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arXiv · 2601.13258

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

Lev Stambler
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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.

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Lev Stambler. 2026-01-19. Towards Simple and Useful One-Time Programs in the Quantum Random Oracle Model. https://arxiv.org/abs/2601.13258

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