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A multi-stage secret sharing scheme with general access structures is proposed on the difficulty of the discrete logarithm problem over finite field. In this scheme, new secrets can be added. The participant set and the access structure can be changed dynamically without updating any participant's secret shadow. In addition, the computational complexity of the proposed scheme is very low because the degree of Lagrange interpolation polynomial used is only one. The proposed scheme has advantages over the existing schemes and is more practical.