本课程面向博士/硕士研究生,纯英文授课,从密码学的角度讲述网络安全的原理、理论和技术。具体的,本课程主要以公钥密码体制中最经典的RSA公钥加密算法,Elgamal公钥加密算法以及椭圆曲线公钥加密算法为驱动,对这些算法涉及的数学基础知识进行系统性的介绍。通过本课程的学习,希望同学们能够对整除、同余、群以及椭圆曲线等初等数论和抽象代数的知识进行掌握和融会贯通,并在此基础上理解RSA,Elgamal以及ECC公钥加密算法的工作原理。
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Overview
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Syllabus
- 0.Network Security- Theory and Technology
- 1.An Introduction of Public Key Cryptography
- 1.1 Private Key Cryptography
- 1.2 Why Public Key Cryptography matters?
- 1.3 What is Public Key Cryptography?
- 1.4 Evolutions and Opportunities in Public Key Cryptography
- 2.Mathematical Foundations of PKC
- 2.1 Basic Group Theory
- 2.2 Cyclic Group
- 3.RSA PKC: from theory to practice
- 3.0 RSA Public Key Cryptosystem- from theory to practice
- 3.1 Primality Test
- 3.2 The Fast Powering Algorithm
- 4.Elgamal PKC
- 4.Elgamal PKC
- 5.Elliptic Curve Public Key Cryptography
- 5.Elliptic Curve Public Key Cryptography
- Final Exam
Taught by
Xiong Hu