In recent years, with the increasing digitization of various information and assets, signature technologies to guarantee data integrity have been actively researched. Among them, group signature is a signature protocol that is suitable for generating signatures by a representative of a group such as a company. In a group signature, a group is formed by multiple users. In order to reduce the size of the group signature, a technique called accumulator is sometimes used. The accumulator compresses the original set of data into a single small value and uses the compressed value to prove that each element of the set is included. In order to use a large number of data at once, the accumulator is required to have functions to update the source of the set efficiently and to prove multiple elements simultaneously. Libert et al. and Ling et al. proposed an accumulator based on the lattice problem, and proposed a group signature protocol using it. However, there are problems in the efficient update of the source of the set and the simultaneous proof function. In this study, we propose an efficient update function of the source of a set based on the lattice problem. Furthermore, we apply the proposed update function to Ling et al.'s group signature, and improve the signature protocol by changing the information to be disclosed to each user.