Abstract: A dynamic cheat-proof multi-group-secret sharing scheme based on the discrete logarithm and lagrange interpolation formula is proposed.In the proposed scheme，m groups of secrets being shared among n participants，each group of secrets has a different threshold access structure and includes a distinct number of secrets.Each participant selects her/his shadow by her/himself and the dealer don’t know the shadow of any participant，so there is not need a security channel.Each participant is able to check whether another participant provides the valid information or not in the recovery phase.Each participant holds only one shadow while sharing many groups’ secrets with other participants.The security of the proposed scheme can be guaranteed due to the difficulty in solving the discrete logarithm problem.

摘要： 基于离散对数及拉格朗日插值公式提出了一个动态防欺诈的多组秘密共享方案。在该方案中，m组秘密根据不同的门限值在n个参与者中共享，秘密份额由参与者自己选择，因而秘密分发者和参与者之间不需要维护安全信道，每个参与者可以在恢复阶段验证其他参与者是否进行了欺诈，每个参与者只需持有一个秘密份额就可以实现多组秘密的共享。方案的安全性基于离散对数问题的难解性。