Conjunctive and Disjunctive Compartmented Secret Sharing Schemes using Elliptic Curves

Abstract

This article considers two secret sharing schemes; conjunctive compartmented and disjunctive compartmented. The aim of the proposed schemes is that if there is a group of companies having many compartments, a specified number of users from each compartment of every company has to collaborate to access the secret key for the conjunctive compartmented scheme. While in a disjunctive compartmented scheme, any company with a predetermined number of users from each compartment can get the secret key. The schemes we have proposed use elliptic curves and bilinear pairings. Our schemes are verifiable and efficient. The proposed schemes are illustrated in full detail by concrete examples using SageMath.