This document proposes a novel approach for secure group data sharing in cloud computing using a symmetric balanced incomplete block design (SBIBD). The approach aims to enable anonymous yet traceable data sharing among group members in the cloud. It uses the concept of group signature and SBIBD to efficiently generate a common group key for encrypting and decrypting shared data, providing security while supporting group data sharing. The SBIBD and group signature techniques are used to achieve privacy, security, traceability and efficient access control. Experimental results demonstrate the effectiveness of generating the group key and uploading/accessing encrypted files through the group manager. The proposed approach supports dynamic membership changes and is secure and efficient for group data sharing in cloud computing.