharing

  • Oriol Farràs
  • Carles Padró
  • Chaoping Xing
  • An Yang
Conference paper

DOI: 10.1007/978-3-642-25385-0_33

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7073)
Cite this paper as:
Farràs O., Padró C., Xing C., Yang A. (2011) Natural Generalizations of Threshold Secret Sharing. In: Lee D.H., Wang X. (eds) Advances in Cryptology – ASIACRYPT 2011. ASIACRYPT 2011. Lecture Notes in Computer Science, vol 7073. Springer, Berlin, Heidelberg

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 
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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Oriol Farràs
    • 1
    • 2
  • Carles Padró
    • 3
  • Chaoping Xing
    • 3
  • An Yang
    • 3
  1. 1.Universitat Rovira i VirgiliTarragonaSpain
  2. 2.Ben Gurion UniversityBe’er ShevaIsrael
  3. 3.Nanyang Technological UniversitySingapore

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