Oblivious Pseudo-Random Functions via Garbled Circuits

An Oblivious Pseudo-Random Function (OPRF) is a protocol that allows two parties – a server and a user – to jointly compute the output of a Pseudo-Random Function (PRF). The server holds the key for the PRF and the user holds an input on which the function shall be evaluated. The user learns the correct output while the inputs of both parties remain private. If the server can additionally prove to the user that several executions of the protocol were performed with the same key, we call the OPRF verifiable.
One way to construct an OPRF protocol is by using generic tools from multi-party computation, like Yao’s seminal garbled circuits protocol. Garbled circuits allow two parties to evaluate any boolean circuit, while the input that each party provides to the circuit remains hidden from the respective other party. An approach to realizing OPRFs based on garbled circuits was e.g. mentioned by Pinkas et al. (ASIACRYPT ’09). But OPRFs are used as a building block in various cryptographic protocols. This frequent usage in conjunction with other building blocks calls for a security analysis that takes composition, i.e., the usage in a bigger context into account.
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In this work, we give the first construction of a garbled-circuit-based OPRF that is secure in the universal composability model by Canetti (FOCS ’01). This means the security of our protocol holds even if the protocol is used in arbitrary execution environments, even under parallel composition. We achieve a passively secure protocol that relies on authenticated channels, the random oracle model, and the security of oblivious transfer. We use a technique from Albrecht et al. (PKC ’21) to extend the protocol to a verifiable OPRF by employing a commitment scheme. The two parties compute a circuit that only outputs a PRF value if a commitment opens to the right server-key.
Further, we implemented our construction and compared the concrete efficiency with two other OPRFs. We found that our construction is over a hundred times faster than a recent lattice-based construction by Albrecht et al. (PKC ’21), but not as efficient as the state-of-the-art protocol from Jarecki et al. (EUROCRYPT ’18), based on the hardness of the discrete logarithm problem in certain groups. Our efficiency-benchmark results imply that – under certain circumstances – generic techniques as garbled circuits can achieve substantially better performance in practice than some protocols specifically designed for the problem.
Büscher et al. (ACNS ’20) showed that garbled circuits are secure in the presence of adversaries using quantum computers. This fact combined with our results indicates that garbled-circuit-based OPRFs are a promising way towards efficient OPRFs that are secure against those quantum adversaries.