Recent applications and growth on the internet have generated a lot of popularity and adoption of cloud computing which aims to assure the various computing resources. Data storage is one of the primary resources offered by the cloud; however, considering the multiple users in the particular cloud raises major concerns due to security. Recent researches shown great potential for providing efficient data sharing with multiple users. However, tracing of the data provider is still concerned to be a major issue. Hence, this research work proposes identifiable data sharing for multiple users (IDSMU) mechanism which aims to provide security for multiple users in a particular cloud group. At first, IDSMU creates the general participants (GP)-key for secure access to data. Further, IDSMU creates the trusted participants (TP) based on the reputation which further helps in creating the key generation. A novel signature scheme is used for identifying the participants; IDSMU is evaluated on computation count and efficiency is proved by comparing with an existing model considering computation count.