Mustafa Atici
ABSTRACT
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.
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Digital Library
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Index Terms
- Vector space secret sharing and an efficient algorithm to construct a ϕ function
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