Towards Quantum One-Time Memories from Stateless Hardware
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 making at most 0.114n adaptive queries to the token (for n the key size), 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 give two impossibility results showing certain assumptions in our scheme cannot be relaxed.
Keywords
Cite
@article{arxiv.1810.05226,
title = {Towards Quantum One-Time Memories from Stateless Hardware},
author = {Anne Broadbent and Sevag Gharibian and Hong-Sheng Zhou},
journal= {arXiv preprint arXiv:1810.05226},
year = {2021}
}
Comments
36 pages. Followup to withdrawn paper arXiv:1511.01363v1; this new paper has different security claims and proof techniques. v2: Various updates, including further fleshing out of Gutoski/Watrous SDP framework for security, and evidence potentially supporting conjecture for polynomial security. v3: Published version (to appear in Quantum), updates to improve SDP exposition and to conjectures