Oracle Indistinguishability and Its Applications

There are many 'cascade-type' constructions in symmetric key cryptography. For these, the output of a PRF (or a block cipher) is cascaded to the key of the next PRF, and this continues until all blocks of the given message are exhausted. In order to prove the security of these constructions, traditionally multi-oracle families, together with query-based hybrid arguments are used, but these produce longer proofs which cannot be extended to quantum security. In this paper, we point that the oracle indistinguishability, first formalized by Zhandry and later extended by Song and Yun, is a useful tool for proving security of cascade-type constructions, both classically and quantumly. To illustrate this, using oracle indistinguishability, we give a classical security proof of NMAC. Also, we prove that the RC (Randomized Cascade) construction, which gives a PRF out of a weak PRF, is secure, both classically and quantumly.