摘 要
本文介绍了现代代数学在密码学中的应用，包括群论、域论和码论在对称和非对称加密中的具体应用。对称加密算法如DES、AES等基于群的理论研究，非对称加密算法如Diffie-Hellman密钥交换算法、Elgamal密码算法等也都是基于群论进行设计和分析的。域论在对称密码算法中使用布尔函数和卷积码实现在群上达到对称加密处理，也用于设计非对称加密算法如RSA、ECC算法等。码论常用于设计签名算法和认证机制，可以大大提高算法的安全性。现代代数学在密码学中的应用是信息安全保护的重要技术支撑。
关键词：现代代数学；密码学；对称加密；非对称加密
Application of modern algebra to cryptography
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Abstract：This paper introduces the application of modern algebra in cryptography, including the specific application of group theory, field theory and code theory in symmetric and asymmetric encryption. Symmetric encryption algorithms such as DES, AES and other group-based theoretical research, asymmetric encryption algorithms such as Diffie-Hellman key exchange algorithm, Elgamal cryptography algorithm are also based on group theory design and analysis. Domain theory uses Boolean functions and convolutional codes in symmetric cryptography algorithms to achieve symmetric encryption processing on groups, and is also used in the design of asymmetric encryption algorithms such as RSA and ECC algorithms. Code theory is often used to design signature algorithms and authentication mechanisms, which can greatly improve the security of algorithms. The application of modern algebra in cryptography is an important technical support for information security protection.
Key words: Modern algebra; Cryptography; Symmetric encryption; Asymmetric encryption
目 录
1 引言 1
2 密码学基础 1
2.1 密码学概述 1
2.2 对称加密算法 2
2.3 非对称加密算法 3
3 现代代数学在密码学中的应用 3
3.1 群论在密码学中的应用 3
3.2 域论在密码学中的应用 4
3.3 码论在密码学中的应用 5
结论 6
参考文献 6
致谢 7
