Paper 2025/2215 Original: eprint.iacr.org/2025/2215 ↗

Obfuscating Pseudorandom Functions is Post-Quantum Complete

Abstract

The last decade has seen remarkable success in designing and uncovering new applications of indistinguishability obfuscation (i$\mathcal{O}$). The main pressing question in this area is whether post-quantum i$\mathcal{O}$ exists. All current lattice-based candidates rely on new, non-standard assumptions, many of which are known to be broken. To make systematic progress on this front, we investigate the following question: can general-purpose i$\mathcal{O}$ be reduced, assuming only learning with errors (LWE), to obfuscating a smaller class of functions? The specific class of functions we consider are {\em pseudorandom functions} (PRFs), which constitute a natural functionality of independent interest. We show the following results: - We construct exponentially-efficient i$\mathcal{O}$ (xi$\mathcal{O}$) for general circuits based on LWE in the pseudorandom oracle model -- a variant of the Random Oracle model (Jain et al., CRYPTO'23). Our construction requires the pseudorandom oracle model heuristic to hold for a specific pseudorandom function and we prove its security against classical adversaries. - We construct (post-quantum) i$\mathcal{O}$ for general circuits in the standard model based on (post-quantum) sub-exponentially secure LWE and (post-quantum) sub-exponentially secure {\em average-case} i$\mathcal{O}$ -- a natural notion of i$\mathcal{O}$ for pseudorandom functions that we define. To obtain these results, we generalize the ``encrypt-evaluate-decrypt'' paradigm used in prior works by replacing the use of fully homomorphic encryption with succinct secure two-party computation where parties obtain additive output shares (Boyle et al., EUROCRYPT'25 and Abram et al., STOC'25).