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Journal of Inforamtion Science and Engineering, Vol.15 No.5, pp.679-689 (September 1999)
Constructing Perfect Secret Sharing Schemes for General
And Uniform Access Structures

Hung-Min Sun and Shiuh-Pyng Shieh+
Department of Computer Science and Information Engineering
National Cheng Kung University
Tainan, Taiwan 701, R.O.C.
+Department of Computer Science and Information Engineering
National Chiao Tung University
Hsinchu, Taiwan 300, R.O.C.

A perfect secret sharing scheme allows a secret K to be shared among a set of participants in such a way that only qualified subsets of participants can recover the secret, and unqualified subsets of participants obtain no information regarding the secret. In this paper, we propose a construction of perfect secret sharing schemes with uniform, generalized access structures of rank 3. Compared with other constructions, our construction has some improved lower bounds on the information rate. In addition, we also generalize the construction to perfect secret sharing schemes with uniform, generalized access structures of constant rank.

Keywords: cryptography, information security, secret sharing schemes, threshold schemes, information theory, access structures

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Received May 13, 1997; accepted March 10, 1998.
Communicated by Jean-Lien C. Wu.
* This work was supported in part by the National Science Council, Taiwan, R.O.C. under Grant NSC 87-2213-E-324-003.