Verifiable Self-Selecting Secret Sharing Based on Elliptic Curves

Abstract

In distributed systems, as any network architecture, cryptography has a vital role in communication security, and sharing a secret represents a jump in this field where the secret depends on a group instead of a single person. In this article, the authors propose a method to share a multi secrets matrix represented by an image, that could be reconstructed without any loss by an access structure over a distributed system. The presented approach has a verifiable property, where each candidate possesses the advantage to verify the validity of his shadow. The security level of the scheme is based on elliptic curve discrete logarithm problem and the opportunity of allowing each side to generate a private sub-secret key for the sharing. The benefit of this method is justified by the absence of information loss and a lower timing results.