Secret Sharing Schemes on Access Structures with Intersection Number Equal to One
The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that is, access structures such that there is at most one participant in the intersection of any two minimal qualified subsets. Examples of such access structures are those defined by finite projective planes and those defined by graphs. In this work, ideal access structures with intersection number equal to one are completely characterized and bounds on the optimal information rate are provided for the non-ideal case.
KeywordsCryptography secret sharing schemes information rate ideal schemes
Unable to display preview. Download preview PDF.
- 1.Blakley, G.R.: Safeguarding cryptographic keys. AFIPS Conference Proceedings 48 (1979) 313–317Google Scholar
- 3.Blundo, C., De Santis, A., Gargano, L., Vaccaro, U.: On the information rate of secret sharing schemes. Advances in Cryptology CRYPTO’92. Lecture Notes in Comput. Sci. 740 148–167Google Scholar
- 9.Dembowski, P.: Finite geometries. Reprint of the 1968 original. Classics in Mathematics. Springer-Verlag, Berlin, 1997Google Scholar
- 10.Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing any access structure. Proc. IEEE Globecom’87 (1987) 99–102Google Scholar
- 13.Martí-Farré, J., Padró, C.: Secret sharing schemes with three or four minimal qualified subsets. Cryptology ePrint Archive (2002) Report 2002/050, http://eprint.iacr.org/