How to check the integrity of a key received through mail using symmetric encryption? I would like to provide access to encrypted data through a cloud service provider, using a pay-as-you-go model. This means that we will sometimes need to revoke a user's access to the data. To restrict a revoked user's access, the CSP will re-encrypt the data and send the new key to valid users only through their mail.

Before using the new key they received by mail, however, the users will presumably need some way to verify its integrity and authenticity. If possible, I would like to implement this using only symmetric encryption (like AES) instead of asymmetric encryption like RSA. Is this possible, and if so, how?
Unfortunately, symmetric encryption do not provide integrity and digital signature functions. This is because symmetric encryption uses the same key for exncryption and decryption. This means that any who owns the decryption key can alter the data and no one will notice that the data is altered, because the same key was used for encryption.

This means that data integrity can be provided only by using asymmetric cryptography.