On the (Im)possibility of key dependent encryption

We study the possibility of constructing encryption schemes secure under messages that are chosen depending on the key k of the encryption scheme itself. We give the following separation results that hold both in the private and in the public key settings: Let be the family of poly(n)-wise independent hash-functions. There exists no fully-black-box reduction from an encryption scheme secure against key-dependent messages to one-way permutations (and also to families of trapdoor permutations) if the adversary can obtain encryptions of h(k) for . There exists no reduction from an encryption scheme secure against key-dependent messages to, essentially, any cryptographic assumption, if the adversary can obtain an encryption of g(k) for an arbitrary g, as long as the reduction's proof of security treats both the adversary and the function g as black boxes.