An Ideal Secret Sharing Scheme Realizing an Access Structure Based on a Finite Projective Plane of Order 3

Abstract

A secret sharing scheme is one of cryptographic primitives to share a secret among participants so that only qualified subsets of participants can access the secret. In this paper, we give a new access structure with 13 participants based on a finite projective plane of order 3 and construct an ideal secret sharing scheme realizing the access structure. The minimal qualified set of the access structure consists of all the lines of the finite projective plane as well as all the collection of 7-point sets satisfying a certain property. The soundness of the scheme is established theoretically together with exhaustive search by computer.