Verifiable Threshold Scheme in Multi-Secret Sharing Distributions upon Extensions of ECC
Wireless Personal Communications: An International Journal
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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,2 P_2 + ... + a_i,t Pt 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.