Towards Quantum One-Time Memories from Stateless Hardware

TL;DR

This paper introduces a quantum-based scheme utilizing stateless hardware tokens to construct statistically secure one-time memories, advancing cryptographic primitives with a focus on simplicity and security proofs.

Contribution

It proposes a novel quantum scheme for OTMs using stateless tokens, with security proofs in the quantum UC framework, and demonstrates certain impossibility results.

Findings

Security holds against up to 0.114n adaptive queries

Scheme is of the prepare-and-measure type, simplifying implementation

Certain assumptions in the scheme are proven to be necessary

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.