Oblivious Polynomial Evaluation and Secure Set-Intersection from Algebraic PRFs

In this paper, we study the two fundamental functionalities oblivious polynomial evaluation in the exponent and set-intersection and introduce a new technique for designing efficient secure protocols for these problems (and others). Our starting point is the technique (Benabbas et al. in CRYPTO, 2011) for verifiable delegation of polynomial evaluations, using algebraic PRFs. We use this tool, that is useful to achieve verifiability in the outsourced setting, in order to achieve privacy in the standard two-party setting. Our results imply new simple and efficient oblivious polynomial evaluation (OPE) protocols. We further show that our OPE protocols are readily used for secure set-intersection, implying much simpler protocols in the plain model. As a side result, we demonstrate the usefulness of algebraic PRFs for various search functionalities, such as keyword search and oblivious transfer with adaptive queries. Our protocols are secure under full simulation-based definitions in the presence of malicious adversaries.