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A dynamic and verifiable multiple secrets sharing scheme with general access structure, is proposed in this paper. The scheme only needs to construct degree Lagrange interpolation polynomial and secrets can be shared in each sharing process without secure channel. That allows each participant to choose his secret shadow by himself and cheating is verifiable. In addition, it can dynamically change the participant set, the qualified subset and even the number of the shared secrets without refreshing any participantpsilas secret shadow. Furthermore because the scheme is based on general access structure, it will be more flexible and easier to implement than the threshold one. The security of the proposed scheme is based on the Shamirpsilas secret sharing scheme and the intractability of the discrete logarithm. In a word, the scheme is secure, efficient and could provide great capabilities for many applications, such as in multi-user work.