In our scheme, as with the suggestion, we realize revocation through updating the private keys of the unrevoked users. But unlike that work which trivially concatenates time period with identity for key generation/update and requires to re-issue the whole private key for unrevoked users, we propose a novel collusion-resistant key issuing technique: we employ a hybrid private key for each user, in which an AND gate is involved to connect and bound two subcomponents, namely the identity component and the time component. Furthermore, we consider realizing revocable IBE with a semi-honest KU-CSP. To achieve this goal, we present a security enhanced construction under the recently formalized Refereed Delegation of Computation (RDoC) model.