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 $(1 - ε)$ success on one basis has conjugate-basis guessing probability at most $\frac{1}{2m} + O(ε^\frac{1}{4})$. (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.

翻译：我们在随机预言机模型中构建了模拟安全的一次性存储器（OTM），并提出了一个合理的论证，以证明其能抵御具有有界且自适应深度的量子敌手。我们的贡献包括：（1）一个仅使用单量子比特维斯特态和合取混淆（可由LPN构造）的简单方案：无需复杂的纠缠或量子密码技术。（2）一个新的POVM界，我们证明了任何在一个基上达到$(1 - ε)$成功率的测量，其在共轭基上的猜测概率至多为$\frac{1}{2m} + O(ε^\frac{1}{4})$。（3）在量子随机预言机模型中的模拟安全OTM，其中敌手只能以经典方式查询随机预言机。（4）自适应深度安全性，通过非正式地应用Arora等人提出的提升定理，我们推测其能抵御在随机预言机查询之间具有多项式量子电路深度的敌手。抵御自适应、深度有界的量子敌手的安全性，捕捉了对基于单量子比特态构建的OTM的许多现实攻击；因此，我们的工作为实用且真正安全的一次性程序铺平了道路。此外，深度有界的自适应敌手模型可能允许将一次性存储器编码到纠错存储态中，这为能够长期持续存在的一次性程序的实现打开了大门。