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Toward the Impossibility of Perfect Complete Quantum PKE from OWFs

Authors Longcheng Li , Qian Li , Xingjian Li , Qipeng Liu

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Author Details

Longcheng Li
  • State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China
Qian Li
  • Shenzhen International Center for Industrial and Applied Mathematics, Shenzhen Research Institute of Big Data, China
Xingjian Li
  • Tsinghua University, Beijing, China
Qipeng Liu
  • University of California, San Diego, La Jolla, CA, USA

Funding

  • Li, Qian: Qian Li’s work was supported by Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone Project (No.HZQSWS-KCCYB-2024016).

Cite As Get BibTex

Longcheng Li, Qian Li, Xingjian Li, and Qipeng Liu. Toward the Impossibility of Perfect Complete Quantum PKE from OWFs. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 71:1-71:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.71

Abstract

In this paper, we study the impossibility of constructing perfect complete quantum public key encryption (QPKE) from quantumly secure one-way functions (OWFs) in a black-box manner. We show that this problem is connected to a fundamental conjecture about the roots of low-degree polynomials on the Boolean hypercube. Informally, the conjecture asserts that for every nonconstant low-degree polynomial, there exists a universal (randomized) way to modify a small number of input bits such that, for every input string, the polynomial evaluated on the modified input string avoids 0 with sufficiently large probability (over the choice of how the input string is modified). Assuming this conjecture, we demonstrate the impossibility of constructing QPKE from quantumly secure one-way functions in a black-box manner, by employing the information-theoretical approach recently developed by Li, Li, Li, and Liu (CRYPTO'24). Towards resolving this conjecture, we provide various pieces of evidence supporting it and prove some special cases. In particular, we fully rule out perfect QPKE from OWFs when the key generation algorithm only makes a logarithmic number of quantum queries, improving the previous work, which can only handle classical queries.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic primitives
  • Theory of computation → Quantum complexity theory
Keywords
  • Qautnum public-key encryption
  • Boolean function analysis

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