Random Oracles and Auxiliary Input

We introduce a variant of the random oracle model where oracledependent auxiliary input is allowed. In this setting, the adversary gets an auxiliary input that can contain information about the random oracle. Using simple examples we show that this model should be preferred over the classical variant where the auxiliary input is independent of the random oracle. In the presence of oracle-dependent auxiliary input, the most important proof technique in the random oracle model—lazy sampling—does not apply directly. We present a theorem and a variant of the lazy sampling technique that allows one to perform proofs in the new model almost as easily as in the old one. As an application of our approach and to illustrate how existing proofs can be adapted, we prove that RSA-OAEP is IND-CCA2 secure in the random oracle model with oracle-dependent auxiliary input.