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所在平台: Udemy |
课程主页: https://www.udemy.com/course/the-mathematics-of-cryptography-with-dr-james-grime/
课程评论：没有评论
**课程名称：** 密码学的数学原理 (The Mathematics of Cryptography) **讲师：** James Grime 博士 (Dr James Grime) **课程概述：** 本课程深入探讨密码学的世界，这是一门关于秘密和秘密信息的科学。我们将从基础密码（如单字母替换和多字母替换密码）及其破解方法开始，逐步深入到更复杂的密码系统，包括二战时期著名的恩尼格玛密码机 (Enigma Machine) 以及现代互联网加密技术。 课程时长超过 6 小时的讲座，并提供额外的 2 小时练习和解答视频，帮助您巩固所学知识。 **课程内容亮点：** * **基础密码学：** 涵盖单字母替换 (Monoalphabetic ciphers) 和多字母替换 (Polyalphabetic ciphers) 密码。 * **关键数学概念：** 引入模运算 (Modular arithmetic)、集合 (sets)、函数 (functions)、概率 (probability)、统计 (statistics)、组合学 (combinatorics) 和数论 (number theory) 等重要数学概念。 * **经典密码技术：** 学习替换密码 (Substitution ciphers)、置换密码 (Transposition ciphers)、通勤密码 (Commuting ciphers)。 * **密码破解工具：** 掌握频率分析 (Frequency analysis)、维吉尼亚密码 (The Vigenere cipher) 的破解方法，如卡西斯基检验 (The Kasiski test) 和重合指数 (Index of Coincidence) / 弗里德曼检验 (The Friedman test)。 * **标志性密码系统：** 详细讲解恩尼格玛密码机 (The Enigma Machine) 的工作原理及其破解。 * **现代加密技术：** 介绍公钥密码学 (Public Key Cryptography)，包括迪菲-赫尔曼密钥交换 (Diffie-Hellman)、椭圆曲线密码学 (Elliptic curve cryptography)、RSA 互联网加密 (RSA internet encryption) 和数字签名 (Digital signatures)。 * **密码学的未来：** 对密码学的未来发展进行简要展望。 **学习目标：** 通过本课程，您将： * 理解密码学背后的数学原理。 * 掌握多种经典和现代密码技术。 * 学习并应用关键的数学概念。 * 探讨“是否存在牢不可破的密码”这一问题。 **课程特色：** * **自成体系：** 课程内容独立，无需额外背景知识，并提供配套笔记供学习者完成。 * **实践导向：** 每章后均提供大量练习题及详细解答，帮助学习者检验掌握程度。 * **趣味性与应用性：** 密码学涉及广泛的数学主题，是数学最迷人的应用领域之一。 本课程适合所有对数学和秘密信息感兴趣的学习者。
Cryptography is the science of secrets and secret messages. In this course we will learn more about the mathematics behind codes and code breaking.The course will start with easy ciphers and how they were broken, before moving to more sophisticated ciphers including the famous World War II Enigma machine and modern internet encryption.The course contains over 6 hours of lectures, with an additional 2 hours of exercises and solution videos.Topics covered in the course include:Monoalphabetic ciphers;Modular arithmetic;Polyalphabetic ciphers;The Enigma Machine; andPublic Key Cryptography.During this course we will introduce many important mathematical concepts including modular arithmetic, sets, functions, probability, statistics, combinatorics and number theory.Ciphers and techniques in the course include:Substitution ciphers;Transposition ciphers;Commuting ciphers;Frequency analysis;The Vigenere cipher;The Kasiski test;Index of Coincidence;The Friedman test;Diffie-Hellman;Elliptic curve cryptography;RSA internet encryption; andDigital signatures.Finally, we will end the course with a brief look at the future of cryptography.The course is intended to be self-contained and comes with a set of notes that you can complete as we go through the course.The course comes with many exercises after each section, with solutions, that allow you to test what you have learnt.Cryptography touches on a broad range of topics and is one of the most fascinating applications of maths. By the end of this short course, we will have introduced several fundamental ideas in mathematics, and even answer whether there such a thing as an unbreakable code.
