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Towards Quantum One-Time Memories from Stateless Hardware

Authors Anne Broadbent, Sevag Gharibian, Hong-Sheng Zhou

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  • Theory of computation → Cryptographic protocols
Keywords
  • quantum cryptography
  • one-time memories
  • semi-definite programming

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Abstract

A central tenet of theoretical cryptography is the study of the minimal assumptions required to implement a given cryptographic primitive. One such primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and Rothblum [CRYPTO 2008], which is a classical functionality modeled after a non-interactive 1-out-of-2 oblivious transfer, and which is complete for one-time classical and quantum programs. It is known that secure OTMs do not exist in the standard model in both the classical and quantum settings. Here, we propose a scheme for using quantum information, together with the assumption of stateless (i.e., reusable) hardware tokens, to build statistically secure OTMs. Via the semidefinite programming-based quantum games framework of Gutoski and Watrous [STOC 2007], we prove security for a malicious receiver, against a linear number of adaptive queries to the token, in the quantum universal composability framework, but leave open the question of security against a polynomial amount of queries. Compared to alternative schemes derived from the literature on quantum money, our scheme is technologically simple since it is of the "prepare-and-measure" type. We also show our scheme is "tight" according to two scenarios.

Cite As Get BibTex

Anne Broadbent, Sevag Gharibian, and Hong-Sheng Zhou. Towards Quantum One-Time Memories from Stateless Hardware. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.TQC.2020.6

Author Details

Anne Broadbent
  • Department of Mathematics and Statistics, University of Ottawa, Canada
Sevag Gharibian
  • Department of Computer Science, Paderborn University, Germany
  • Department of Computer Science, Virginia Commonwealth University, Richmond, VA, USA
Hong-Sheng Zhou
  • Department of Computer Science, Virginia Commonwealth University, Richmond, VA, USA

Funding

  • Broadbent, Anne: U.S. Air Force Office of Scientific Research under award number FA9550-17-1-0083, Canada’s NSERC, Ontario ERA, and the University of Ottawa’s Research Chairs program.
  • Gharibian, Sevag: NSF grants CCF-1526189 and CCF-1617710.

Acknowledgements

We thank referees for pointing out the impossibility result against quantum queries applies only if we model the token as a reversible process, as well as for finding an error in a prior version of this work. We thank Kai-Min Chung and Jamie Sikora for related discussions.

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