International Association for Cryptologic Research

International Association
for Cryptologic Research


A Combinatorial Approach to Quantum Random Functions

Nico Döttling
Giulio Malavolta
Sihang Pu
DOI: 10.1007/978-3-030-64834-3_21
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Abstract: Quantum pseudorandom functions (QPRFs) extend the classical security of a PRF by allowing the adversary to issue queries on input superpositions. Zhandry [Zhandry, FOCS 2012] showed a separation between the two notions and proved that common construction paradigms are also quantum secure, albeit with a new ad-hoc analysis. In this work, we revisit the question of constructing QPRFs and propose a new method starting from small-domain (classical) PRFs: At the heart of our approach is a new domain-extension technique based on bipartite expanders. Interestingly, our analysis is almost entirely classical. As a corollary of our main theorem, we obtain the first (approximate) key-homomorphic quantum PRF based on the quantum intractability of the learning with errors problem.
Video from ASIACRYPT 2020
  title={A Combinatorial Approach to Quantum Random Functions},
  booktitle={Advances in Cryptology - ASIACRYPT 2020},
  author={Nico Döttling and Giulio Malavolta and Sihang Pu},