How to Construct Quantum Random Functions

Pseudorandom functions (PRFs) are one of the foundational concepts in theoretical computer science, with numerous applications in complexity theory and cryptography. In this work, we study the security of PRFs when evaluated on quantum superpositions of inputs. The classical techniques for arguing the security of PRFs do not carry over to this setting, even if the underlying building blocks are quantum resistant. We therefore develop a new proof technique to show that many of the classical PRF constructions remain secure when evaluated on superpositions.