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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/mathematical-foundations-cryptography
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课程名称：密码学的数学基础 概述：欢迎参加应用密码学入门课程的第二部分。在本课程中，您将学习构成密码学和密码分析方法基础的基本数学原理和函数。这些原理和函数将有助于理解第三和第四课程中探讨的对称和非对称密码学方法。如果您对网络安全领域较为陌生，这些主题对您尤为重要。建议您具备计算机科学的基本知识以及代数和概率等基本数学技能。 大纲： 1. **整数基础**：本模块在密码学基础的基础上，聚焦包括素数的使用、模算术、理解乘法逆元和扩展欧几里得算法等数学基础。完成此模块后，您将能够理解一些密码算法中所需的基本数学要求，并具备一些应用的实际知识。 2. **模幂运算**：深入了解模幂运算对理解密码学数学至关重要。本模块将涵盖平方乘法法、欧拉定理及其函数，并演示离散对数的使用。完成此模块后，您将理解密码算法的基本数学要求，并具备相关应用的知识。 3. **中国剩余定理**：本模块在先前的数学基础上，探讨整数的转换和中国剩余定理解表达式，以及这些表达式的能力和局限性。完成此模块后，您将理解中国剩余定理的概念及其在密码学中的应用。 4. **素性测试**：最后，我们将以试除法、费马定理和米勒-拉宾算法的模块结束本课程。完成此模块后，您将理解如何测试一个或多个对于素数值成立的等式，以及如何检查这些等式是否适用于我们想要测试的素性数。 通过以上模块的学习，您将掌握密码学的必备数学基础，为深入理解密码学的实际应用打下坚实的基础。
Name:Integer Foundations
Description:Building upon the foundation of cryptography, this module focuses on the mathematical foundation including the use of prime numbers, modular arithmetic, understanding multiplicative inverses, and extending the Euclidean Algorithm. After completing this module you will be able to understand some of the fundamental math requirement used in cryptographic algorithms. You will also have a working knowledge of some of their applications.
Name:Modular Exponentiation
Description:A more in-depth understanding of modular exponentiation is crucial to understanding cryptographic mathematics. In this module, we will cover the square-and-multiply method, Eulier's Totient Theorem and Function, and demonstrate the use of discrete logarithms. After completing this module you will be able to understand some of the fundamental math requirement for cryptographic algorithms. You will also have a working knowledge of some of their applications.
Name:Chinese Remainder Theorem
Description:The modules builds upon the prior mathematical foundations to explore the conversion of integers and Chinese Remainder Theorem expression, as well as the capabilities and limitation of these expressions. After completing this module, you will be able to understand the concepts of Chinese Remainder Theorem and its usage in cryptography.
Name:Primality Testing
Description:Finally we will close out this course with a module on Trial Division, Fermat Theorem, and the Miller-Rabin Algorithm. After completing this module, you will understand how to test for an equality or set of equalities that hold true for prime values, then check whether or not they hold for a number that we want to test for primality.
Welcome to Course 2 of Introduction to Applied Cryptography. In this course, you will be introduced to basic mathematical principles and functions that form the foundation for cryptographic and cryptanalysis methods. These principles and functions will be helpful in understanding symmetric and asymmetric cryptographic methods examined in Course 3 and Course 4. These topics should prove especially useful to you if you are new to cybersecurity. It is recommended that you have a basic knowledge of computer science and basic math skills such as algebra and probability.
