Towards Simple and Useful One-Time Programs in the Quantum Random Oracle Model

TL;DR

This paper presents a simple, simulation-secure construction of one-time memories in the quantum random oracle model, secure against realistic quantum adversaries with bounded or adaptive depth, advancing practical quantum cryptography.

Contribution

It introduces a minimal scheme using single-qubit states and a new POVM bound, along with security proofs against depth-bounded quantum adversaries in the random oracle model.

Findings

Construction of simulation-secure OTMs using single-qubit Wiesner states.

A new POVM bound limiting conjugate-basis guessing probability.

Security against classical-query adversaries and conjectured security against depth-bounded quantum adversaries.

Abstract

We construct simulation-secure one-time memories (OTM) in the random oracle model, and present a plausible argument for their security against quantum adversaries with bounded and adaptive depth. Our contributions include: (1) A simple scheme where we use only single-qubit Wiesner states and conjunction obfuscation (constructible from LPN): no complex entanglement or quantum cryptography is required. (2) A new POVM bound where e prove that any measurement achieving $(1 - \epsilon)$ success on one basis has conjugate-basis guessing probability at most $\frac{1}{2m} + O(\epsilon^\frac{1}{4})$. (3) Simultation-secure OTMs in the quantum random oracle model where an adversary can only query the random oracle classically. (4) Adaptive depth security where, via an informal application of a lifting theorem from Arora et al., we conjecture security against adversaries with polynomial quantum circuit depth between random oracle queries. Security against adaptive, depth-bounded, quantum adversaries captures many realistic attacks on OTMs built from single-qubit states; our work thus paves the way for practical and truly secure one-time programs. Moreover, depth bounded adaptive adversarial models may allow for encoding one-time memories into error corrected memory states, opening the door to implementations of one-time programs which persist for long periods of time.