Paper 2025/152

Efficient Quantum-safe Distributed PRF and Applications: Playing DiSE in a Quantum World

Abstract

We propose the first $\mathit{\text{distributed}}$ version of a simple, efficient, and provably quantum-safe pseudorandom function (PRF). The distributed PRF (DPRF) supports arbitrary threshold access structures based on the hardness of the well-studied Learning with Rounding (LWR) problem. Our construction (abbreviated as $\mathsf{PQDPRF}$) practically outperforms not only existing constructions of DPRF based on lattice-based assumptions, but also outperforms (in terms of evaluation time) existing constructions of: (i) classically secure DPRFs based on discrete-log hard groups, and (ii) quantum-safe DPRFs based on any generic quantum-safe PRF (e.g. AES). The efficiency of $$ stems from the extreme simplicity of its construction, consisting of a simple inner product computation over $$, followed by a rounding to a smaller modulus $$. The key technical novelty of our proposal lies in our proof technique, where we prove the correctness and post-quantum security of $$ (against semi-honest corruptions of any less than threshold number of parties) for a polynomial $$ (equivalently, "modulus to modulus")-ratio. Our proposed DPRF construction immediately enables efficient yet quantum-safe instantiations of several practical applications, including key distribution centers, distributed coin tossing, long-term encryption of information, etc. We showcase a particular application of $$ in realizing an efficient yet quantum-safe version of distributed symmetric-key encryption ($$ -- originally proposed by Agrawal et al. in CCS 2018), which we call $$. For semi-honest adversarial corruptions across a wide variety of corruption thresholds, $$ substantially outperforms existing instantiations of $$ based on discrete-log hard groups and generic PRFs (e.g. AES). We illustrate the practical efficiency of our $$ via prototype implementation of $$.