Instantiating Random Oracles via UCEs

This paper provides a (standard-model) notion of security for (keyed) hash functions, called UCE, that we show enables instantiation of random oracles (ROs) in a fairly broad and systematic way. Goals and schemes we consider include deterministic PKE; message-locked encryption; hardcore functions; point-function obfuscation; OAEP; encryption secure for key-dependent messages; encryption secure under related-key attack; proofs of storage; and adaptively-secure garbled circuits with short tokens. We can take existing, natural and efficient ROM schemes and show that the instantiated scheme resulting from replacing the RO with a UCE function is secure in the standard model. In several cases this results in the first standard-model schemes for these goals. The definition of UCE-security itself is quite simple, asking that outputs of the function look random given some “leakage,” even if the adversary knows the key, as long as the leakage does not permit the adversary to compute the inputs.