Lena Heimberger, Tobias Hennerbichler, Fredrik Meisingseth +2 more
Oblivious Pseudorandom Functions (OPRFs) are an elementary building block in cryptographic and privacy-preserving applications. While there are numerous pre-quantum secure OPRF constructions, it is unclear which of the proposed options for post-quantum secure constructions are practical for modern-day applications. In this work, we focus on isogeny group actions, as the associated low bandwidth leads to efficient constructions. We introduce OPUS, a novel Naor-Reingold-based OPRF from isogenies without oblivious transfer, and show efficient evaluations of the Naor-Reingold PRF using CSIDH and CSI-FiSh. Additionally, we analyze a previous proposal of a CSIDH-based OPRF and that the straightforward instantiation of the protocol leaks the server's private key. As a result, we propose mitigations to address those shortcomings, which require additional hardness assumptions. Our results report a very competitive protocol when combined with lattices for Oblivious Transfer.
ACM Asia Conference on Computer and Communications Security (ASIA CCS)•Jun 28, 2024•14 citations