A (t, n)-Threshold Verified Multi-secret Sharing Scheme Based on ECDLP

In this article, we propose a (t,n) threshold verifiable multi-secret sharing scheme, in which to reconstruct t secrets needs to solve t simultaneous equations. The analysis results show that our scheme is as easy as Yang´s scheme [8] in the secret reconstruction and requires less public values than Chien´s [7] and Yang´s schemes. Furthermore, the shares in our scheme can be verified their validity with t public values based on ECDLP, and there are two verified forms: one is computationally secure as Feldman ´s scheme [12] and other is unconditionally secure as Pedersen´s scheme [13]. In addition, for the main computation: a_i,1P₁ + a_i,2P₂ + _hellip + a_i,tP_t in our scheme, we present a new method based on the signed factorial expansion and implement it, the results show that it is more efficient than the current public methods. Thus our scheme is a secure and efficient (t,n) threshold verified multi-secret sharing scheme.