Abstract
A perfect secret sharing scheme is a system for the protection of a secret among a number of participants in such a way that only certain subsets of these participants can reconstruct the secret, and the remaining subsets can obtain no additional information about the secret. The efficiency of a perfect secret sharing scheme can be assessed in terms of its information rates. In this paper we discuss techniques for obtaining bounds on the information rates of perfect secret sharing schemes and illustrate these techniques using the set of monotone access structures on five participants. We give a full listing of the known informtion rate bounds for all the monotone access structures on five participants.
Similar content being viewed by others
References
R. Blom, An Optimal class of symmetric key generation systems. Advances in Cryptology-Eurocrypt '84, Lecture Notes in Computer Science, Vol. 209 (1984) 335–338.
C. Blundo, A. De Santis, A. Herzberg, S. Kutten, U. Vaccaro, and M. Yung. Perfectly-secure key distribution for dynamic conferences. Advances in Cryptology-Crypto '92, Lecture Notes in Computer Science, Vol. 740 (1993) 471–486.
J. W. P. Hirschfeld: Projective geometries over finite fields, Clarendon Press (1979).
W.-A. Jackson and K. M. Martin. Geometric secret sharing schemes and their duals. Des. Codes Cryptogr. Vol. 4 (1994) 83–95.
W.-A. Jackson, K. M. Martin, and C. M. O'Keefe. Multisecret threshold schemes. Advances in Cryptology-Crypto '93, Lecture Notes in Computer Science, Vol. 773 (1994) 126–135.
R. Lidl and H. Niederreiter: Finite Fields, Cambridge University Press, Cambridge (1983).
T. Matsumoto and H. Imai. On the key predistribution system: A practical solution to the key predistribution problem. Advances in Cryptology: Crypto '87, Lecture Notes in Computer Science, Vol. 293 (1987) 185–193.
G. J. Simmons. An introduction to shared secret and/or shared control schemes and their application. Con-temporary Cryptology: The Science of Information Integrity, IEEE Press (1992).
D. R. Stinson. An explication of secret sharing schemes. Des. Codes Cryptogr. Vol. 2 (1992) 357–390.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jackson, WA., Martin, K.M. Perfect Secret Sharing Schemes on Five Participants. Designs, Codes and Cryptography 9, 267–286 (1996). https://doi.org/10.1023/A:1027328505246
Issue Date:
DOI: https://doi.org/10.1023/A:1027328505246