On Central Primitives for Quantum Cryptography with Classical Communication

Abstract

Recent work has introduced the “Quantum-Computation Classical-Communication” (QCCC) (Chung et al.) setting for cryptography. There has been some evidence that One Way Puzzles ($\textsf{OWPuzz}$) are the natural central cryptographic primitive for this setting (Khurana and Tomer). For a primitive to be considered central it should have several characteristics. It should be well behaved (which for this paper we will think of as having amplification, combiners, and universal constructions); it should be implied by a wide variety of other primitives; and it should be equivalent to some class of useful primitives. We present combiners, correctness and security amplification, and a universal construction for $\textsf{OWPuzz}$. Our proof of security amplification uses a new and cleaner construction of EFI from $\textsf{OWPuzz}$ (in comparison to the result of Khurana and Tomer) that generalizes to weak $\textsf{OWPuzz}$ and is the most technically involved section of the paper. It was previously known that $\textsf{OWPuzz}$ are implied by other primitives of interest including commitments, symmetric key encryption, one way state generators ($\textsf{OWSG}$), and therefore pseudorandom states ($\textsf{PRS}$). However we are able to rule out $\textsf{OWPuzz}$’s equivalence to many of these primitives by showing a black box separation between general $\textsf{OWPuzz}$ and a restricted class of $\textsf{OWPuzz}$ (those with efficient verification, which we call $\mathsf {EV-OWPuzz}$). We then show that $\mathsf {EV-OWPuzz}$ are also implied by most of these primitives, which separates them from $\textsf{OWPuzz}$ as well. This separation also separates extending $\textsf{PRS}$ from highly compressing $\textsf{PRS}$ answering an open question of Ananth et al.