This article introduces a new concept of encryption, the cooperative encryption (CORE), to control encryption capability, i.e., only permitted (not any) users can encrypt messages with their public keys. In CORE, any message encrypted with a user public key can be decrypted only after it is matured by the security mediator (SEM). Compared with the other security controllable encryption systems, CORE can be more flexibly applied to various encryption systems, e.g., identity-based and attribute-based encryptions, supported by encrypting user private keys tightly. Moreover, CORE can directly revoke the corrupted SEM without re-issuing user private keys and prevent from producing a complete ciphertext, which is not cooperatively computed with the SEM, by users with the disclosed security mediated keys. Generally, CORE is of unique interest in fully controlling user encryption/decryption behaviors in controllable security services, and supporting distributed SEMs for large scale networks. This work also develops the framework of CORE, and proposes two constructions of CORE to identity-based and attribute-based encryptions, which are empowered to achieve two essential security properties, i.e., immediate revocation and unforgeable encryption. In addition, this work analyzes the security and performance of the proposed schemes. Overall, CORE provides a new notion of controllable security without involving any trust authority or key management server.