J. Martí-Farré and C.
Padró.
Ideal secret sharing schemes whose
minimal qualified subsets have at most three participants.
Fifth
Conference on
Security and Cryptography for Networks, SCN 2006, Lecture Notes in Computer Science 4116 (2006) 201-215. Maiori, Italy,
2006.
Abstract
One of the main open problems in secret sharing is the characterization
of the access structures of ideal secret sharing schemes. As a
consequence of the results by Brickell and Davenport, every one of
those access structures is related in a certain way to a unique
matroid. We study this open problem for access structures with rank
three, that is, structures whose minimal qualified subsets have at most
three participants. We prove that all access structures with rank three
that are related to matroids with rank greater than three are ideal.
After the results in this paper, the only open problem in the
characterization of the ideal access structures with rank three is to
characterize the matroids with rank three that can be represented by an
ideal secret sharing scheme.