An Efficient Threshold Verifiable Multi-Secret Sharing Scheme Using Generalized Jacobian of Elliptic Curves

In a (t,n)-threshold secret sharing scheme, a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together, but no group of fewer than t participants can do. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao, and the intractability of the elliptic curve discrete logarithm problem (ECDLP) by using generalized Jacobian of elliptic curves. The proposed scheme has all the benefits of Shao and Cao, however, our scheme no need to a secure channel. Furthermore, we exploit the techniques via elliptic curves to perform the scheme. This can be very important because the hardness of discrete logarithm problem on elliptic curves increases security of the proposed scheme.