A verifiable secret sharing scheme without dealer in vector space

Based on the (+, +) homomorphism property of shamir´s (t, n) secret sharing scheme, Harn and Lin proposed a (n, t, n) secret sharing scheme, in which each shareholder also acts as a dealer and the master secret was decided by the sub-secret of each shareholder. But this scheme is only suited to the threshold access structure. In this paper, we firstly define the (+, +) homomorphism property of secret sharing scheme in vector space. Then we extend the idea of (n, t, n) secret sharing scheme to vector space access structure, and define the secret sharing scheme without dealer in vector space and propose a verifiable secret sharing scheme without dealer in vector space based on the intractability of discrete logarithm. Compared with Harn and Lin´s (n, t, n) secret sharing scheme, the proposed scheme is more general and is applied more widely since it is suited to vector space access structure.