Deterministic random oracles

The Random Oracle model popularized by Bellare and Rogaway in 1993 has proven to be hugely successful, allowing cryptographers to give security proofs for very efficient and practical schemes. In this paper, we discuss the possibility of using an incompressible but fixed, "algorithmically random" oracle instead of the standard random oracle and show that this approach allows for rather similar results to be proven but in a completely different way. We also show that anything provably secure in the standard random oracle model is also secure with respect to any algorithmically random oracle and then discuss the implications.