Security analysis of a multi-receiver identity-based key encapsulation mechanism

In INDOCRYPT 2006, Chatterjee and Sarkar suggested a multi-receiver identity-based key encapsulation mechanism that is secure in the full model without random oracles. Until now, it has been believed that their scheme is the only one to provide such a security feature, while achieving sub-linear size ciphertext. In this letter, we show that their scheme is insecure in the sense that any revoked user can retrieve a message encryption key, even without colluding with other revoked users. Our attack comes from an analysis of a publicly computable surjective function used in the scheme.