We instantiate the hash-then-evaluate paradigm for pseudorandom functions (PRFs), \(\textsf{PRF}(k,x):=\textsf{wPRF}(k,\textsf{RO}(x))\) , which builds a PRF \(\textsf{PRF}\) from a weak PRF \(\textsf{wPRF}\) via a public pre-processing random oracle \(\textsf{RO}\) . In applications to secure multiparty computation (MPC), only the low-complexity \(\textsf{wPRF}\) performs secret-depending operations. Our construction replaces \(\textsf{RO}\) by \(f(k_\textsf{H},\textsf{elf}(x))\) , where f is a non-adaptive PRF and the key \(k_\textsf{H}\) is public and thus known to the distinguishing adversary. We show that, perhaps surprisingly, several existing weak PRF candidates are plausibly also secure when their inputs are generated by \(f(k_\textsf{H},\textsf{elf}(.))\) . Firstly, analogous cryptanalysis applies (because pseudorandomness of f implies good statistical properties) and/or secondly an attack against the weak PRF with such pseudorandom inputs generated by f would imply surprising results such as key agreement from the hardness of the high-noise version of the Learning Parity with Noise (LPN) when implementing both \(\textsf{wPRF}\) and f from this assumption. Our simple transformation of replacing \(\textsf{RO}(\cdot )\) public pre-processing by \(f(k_\textsf{H},\textsf{elf}(x))\) public pre-processing applies to the entire family of PRF-style functions. Specifically, we obtain results for oblivious PRFs, which are a core building block for password-based authenticated key exchange (PAKE) and private set intersection (PSI) protocols, and we also obtain results for pseudorandom correlation functions (PCF), which are a key tool for silent oblivious transfer (OT) extension.
