The size of a share must be large

  • László Csirmaz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 950)


A secret sharing scheme permits a secret to be shared among participants of an n-element group in such a way that only qualified subsets of participants can recover the secret. If any non-qualified subset has absolutely no information on the secret, then the scheme is called perfect. The share in a scheme is the information what a participant must remember. We prove that for each n there exists an access structure on n participants so that any perfect sharing scheme must give some participant a share which is at least about n/log n times the secret size. We also show that the best possible result achievable by the information theoretic method used here is n times the secret size.

Key words

Secret sharing ideal secret sharing schemes polymatroid structures perfect security 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • László Csirmaz
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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