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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.

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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}
}

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DOI: 10.4230/LIPIcs.DISC.2024.32

Quantum Byzantine Agreement Against Full-Information Adversary

Authors: Longcheng Li, Xiaoming Sun, and Jiadong Zhu

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract

We exhibit that, when given a classical Byzantine agreement protocol designed in the private-channel model, it is feasible to construct a quantum agreement protocol that can effectively handle a full-information adversary. Notably, both protocols have equivalent levels of resilience, round complexity, and communication complexity. In the classical private-channel scenario, participating players are limited to exchanging classical bits, with the adversary lacking knowledge of the exchanged messages. In contrast, in the quantum full-information setting, participating players can exchange qubits, while the adversary possesses comprehensive and accurate visibility into the system’s state and messages. By showcasing the reduction from quantum to classical frameworks, this paper demonstrates the strength and flexibility of quantum protocols in addressing security challenges posed by adversaries with increased visibility. It underscores the potential of leveraging quantum principles to improve security measures without compromising on efficiency or resilience. By applying our reduction, we demonstrate quantum advantages in the round complexity of asynchronous Byzantine agreement protocols in the full-information model. It is well known that in the full-information model, any classical protocol requires Ω(n) rounds to solve Byzantine agreement with probability one even against Fail-stop adversary when resilience t = Θ(n) [Attiya and Censor, 2008]. We show that quantum protocols can achieve O(1) rounds (i) with resilience t < n/2 against a Fail-stop adversary, and (ii) with resilience t < n/(3+ε) against a Byzantine adversary for any constant ε > 0, therefore surpassing the classical lower bound.

Cite as

Longcheng Li, Xiaoming Sun, and Jiadong Zhu. Quantum Byzantine Agreement Against Full-Information Adversary. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li_et_al:LIPIcs.DISC.2024.32,
  author =	{Li, Longcheng and Sun, Xiaoming and Zhu, Jiadong},
  title =	{{Quantum Byzantine Agreement Against Full-Information Adversary}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{32:1--32:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.32},
  URN =		{urn:nbn:de:0030-drops-212582},
  doi =		{10.4230/LIPIcs.DISC.2024.32},
  annote =	{Keywords: Byzantine agreement, Quantum computation, Full-information model}
}

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Toward the Impossibility of Perfect Complete Quantum PKE from OWFs

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Quantum Byzantine Agreement Against Full-Information Adversary

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