License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2023.24
URN: urn:nbn:de:0030-drops-175278
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17527/
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Brakerski, Zvika ; Canetti, Ran ; Qian, Luowen

On the Computational Hardness Needed for Quantum Cryptography

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LIPIcs-ITCS-2023-24.pdf (0.8 MB)

Abstract

In the classical model of computation, it is well established that one-way functions (OWF) are minimal for computational cryptography: They are essential for almost any cryptographic application that cannot be realized with respect to computationally unbounded adversaries. In the quantum setting, however, OWFs appear not to be essential (Kretschmer 2021; Ananth et al., Morimae and Yamakawa 2022), and the question of whether such a minimal primitive exists remains open.
We consider EFI pairs - efficiently samplable, statistically far but computationally indistinguishable pairs of (mixed) quantum states. Building on the work of Yan (2022), which shows equivalence between EFI pairs and statistical commitment schemes, we show that EFI pairs are necessary for a large class of quantum-cryptographic applications. Specifically, we construct EFI pairs from minimalistic versions of commitments schemes, oblivious transfer, and general secure multiparty computation, as well as from QCZK proofs from essentially any non-trivial language. We also construct quantum computational zero knowledge (QCZK) proofs for all of QIP from any EFI pair.
This suggests that, for much of quantum cryptography, EFI pairs play a similar role to that played by OWFs in the classical setting: they are simple to describe, essential, and also serve as a linchpin for demonstrating equivalence between primitives.

BibTeX - Entry

@InProceedings{brakerski_et_al:LIPIcs.ITCS.2023.24,
  author =	{Brakerski, Zvika and Canetti, Ran and Qian, Luowen},
  title =	{{On the Computational Hardness Needed for Quantum Cryptography}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{24:1--24:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17527},
  URN =		{urn:nbn:de:0030-drops-175278},
  doi =		{10.4230/LIPIcs.ITCS.2023.24},
  annote =	{Keywords: quantum cryptography, efi, commitment scheme, oblivious transfer, zero knowledge, secure multiparty computation}
}

Keywords: quantum cryptography, efi, commitment scheme, oblivious transfer, zero knowledge, secure multiparty computation
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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