Faster Secure Comparisons with Offline Phase for Efficient Private Set Intersection

In a Private section intersection (PSI) protocol, Alice and Bob compute the intersection of their respective sets without disclosing any element not in the intersection. PSI protocols have been extensively studied in the literature and are deployed in industry. With state-of-the-art protocols achieving optimal asymptotic complexity, performance improvements are rare and can only improve complexity constants. In this paper, we present a new private, extremely efficient comparison protocol that leads to a PSI protocol with low constants. A useful property of our comparison protocol is that it can be divided into an online and an offline phase. All expensive cryptographic operations are performed during the offline phase, and the online phase performs only four fast field operations per comparison. This leads to an incredibly fast online phase, and our evaluation shows that it outperforms related work, including KKRT (CCS 16), VOLE-PSI (EuroCrypt 21), and OKVS (Crypto 21). We also evaluate standard approaches to implement the offline phase using different trust assumptions: cryptographic, hardware, and a third party (dealer model).