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 in order to recover the secret key. 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 algorithm to construct such φ function(s) for given access structures. Using the φ function, we also give an algorithm to construct secret sharing scheme for the access structures.
- M. Atici, Secret Sharing Scheme: Vector Space Secret Sharing Scheme and &phis; Function, IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, August 26--29, Istanbul-Turkey. Google Scholar
Digital Library
- M. Atici,Vector Space Secret Sharing and an Efficient Algorithm to Construct a &phis; Function, ACMSE'13, April 4--6, 2013, Savannah, GA, USA. Google ScholarDigital Library
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- Efficient Algorithm to Construct Perfect Secret Sharing Scheme for a Given Access Structure
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