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 multisecret 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.