A fair and efficient mutual private set intersection protocol from a two-way oblivious pseudorandom function

Abstract

We present a two-way Oblivious Pseudorandom Function (mOPRF) secure in the malicious model under the Decisional Composite Residuosity (DCR) and Decisional Diffie-Hellman (DDH) assumptions. Using this mOPRF, we construct an optimistic mutual Private Set Intersection (mPSI) protocol preserving fairness. Unlike existing optimistic protocols our mPSI supports semi-trusted arbiter instead of fully-trusted arbiter. Semi-trusted arbiter never get access to the private information of any of the parties while follow the protocol honestly. Our design is the first fair mPSI with linear communication and computation complexities, and is proven to be secure in the standard model against malicious parties under Decisional q-Diffie-Hellman Inversion (Dq-DHI), DCR and DDH assumptions.