Paper 2024/544 Original: eprint.iacr.org/2024/544 ↗

A post-quantum Distributed OPRF from the Legendre PRF

Abstract

A distributed OPRF enables a client to evaluate a pseudo-random function on a client-chosen input using a distributed key shared among multiple servers, ensuring that the servers learn nothing about the input or output, while the client learns nothing about the key. We present a post-quantum OPRF suitable for a distributed server setting, requiring only two rounds of communication between the client and servers, with server-to-server communication limited to a pre-computation phase. Our approach leverages the Legendre PRF, computed through a single MPC multiplication and opening during the online phase. We introduce a novel MPC technique that achieves multiplication and opening in one round using replicated secret sharing (RSS) in a malicious adversarial model. This allows for the quantum-secure, verifiable evaluation of the Legendre OPRF against malicious adversaries under a threshold assumption, without requiring inter-server communication. Beyond the Legendre PRF, this method is also of interest for general MPC operations. To our knowledge, our distributed OPRF (dOPRF) is the first post-quantum construction with these properties. We compare our approach to state-of-the-art MPC solutions and provide an implementation of our proposed dOPRF, benchmarking it against existing OPRF constructions. In our comparison, our dOPRF protocol demonstrates superior efficiency.