Encryption Schemes Using Random Oracles: From Classical to Post-Quantum Security

Abstract

The security proofs of post-quantum cryptographic schemes often consider only classical adversaries. Therefore, whether such schemes are really post-quantum secure remains unknown until the proofs take quantum adversaries into account. Switching to a quantum adversary might require to adapt the security notion. In particular, post-quantum security proofs for schemes which use random oracles have to be in the quantum random oracle model (QROM), while classical security proofs are in the random oracle model (ROM). We remedy this state of affairs by introducing a framework to obtain post-quantum security of public key encryption schemes which use random oracles. We define a class of encryption schemes, called oracle-simple, and identify game hops which are used to prove such schemes secure in the ROM. For these game hops, we state both simple and sufficient conditions to validate that a proof also holds in the QROM. The strength of our framework lies in its simplicity, its generality, and its applicability. We demonstrate this by applying it to the code-based encryption scheme (Formula Presented) (Round 2 NIST candidate) and the lattice-based encryption scheme LARA (FC 2019). Thereby we prove that both schemes are post-quantum secure, which had not been shown before.