[论文解读] Single-Round Proofs of Quantumness from Knowledge Assumptions

Petia Arabadjieva, Alexandru Gheorghiu+2 more|arXiv (Cornell University)|May 24, 2024

Quantum Mechanics and Applications被引用 2

一句话总结

本文首次基于标准知识假设（即知识-指数假设与知识-格点点假设）提出了单轮量子性证明，实现了高效、适用于近期量子设备的认证，且无需中间测量。作者将基于DDH和LWE的多轮协议编译为单轮版本，实现了完备性1与可soundness 3/4，其量子电路规模与现有多轮协议相当。

ABSTRACT

A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the certification of quantum devices. Existing single-round protocols (like asking the quantum computer to factor a large number) require large quantum circuits, whereas multi-round ones use smaller circuits but require experimentally challenging mid-circuit measurements. As such, current proofs of quantumness are out of reach for near-term devices. In this work, we construct efficient single-round proofs of quantumness based on existing knowledge assumptions. While knowledge assumptions have not been previously considered in this context, we show that they provide a natural basis for separating classical and quantum computation. Specifically, we show that multi-round protocols based on Decisional Diffie-Hellman (DDH) or Learning With Errors (LWE) can be "compiled" into single-round protocols using a knowledge-of-exponent assumption or knowledge-of-lattice-point assumption, respectively. We also prove an adaptive hardcore-bit statement for a family of claw-free functions based on DDH, which might be of independent interest. Previous approaches to constructing single-round protocols relied on the random oracle model and thus incurred the overhead associated with instantiating the oracle with a cryptographic hash function. In contrast, our protocols have the same resource requirements as their multi-round counterparts without necessitating mid-circuit measurements, making them, arguably, the most efficient single-round proofs of quantumness to date. Our work also helps in understanding the interplay between black-box/white-box reductions and cryptographic assumptions in the design of proofs of quantumness.

研究动机与目标

• 设计一种高效且可在近期量子设备上实现的单轮量子性证明。
• 消除交互式量子性证明中对中间测量的需求，此类测量在实验上具有挑战性。
• 证明知识假设（如LK-𝜖与知识-指数）可作为区分经典与量子计算的基础。
• 提供一种比以往依赖随机预言模型的单轮协议更高效的替代方案，避免了额外的密码学开销。

提出的方法

• 作者基于LWE问题与LK-𝜖假设构造了一个e2NTCF（可提取的双面非交互式无爪族），以GLWE与FLWE为核心组件。
• 证明在LK-1/4假设下，GLWE族满足可提取性属性，确保任何成功的经典敌手必须掌握原像知识。
• 协议利用FLWE与GLWE的单射不变族性质，确保可从接近的格点唯一恢复原像。
• 通过GENTRAP机制生成陷门，构造具有特定格结构的密钥，从而支持知识假设的应用。
• 通过让验证者发出挑战、证明者以单个量子态响应的方式，将协议编译为单轮量子性证明，该响应可被经典验证。
• 通过证明任何以高概率成功的经典策略必然违反知识假设（该假设被视为困难）来建立可soundness。

实验结果

研究问题

• RQ1 能否在不依赖随机预言模型的前提下构造单轮量子性证明，从而避免哈希函数实例化的开销？
• RQ2 能否利用LK-𝜖或知识-指数等知识假设来构建高效、单轮的量子性证明？
• RQ3 是否可能在保持与多轮协议相同量子电路规模的同时，将交互减少至单轮？
• RQ4 与传统假设（如DDH或LWE）相比，知识假设在量子性证明协议中的安全性与效率表现如何？

主要发现

• 本文基于LWE问题与LK-1/4假设，构建了完备性为1、可soundness为3/4的单轮量子性证明。
• 该协议仅需与现有多轮协议相同规模的小型量子电路，适用于NISQ设备。
• 通过使用知识假设而非依赖测量的交互挑战，该构造避免了实验上具有挑战性的中间测量。
• 作者证明了在LK-1/4假设下，GLWE族满足可提取性属性，从而支持安全的量子性证明。
• 证明了一个基于DDH的新自适应强位函数陈述，该结果可能在密码学中具有独立价值。
• 本工作表明，知识假设为交互式证明系统中区分经典与量子计算提供了自然且高效的基石。