A note on the security of KHL scheme

A public key trace and revoke scheme combines the functionality of broadcast encryption with the capability of traitor tracing. In Asiacrypt 2003, Kim, Hwang and Lee proposed a public key trace and revoke scheme (referred to as KHL scheme), and gave the security proof to support that their scheme is z-resilient against adaptive chosen-ciphertext attacks, in which the adversary is allowed to adaptively issue decryption queries as well as adaptively corrupt up to z users. In the passed ten years, KHL scheme has been believed as one of the most efficient public key trace and revoke schemes with z-resilience against adaptive chosen-ciphertext attacks under the well-studied DDH assumption. However, in this paper, by giving a concrete attack, we indicate that KHL scheme is actually not secure against adaptive chosen-ciphertexts, even without corruption of any user. We then identify the flaws in the security proof for KHL-scheme, and discuss the consequences of the attack.