Correcting Subverted Random Oracles

The random oracle methodology has proven to be a powerful tool for designing and reasoning about cryptographic schemes. In this paper, we focus on the basic problem of correcting faulty or adversarially corrupted random oracles, so that they can be confidently applied for such cryptographic purposes. We prove that a simple construction can transform a "subverted" random oracle which disagrees with the original one at a small fraction of inputs into an object that is indifferentiable from a random function, even if the adversary is made aware of all randomness used in the transformation. Our results permit future designers of cryptographic primitives in typical kleptographic settings (i.e., those permitting adversaries that subvert or replace basic cryptographic algorithms) to use random oracles as a trusted black box.