Communications of the ACM
Cryptography: Theory and Practice,Second Edition
Cryptography: Theory and Practice,Second Edition
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Secret Sharing Scheme: Vector Space Secret Sharing and F Function
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
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The threshold scheme, the monotone circuit construction, and the vector space construction are some of the well-known secret sharing schemes in cryptography. The threshold and monotone circuit secret sharing schemes are fairly easy to construct for any given access structure Γ. The construction of a secret sharing scheme realizing a given access structure Γ with Vector Space Construction requires the existence of a function φ from a set of participants into a vector space, that is, φ: P → (Zp)d. This function φ must satisfy certain conditions. There is no known algorithm to construct such a function φ in general. Constructions are mainly done by trial and error. In this paper, we develop polynomial algorithms to construct φ functions for vector space secret sharing scheme realizing certain types of access structures. Some examples are given to illustrate the algorithms.