An attack on a dynamic multi-secret sharing scheme and enhancing its security

In this paper we have analysed Zou and Zhang's scheme from the security point of view. An attack is proposed on verifiability and non secure channel in this paper. We have proved that this scheme needs a secure channel although this scheme has been proposed without a secure channel; in addition this scheme is not completely verifiable i.e. although the combiner verifies the scheme but the participants can cheat. Elliptic curves and bilinear maps together with the difficultly of solving discrete logarithm problems, a verifiable secret sharing scheme is proposed. Furthermore the proposed scheme has this property that all participants can select their shares; so the dealer can't cheat on the shares of participants. Security analyses show that our modifications on the proposed scheme solve both of the mentioned problems. In addition our modifications reduce the public values published by the dealer; so we have modified this scheme to an enhanced practical scheme.