Abstract: The challenge of designing a dynamic group signature scheme is to construct an efficient group member revocation mechanism. We design a new revocation mechanism. For the group manager and group member, all need to do is to communicate with the revocation Turing. When the Turing determines their identities, the revocation token is added into the revocation list to complete the revocation operation. So it is more suitable for groups with more members. Using this mechanism, we propose a new dynamic group signature scheme based on learning with errors (LWE) problem and the small integer solution (SIS) assumption, in which any user can join and leave the group at any time. Compared with existing schemes, group public key is fixed in length and shorter. When a user joins into the group, he needs less downloads. So, we can provide a higher efficiency in practical applications.