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Documents authored by Li, Xingjian

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DOI: 10.4230/LIPIcs.ITCS.2025.71
Toward the Impossibility of Perfect Complete Quantum PKE from OWFs

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

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

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.
Cite as

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)

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@InProceedings{li_et_al:LIPIcs.ITCS.2025.71,
  author =	{Li, Longcheng and Li, Qian and Li, Xingjian and Liu, Qipeng},
  title =	{{Toward the Impossibility of Perfect Complete Quantum PKE from OWFs}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{71:1--71:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.71},
  URN =		{urn:nbn:de:0030-drops-226999},
  doi =		{10.4230/LIPIcs.ITCS.2025.71},
  annote =	{Keywords: Qautnum public-key encryption, Boolean function analysis}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.72
Classical vs Quantum Advice and Proofs Under Classically-Accessible Oracle

Authors: Xingjian Li, Qipeng Liu, Angelos Pelecanos, and Takashi Yamakawa

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
It is a long-standing open question to construct a classical oracle relative to which BQP/qpoly ≠ BQP/poly or QMA ≠ QCMA. In this paper, we construct classically-accessible classical oracles relative to which BQP/qpoly ≠ BQP/poly and QMA ≠ QCMA. Here, classically-accessible classical oracles are oracles that can be accessed only classically even for quantum algorithms. Based on a similar technique, we also show an alternative proof for the separation of QMA and QCMA relative to a distributional quantumly-accessible classical oracle, which was recently shown by Natarajan and Nirkhe.
Cite as

Xingjian Li, Qipeng Liu, Angelos Pelecanos, and Takashi Yamakawa. Classical vs Quantum Advice and Proofs Under Classically-Accessible Oracle. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 72:1-72:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li_et_al:LIPIcs.ITCS.2024.72,
  author =	{Li, Xingjian and Liu, Qipeng and Pelecanos, Angelos and Yamakawa, Takashi},
  title =	{{Classical vs Quantum Advice and Proofs Under Classically-Accessible Oracle}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{72:1--72:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.72},
  URN =		{urn:nbn:de:0030-drops-196009},
  doi =		{10.4230/LIPIcs.ITCS.2024.72},
  annote =	{Keywords: quantum computation, computational complexity}
}
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