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Optimal Non-perfect Uniform Secret Sharing Schemes

  • Oriol Farràs
  • Torben Hansen
  • Tarik Kaced
  • Carles Padró
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8617)

Abstract

A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this end, we extend the known connections between polymatroids and perfect secret sharing schemes to the non-perfect case.

In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information that every subset of participants obtains about the secret value. We prove that there exists a secret sharing scheme for every access function.

Uniform access functions, that is, the ones whose values depend only on the number of participants, generalize the threshold access structures. Our main result is to determine the optimal information ratio of the uniform access functions. Moreover, we present a construction of linear secret sharing schemes with optimal information ratio for the rational uniform access functions.

Keywords

Secret sharing Non-perfect secret sharing Information Ratio Polymatroid 

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Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Oriol Farràs
    • 1
  • Torben Hansen
    • 2
  • Tarik Kaced
    • 3
  • Carles Padró
    • 4
  1. 1.Universitat Rovira i VirgiliTarragonaSpain
  2. 2.Aarhus UniversityAarhusDenmark
  3. 3.The Chinese University of Hong KongHong Kong
  4. 4.Nanyang Technological UniversitySingapore

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