With data storage and sharing services in the cloud, users can easily modify and share data as a group. To ensure share data integrity can be verified publicly, users in the group need to compute signatures on all the blocks in shared data. Different blocks in shared data are generally signed by different users due to data modifications performed by different users. For security reasons, once a user is revoked from the group, the blocks which were previously signed by this revoked user must be re-signed by an existing user. The straight forward method, which allows an existing user to download the corresponding part of shared.............