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On Central Primitives for Quantum Cryptography with Classical Communication

Kai-Min Chung, Eli Goldin, Matthew Gray

TL;DR

This work identifies one-way puzzles ($OWPuzz$) as a natural central primitive for quantum cryptography with classical communication ($QCCC$) and develops a cohesive framework connecting them to EFI/EFID/EFI primitives. It provides a cleaner EFI-from-$OWPuzz$ construction, robust combiners, and universal constructions, along with amplification techniques that transform weakened puzzles into strong ones. The paper also analyzes efficient verifiability, proving black-box separations between $OWPuzz$ and $EV$-$OWPuzz$, and shows equivalences to random-input and distributional variants, thereby unifying several formulations of centrality. Collectively, these results outline how many $QCCC$ primitives can be built from $OWPuzz$ while highlighting fundamental barriers to certain black-box reductions, and they clarify the relationships between $OWPuzz$, EFID/EFI, and PRS in the quantum setting.

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 (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 OWPuzz. Our proof of security amplification uses a new and cleaner version construction of EFI from OWPuzz (in comparison to the result of Khurana and Tomer) that generalizes to weak OWPuzz and is the most technically involved section of the paper. It was previously known that OWPuzz are implied by other primitives of interest including commitments, symmetric key encryption, one way state generators (OWSG), and therefore pseudorandom states (PRS). However we are able to rule out OWPuzz's equivalence to many of these primitives by showing a black box separation between general OWPuzz and a restricted class of OWPuzz (those with efficient verification, which we call EV-OWPuzz). We then show that EV-OWPuzz are also implied by most of these primitives, which separates them from OWPuzz as well. This separation also separates extending PRS from highly compressing PRS answering an open question of Ananth et. al.

On Central Primitives for Quantum Cryptography with Classical Communication

TL;DR

This work identifies one-way puzzles () as a natural central primitive for quantum cryptography with classical communication () and develops a cohesive framework connecting them to EFI/EFID/EFI primitives. It provides a cleaner EFI-from- construction, robust combiners, and universal constructions, along with amplification techniques that transform weakened puzzles into strong ones. The paper also analyzes efficient verifiability, proving black-box separations between and -, and shows equivalences to random-input and distributional variants, thereby unifying several formulations of centrality. Collectively, these results outline how many primitives can be built from while highlighting fundamental barriers to certain black-box reductions, and they clarify the relationships between , EFID/EFI, and PRS in the quantum setting.

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 (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 OWPuzz. Our proof of security amplification uses a new and cleaner version construction of EFI from OWPuzz (in comparison to the result of Khurana and Tomer) that generalizes to weak OWPuzz and is the most technically involved section of the paper. It was previously known that OWPuzz are implied by other primitives of interest including commitments, symmetric key encryption, one way state generators (OWSG), and therefore pseudorandom states (PRS). However we are able to rule out OWPuzz's equivalence to many of these primitives by showing a black box separation between general OWPuzz and a restricted class of OWPuzz (those with efficient verification, which we call EV-OWPuzz). We then show that EV-OWPuzz are also implied by most of these primitives, which separates them from OWPuzz as well. This separation also separates extending PRS from highly compressing PRS answering an open question of Ananth et. al.
Paper Structure (33 sections, 60 theorems, 87 equations, 2 figures)

This paper contains 33 sections, 60 theorems, 87 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Technical Overview
  3. A cleaner construction of EFI pairs from any one-way puzzle
  4. Building a KL-hard to sample distribution from a one-way puzzle
  5. Building a non-uniform EFID pair from a KL-hard to sample distribution
  6. From non-uniform EFID pairs to EFI pairs
  7. Combiners and universal constructions
  8. Amplification of one-way puzzles
  9. Building strong one-way puzzles from non-uniform EFID
  10. Relationships with other QCCC primitives
  11. Efficiently verifiable one-way puzzles
  12. Equivalence to variant definitions
  13. Open Questions
  14. Preliminaries
  15. Definitions of QCCC primitives
  16. ...and 18 more sections

Key Result

Theorem 1

If there exists a weak one-way puzzle, then there exists an EFI pair.

Figures (2)

  • Figure 1: All implications known about one-way puzzles ($\mathsf{OWPuzz}$) and efficiently verifiable one-way puzzles $(\mathsf{EV-OWPuzz})$.
  • Figure 2: The construction of VZ12HRV10 applied to a one-way puzzle $\mathsf{Samp} \to (k,s)$. The idea is that many samples are taken and arranged in a grid. Then, each row is given a random offset, with both sides truncated. Finally, some number of random bits are extracted from each column using a pairwise-independent hash $\mathsf{Ext}$. This produces a pseudorandom string with less than full entropy, and we can repeat to get a non-uniform EFID pair.

Theorems & Definitions (107)

  • Theorem 1: Informal version of \ref{['cor:weakowptoefi']}
  • Theorem 2: Informal version of \ref{['cor:owpcomb']}
  • Corollary 1: Informal version of \ref{['thm:uowp']}
  • Theorem 3: Informal version of \ref{['cor:owpcorrect']}
  • Theorem 4: Restatement of \ref{['thm:owpcorramp']}
  • Theorem 5: Restatement of \ref{['thm:owpamplification']}
  • Theorem 6: Theorem 6.2 from KNY23
  • Theorem 7: Theorem 3.2 from KNY23
  • Theorem 8: Theorems A.4 and A.6 from khurana2024commitments and \ref{['thm:nicom', 'thm:qprgtoowp']} in this paper
  • Corollary 2
  • ...and 97 more