In the most present threshold multi-secret sharing scheme, there were some security problems, such as each participant’s shadow was generated by the dealer and the dealer would regenerate participant’s shadow when a participant was added or deleted. To overcome these problems, a (t,n) multi-secret sharing scheme based on the Discrete Logarithm Problem and Lagrange Interpolation Formula was proposed which could adjust the threshold value of a secret dynamically. This scheme has the following properties: 1)Each participant selected his shadow by himself and the dealer don’t know the shadow of any participant; 2)There was no secure channel between the dealer and the participants; 3)The dealer could adjust the threshold value depending on the secure level of different secret; 4)The participant could be dynamically added or deleted without having to redistribute new shadow to the older participant. Moreover, the efficient solutions against multiform cheating of any participant were proposed, therefore the proposed scheme has practicability and highly security.
