sentences: Group data sharing in cloud environments has become a hot topic in recent decades. With the popularity of cloud computing, how to achieve secure and efficient data sharing in cloud environments is an urgent problem to be solved. In addition, how to achieve both anonymity and traceability is also a challenge in the cloud for data sharing. This paper focuses on enabling data sharing and storage for the same group in the cloud with high security and efficiency in an anonymous manner. By leveraging the key agreement and the group signature, a novel traceable group data sharing scheme is proposed to support anonymous multiple users in public clouds. On the one hand, group members can communicate anonymously with respect to the group signature, and the real identities of members can be traced if necessary. On the other hand, a common conference key is derived based on the key agreement to enable group members to share and store their data securely. Note that a symmetric balanced incomplete block design is utilized for key generation, which substantially reduces the burden on members to derive a common conference key. Both theoretical and experimental analyses demonstrate that the proposed scheme is secure and efficient for group data sharing in cloud computing.