Just-in-Time-OPRFs and a Modular Framework for Fast Private Set Intersection

This paper gives a modular and unified framework within which to derive fast protocols for Private Set Intersection (PSI). At the core of this is a new primitive, that we define, and that we call a Just-In-Time OPRF (JIT-OPRF). We show how to obtain PSI generically from any JIT-OPRF, and then how to obtain JIT-OPRFs from Oblivious Transfer (OT) and Vector Oblivious Linear Evaluation (VOLE). We recover as special cases PSI protocols in the literature based on these two assumptions. Our results and proofs throughout are concrete rather than asymptotic, with explicit bounds that allow one to determine security parameters to achieve a desired level (e.g. 128 bits) of proven security in practice. Our results show interesting differences in the concrete security of OT and VOLE based PSI. Beyond the practical contribution of concrete-security, our work adds conceptual simplicity to this area, and opens the door to new PSI protocols via the construction of new JIT-OPRFs.