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Towards Quantum One-Time Memories from Stateless Hardware

Authors Anne Broadbent, Sevag Gharibian, Hong-Sheng Zhou



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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

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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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

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.

Subject Classification

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

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