Cryptology ePrint Archive: Report 2002/106

Secret sharing schemes on access structures with intersection number equal to one

Jaume Marti-Farre and Carles Padro

Abstract: 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 different minimal qualified subsets. The main result in this work is the complete characterization of the ideal access structures with intersection number equal to one. Besides, bounds on the optimal information rate are provided for the non-ideal case.

Category / Keywords: cryptographic protocols / secret sharing, information rate, ideal secret sharing schemes

Publication Info: This is a preliminary version of the paper that appeared in Discrete Applied Mathematics. A previous version appeared in the Proceedings of SCN'02, Amalfi, Italy, 2002

Date: received 30 Jul 2002, last revised 15 Jan 2007

Contact author: matcpl at mat upc es

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Note: 15 January 2007: Publication Info updated.

Version: 20070115:164717 (All versions of this report)

Short URL: ia.cr/2002/106

Discussion forum: Show discussion | Start new discussion