Access Structures of Elliptic Secret Sharing Schemes

It is a central problem in secret sharing to understand the access structures of secret sharing schemes. In Chen and Kramer, secret sharing schemes from algebraic-geometric codes and their applications in secure multiparty computation were proposed and studied. For any given finite field , these secret sharing schemes are ideal ramp secret sharing schemes and allow arbitrarily many players. In this correspondence, we give the access structures explicitly for the elliptic secret sharing schemes from algebraic-geometric (AG) codes associated with elliptic curves. Based on higher degree rational points on elliptic curves, we also construct some nonideal secret sharing schemes with weighted threshold structures.