We propose a generic mediated encryption (GME) system that converts any identity based encryption (IBE) to a mediated IBE. This system is based on enveloping an IBE encrypted message using a user's identity into another IBE envelope, using the identity of a security mediator (SEM) responsible for checking users for revocation. We present two security models based on the role of the adversary whether it is a revoked user or a hacked SEM. We prove that GME is as secure as the SEM's IBE (the envelope) against a revoked user and as secure as the user's IBE (the letter) against a hacked SEM. We also present two instantiations of GME. The first instantiation is based on the Boneh-Franklin (BF) FullIBE system, which is a pairing-based encryption system. The second instantiation is based on the Boneh, Gentry and Hamburg (BGH) system, which is a non pairing-based encryption system.