摘 要
量子计算作为新兴的计算范式，其强大的并行处理能力对传统密码学体系构成挑战与机遇。本研究旨在探讨量子计算在密码学中的应用潜力，聚焦于量子算法对现有加密体制的影响以及新型量子安全密码方案的设计。通过分析Shor算法和Grover算法对经典公钥密码和对称密钥密码的破解效率，揭示了传统密码体制面临的潜在风险。研究采用理论分析与仿真实验相结合的方法，构建了基于量子纠缠特性的密钥分发协议，并提出了一种抗量子攻击的格基密码构造方案。实验结果表明，所设计的量子密钥分发系统具有更高的安全性与稳定性，能够有效抵御量子计算带来的威胁。同时，提出的格基密码方案在保持高效加解密性能的同时，具备较强的抗量子攻击能力。本研究不仅为构建量子安全通信网络提供了理论依据和技术支持，还推动了后量子密码学的发展进程，为未来信息安全体系架构的演进奠定了坚实基础。研究创新性地将量子力学原理应用于密码学领域，提出了兼具理论价值与实际应用前景的新方法，为应对量子计算时代的密码安全挑战提供了重要参考。
关键词：量子计算；密码学；Shor算法；Grover算法；量子密钥分发；格基密码；抗量子攻击；信息安全
Abstract
Quantum computing, as an emerging computational paradigm, poses both challenges and opportunities to traditional cryptographic systems due to its powerful parallel processing capabilities. This study investigates the potential applications of quantum computing in cryptography, focusing on the impact of quantum algorithms on existing encryption schemes and the design of novel quantum-safe cryptographic protocols. By analyzing the efficiency of Shor's algorithm and Grover's algorithm in breaking classical public-key and symmetric-key cryptosystems, this research reveals the potential risks faced by traditional cryptographic infrastructures. The study employs a combination of theoretical analysis and simulation experiments to develop a quantum key distribution protocol based on quantum entanglement properties and proposes a lattice-based cryptographic construction resistant to quantum attacks. Experimental results demonstrate that the designed quantum key distribution system exhibits enhanced security and stability, effectively countering threats posed by quantum computing. Additionally, the proposed lattice-based cryptographic scheme maintains efficient encryption and decryption performance while demonstrating robust resistance to quantum attacks. This research not only provides theoretical foundations and technical support for establishing quantum-safe communication networks but also advances the development of post-quantum cryptography, laying a solid foundation for the evolution of future information security architectures. Innovatively applying principles of quantum mechanics to cryptography, this study introduces new methods with both theoretical significance and practical application prospects, offering important references for addressing cryptographic security challenges in the era of quantum computing.
Keywords：Quantum Computing；Cryptography；Shor Algorithm；Grover Algorithm；Quantum Key Distribution；Lattice-Based Cryptography；Quantum-Resistant；Information Security
目 录
摘 要 I
Abstract II
引 言 1
第一章 量子计算基础与密码学背景 2
1.1 量子计算基本原理 2
1.2 密码学发展概述 2
1.3 量子计算对传统密码学的挑战 3
第二章 量子算法在密码分析中的应用 4
2.1 Shor算法与因子分解 4
2.2 Grover算法与搜索问题 4
第三章 抗量子攻击的密码体制研究 6
3.1 后量子密码学概念 6
3.2 基于格的密码方案 6
3.3 多变量多项式密码系统 7
第四章 量子密钥分发技术探索 8
4.1 量子密钥分发原理 8
4.2实际应用中的挑战与前景 9
结 论 11
参考文献 12
致 谢 13
