A cryptographic method and apparatus is provided in which an identifier-based encryption process is used to encrypt a message with an identifier string that specifies conditions to be checked by a trusted entity before providing a decrypted form of the encrypted message, or enabling its decryption. A further trusted entity is used to verify the identity of the message sender as indicated by a further identifier string, and to provide the sender with a secret key that the sender uses to generate complimentary signature components. These signature components are sent along with the encrypted message and are used, along with other data including the first identifier string and a public key of the further trusted entity, to authenticate the identity of the message sender.