超越NISQ假设：经典可访问随机预言机模型中的一次性存储器

中文摘要 AI 辅助

量子信息使得许多在经典世界中不可能实现的密码学原语成为可能。一系列工作已经在量子对手被限制为噪声中等规模量子（NISQ）计算能力的假设下开发了密码学协议，从而实现了强大的一次性功能。但早期容错量子计算机时代的到来将允许更深的逻辑量子电路，这使得这些基于NISQ的假设的适用性受到质疑。在本工作中，我们采用了如[BDF+11]和[AK22]中的经典可访问随机预言机模型（CAROM），在该模型中，对手仅被允许经典地查询随机预言机。这一限制对于NISQ量子对手来说是有充分动机的，并且在早期容错量子计算机存在的情况下可能仍然合理。然后，我们证明了在CAROM下，一个高效的模拟安全的一次性存储器（OTM）是可能的。我们的协议仅使用BB84态，并具有二次通信复杂度：对于λ比特的消息和整数值参数n=n(λ)和ℓ=ℓ(λ)，该构造使用nℓ个量子比特和(n+2)λ个经典比特，并且对于任何对随机预言机最多进行2^{ℓ/2-1}-1次经典查询的量子对手，其模拟优势至多为(n+3)(3/4)^n。因此，模拟优势在n上是指数级小的。

英文摘要

Quantum information enables many cryptographic primitives that are impossible in the classical world. A line of works has developed cryptographic protocol under the assumption that quantum adversaries are restricted to noisy intermediate-scale quantum (NISQ) computing power, enabling strong one-time functionalities. But the advent of early fault-tolerant quantum computers eras will allow deeper logical quantum circuits, calling into questions the applicability of these NISQ-based assumptions. In this work, we adapt the classically accessible random oracle model (CAROM) as in [BDF+11] and [AK22], in which adversaries are only allowed to classically query the random oracle. The restriction is well motivated for NISQ quantum adversaries and may remain plausible in the presence of early fault-tolerant quantum computers. Then, we show that an efficient simulation-secure one-time memory (OTM) is possible under CAROM. Our protocol uses only BB84 states and has quadratic communication: for a $λ$-bit message and integer-valued parameters $n=n(λ)$ and $\ell=\ell(λ)$, the construction uses $n\ell$ qubits and $(n+2)λ$ classical bits, and for any quantum adversary with at most $2^{\ell/2-1}-1$ classical queries to the random oracle, its simulation advantage is at most $(n+3)\left(\frac{3}{4}\right)^n.$ Hence exponentially small simulation advantage in $n$.

发表机构

• Tsinghua University（清华大学）
• Peking University（北京大学）

机构由 AI 辅助整理，请以论文原文为准。