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

Document Type : Research Paper


1 Department of Pure Mathematics, Faculty of Mathematical Sciences, Uuniversity of Kashan, Kashan, I. R. Iran 8731753153

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran


‎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.


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