LeOPaRd: Towards Practical Post-quantum Oblivious PRFs via 2HashDH Paradigm

In this work, we introduce a more efficient post-quantum oblivious PRF (OPRF) design, called LeOPaRd. Our proposal is round-optimal and supports verifiability and partial obliviousness, all of which are important for practical applications. The main technical novelty of our work is a new method for computing samples of MLWE (Module Learning With Errors) in a two-party setting. To do this, we introduce a new family of (interactive) lattice problems, called MLWE-PRF with re-use (MLWE-PRF-RU). Here, the adversary is given a mix of MLWE and PRF samples where each PRF error is dependent on an adversarially-chosen matrix and the MLWE error. We rigorously study the hardness of MLWE-PRF-RU and provide a reduction from the standard MLWE to MLWE-PRF-RU, establishing a strong security foundation. We believe MLWE-PRF-RU problem family and the intermediate security reductions we introduce along the way can be of independent interest for other interactive protocols.

LeOPaRd exploits this MLWE-PRF-RU assumption to realize a lattice-based OPRF design without relying on heavy machinery such as noise flooding and fully homomorphic encryption used in earlier works. LeOPaRd can feature around 138 KB total communication, compared to 300+ KB in earlier works, while also achieving about 2x reduction in online communication compared to the prior state-of-the-art result. We also identify gaps in some existing constructions and models, and propose appropriate fixes.