Journal of Cryptology

, Volume 10, Issue 4, pp 223–231

The Size of a Share Must Be Large

  • László Csirmaz

DOI: 10.1007/s001459900029

Cite this article as:
Csirmaz, L. J. Cryptology (1997) 10: 223. doi:10.1007/s001459900029


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 nonqualified subset has absolutely no information on the secret, then the scheme is called perfect. The share in a scheme is the information that a participant must remember.

In [3] it was proved that for a certain access structure any perfect secret sharing scheme must give some participant a share which is at least 50\percent larger than the secret size. 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.^1 We also show that the best possible result achievable by the information-theoretic method used here is n times the secret size.

^1 All logarithms in this paper are of base 2.

Key words. Secret sharing, Ideal secret sharing schemes, Polymatroid structures, Perfect security. 

Copyright information

© 1997 International Association for Criptologic Rese 1997

Authors and Affiliations

  • László Csirmaz
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of Sciences HU

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