课程信息
4.6
93 个评分
21 个审阅
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初级

初级

完成时间(小时)

完成时间大约为15 小时

建议:4 weeks, 2-5 hours/week...
可选语言

英语(English)

字幕:英语(English)

您将获得的技能

Number TheoryCryptographyModular Exponentiation
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
初级

初级

完成时间(小时)

完成时间大约为15 小时

建议:4 weeks, 2-5 hours/week...
可选语言

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 4 小时

Modular Arithmetic

In this week we will discuss integer numbers and standard operations on them: addition, subtraction, multiplication and division. The latter operation is the most interesting one and creates a complicated structure on integer numbers. We will discuss division with a remainder and introduce an arithmetic on the remainders. This mathematical set-up will allow us to created non-trivial computational and cryptographic constructions in further weeks....
Reading
10 个视频 (总计 90 分钟), 4 个阅读材料, 13 个测验
Video10 个视频
Numbers6分钟
Divisibility6分钟
Remainders9分钟
Problems6分钟
Divisibility Tests5分钟
Division by 212分钟
Binary System11分钟
Modular Arithmetic12分钟
Applications7分钟
Modular Subtraction and Division11分钟
Reading4 个阅读材料
Python Code for Remainders5分钟
Slides1分钟
Slides1分钟
Slides1分钟
Quiz12 个练习
Divisibility15分钟
Remainders10分钟
Division by 45分钟
Four Numbers10分钟
Division by 10110分钟
Properties of Divisibility10分钟
Divisibility Tests8分钟
Division by 24分钟
Binary System8分钟
Modular Arithmetic8分钟
Remainders of Large Numbers10分钟
Modular Division10分钟
2
完成时间(小时)
完成时间为 4 小时

Euclid's Algorithm

This week we'll study Euclid's algorithm and its applications. This fundamental algorithm is the main stepping-stone for understanding much of modern cryptography! Not only does this algorithm find the greatest common divisor of two numbers (which is an incredibly important problem by itself), but its extended version also gives an efficient way to solve Diophantine equations and compute modular inverses....
Reading
7 个视频 (总计 78 分钟), 4 个阅读材料, 7 个测验
Video7 个视频
Euclid’s Algorithm15分钟
Extended Euclid’s Algorithm10分钟
Least Common Multiple8分钟
Diophantine Equations: Examples5分钟
Diophantine Equations: Theorem15分钟
Modular Division12分钟
Reading4 个阅读材料
Greatest Common Divisor: Code15分钟
Extended Euclid's Algorithm: Code10分钟
Slides1分钟
Slides10分钟
Quiz7 个练习
Greatest Common Divisor10分钟
Tile a Rectangle with Squares20分钟
Least Common Multiple10分钟
Least Common Multiple: Code15分钟
Diophantine Equations15分钟
Diophantine Equations: Code20分钟
Modular Division: Code20分钟
3
完成时间(小时)
完成时间为 4 小时

Building Blocks for Cryptography

Cryptography studies ways to share secrets securely, so that even eavesdroppers can't extract any information from what they hear or network traffic they intercept. One of the most popular cryptographic algorithms called RSA is based on unique integer factorization, Chinese Remainder Theorem and fast modular exponentiation. In this module, we are going to study these properties and algorithms which are the building blocks for RSA. In the next module we will use these building blocks to implement RSA and also to implement some clever attacks against RSA and decypher some secret codes....
Reading
14 个视频 (总计 91 分钟), 3 个阅读材料, 6 个测验
Video14 个视频
Prime Numbers3分钟
Integers as Products of Primes3分钟
Existence of Prime Factorization2分钟
Euclid's Lemma4分钟
Unique Factorization9分钟
Implications of Unique Factorization10分钟
Remainders7分钟
Chinese Remainder Theorem7分钟
Many Modules5分钟
Fast Modular Exponentiation10分钟
Fermat's Little Theorem7分钟
Euler's Totient Function6分钟
Euler's Theorem4分钟
Reading3 个阅读材料
Slides10分钟
Slides10分钟
Slides10分钟
Quiz5 个练习
Integer Factorization20分钟
Remainders8分钟
Chinese Remainder Theorem15分钟
Fast Modular Exponentiation15分钟
Modular Exponentiation8分钟
4
完成时间(小时)
完成时间为 5 小时

Cryptography

Modern cryptography has developed the most during the World War I and World War II, because everybody was spying on everybody. You will hear this story and see why simple cyphers didn't work anymore. You will learn that shared secret key must be changed for every communication if one wants it to be secure. This is problematic when the demand for secure communication is skyrocketing, and the communicating parties can be on different continents. You will then study the RSA cryptosystem which allows parties to exchange secret keys such that no eavesdropper is able to decipher these secret keys in any reasonable time. After that, you will study and later implement a few attacks against incorrectly implemented RSA, and thus decipher a few secret codes and even pass a small cryptographic quest!...
Reading
9 个视频 (总计 67 分钟), 4 个阅读材料, 2 个测验
Video9 个视频
One-time Pad4分钟
Many Messages7分钟
RSA Cryptosystem14分钟
Simple Attacks5分钟
Small Difference5分钟
Insufficient Randomness7分钟
Hastad's Broadcast Attack8分钟
More Attacks and Conclusion5分钟
Reading4 个阅读材料
Many Time Pad Attack10分钟
Slides10分钟
Randomness Generation10分钟
Slides and External References10分钟
Quiz2 个练习
RSA Quizs
RSA Quest - Quiz6分钟
4.6
21 个审阅Chevron Right

热门审阅

创建者 PWNov 22nd 2018

I was really impressed especially with the RSA portion of the course. It was really well explained, and the programming exercise was cleverly designed and implemented. Well done.

创建者 LJan 2nd 2018

A good course for people who have no basic background in number theory , explicit clear explanation in RSA algorithm. Overall,a good introduction course.

讲师

Avatar

Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering
Avatar

Michael Levin

Lecturer
Computer Science
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Vladimir Podolskii

Associate Professor
Computer Science Department

关于 University of California San Diego

UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Innovation is central to who we are and what we do. Here, students learn that knowledge isn't just acquired in the classroom—life is their laboratory....

关于 National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru...

关于 Introduction to Discrete Mathematics for Computer Science 专项课程

Discrete Math is needed to see mathematical structures in the object you work with, and understand their properties. This ability is important for software engineers, data scientists, security and financial analysts (it is not a coincidence that math puzzles are often used for interviews). We cover the basic notions and results (combinatorics, graphs, probability, number theory) that are universally needed. To deliver techniques and ideas in discrete mathematics to the learner we extensively use interactive puzzles specially created for this specialization. To bring the learners experience closer to IT-applications we incorporate programming examples, problems and projects in our courses....
Introduction to Discrete Mathematics for Computer Science

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