AI 中文总结
介绍公钥密码学中量子算术电路，阐述其面临的设计挑战，强调基于测量的反计算等优化策略，回顾基本算术运算的最新设计及量子密码分析中容错运行时和资源估计技术，为评估量子密码分析能力提供基础。
AI 中文摘要
近几十年来，受包括量子纠错码和高效量子算法在内的整个技术栈发展的推动，量子计算迅速发展。其中，量子算术电路是各种有前景算法的基本构建块。尽管其作用关键，但量子算术电路的设计面临着诸如不可克隆定理、量子比特限制和电路深度约束等挑战，这显著影响大规模量子计算的效率。我们在公钥密码分析的背景下概述了量子算术电路，特别强调了基于测量的反计算和条件清洁辅助等优化策略。我们回顾了公钥密码分析中基本算术运算（如加法、乘法和模幂运算）的最新设计。我们还概述了量子密码分析中用于容错运行时和资源估计的技术。简而言之，本章强调了设计资源高效的量子算术电路的策略，为实际评估量子密码分析能力提供了基础。
英文摘要
Quantum computing has advanced rapidly in recent decades, driven by developments across the technology stack, including quantum error-correcting codes and efficient quantum algorithms. Among these, quantum arithmetic circuits serve as fundamental building blocks for various promising algorithms. Despite their crucial role, the design of quantum arithmetic circuits faces challenges arising from the no-cloning theorem, qubit limitations, and circuit depth constraints, which significantly impact the efficiency of large-scale quantum computing. We provide an overview of quantum arithmetic circuits in the context of public-key cryptanalysis, with particular emphasis on optimization strategies such as measurement-based uncomputation and conditionally clean ancilla. We review state-of-the-art designs for essential arithmetic operations in public-key cryptanalysis such as addition, multiplication, and modular exponentiation. We also present an overview of the techniques used for fault-tolerant runtime and resource estimation in quantum cryptanalysis. In brief, this chapter emphasizes strategies for designing resource-efficient quantum arithmetic circuits, providing a basis for realistic evaluations of quantum cryptanalytic capabilities.
