Towards Quantum One-Time Memories from Stateless Hardware

A. Broadbent, S. Gharibian, H.-S. Zhou, (2018).

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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. We prove stand-alone security against a malicious sender, but leave open the question of composable security against a malicious sender, as well as security against a malicious receiver making a polynomial number of adaptive 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.
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Broadbent A, Gharibian S, Zhou H-S. Towards Quantum One-Time Memories from Stateless Hardware. 2018.
Broadbent, A., Gharibian, S., & Zhou, H.-S. (2018). Towards Quantum One-Time Memories from Stateless Hardware.
@article{Broadbent_Gharibian_Zhou_2018, title={Towards Quantum One-Time Memories from Stateless Hardware}, author={Broadbent, Anne and Gharibian, Sevag and Zhou, Hong-Sheng}, year={2018} }
Broadbent, Anne, Sevag Gharibian, and Hong-Sheng Zhou. “Towards Quantum One-Time Memories from Stateless Hardware,” 2018.
A. Broadbent, S. Gharibian, and H.-S. Zhou, “Towards Quantum One-Time Memories from Stateless Hardware.” 2018.
Broadbent, Anne, et al. Towards Quantum One-Time Memories from Stateless Hardware. 2018.
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arXiv 1810.05226

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