このコースについて
17,308 最近の表示

100%オンライン

自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

初級レベル

約16時間で修了

推奨:4 weeks, 2-5 hours/week...

英語

字幕:英語, ギリシャ語

習得するスキル

Number TheoryCryptographyModular Exponentiation

100%オンライン

自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

初級レベル

約16時間で修了

推奨:4 weeks, 2-5 hours/week...

英語

字幕:英語, ギリシャ語

シラバス - 本コースの学習内容

1
4時間で修了

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.

...
10件のビデオ (合計90分), 4 readings, 13 quizzes
10件のビデオ
Numbers6 分
Divisibility6 分
Remainders9 分
Problems6 分
Divisibility Tests5 分
Division by 212 分
Binary System11 分
Modular Arithmetic12 分
Applications7 分
Modular Subtraction and Division11 分
4件の学習用教材
Python Code for Remainders5 分
Slides1 分
Slides1 分
Slides1 分
12の練習問題
Divisibility15 分
Remainders10 分
Division by 45 分
Four Numbers10 分
Division by 10110 分
Properties of Divisibility10 分
Divisibility Tests8 分
Division by 24 分
Binary System8 分
Modular Arithmetic8 分
Remainders of Large Numbers10 分
Modular Division10 分
2
4時間で修了

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.

...
7件のビデオ (合計78分), 4 readings, 7 quizzes
7件のビデオ
Euclid’s Algorithm15 分
Extended Euclid’s Algorithm10 分
Least Common Multiple8 分
Diophantine Equations: Examples5 分
Diophantine Equations: Theorem15 分
Modular Division12 分
4件の学習用教材
Greatest Common Divisor: Code15 分
Extended Euclid's Algorithm: Code10 分
Slides1 分
Slides10 分
7の練習問題
Greatest Common Divisor10 分
Tile a Rectangle with Squares20 分
Least Common Multiple10 分
Least Common Multiple: Code15 分
Diophantine Equations15 分
Diophantine Equations: Code20 分
Modular Division: Code20 分
3
4時間で修了

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.

...
14件のビデオ (合計91分), 4 readings, 6 quizzes
14件のビデオ
Prime Numbers3 分
Integers as Products of Primes3 分
Existence of Prime Factorization2 分
Euclid's Lemma4 分
Unique Factorization9 分
Implications of Unique Factorization10 分
Remainders7 分
Chinese Remainder Theorem7 分
Many Modules5 分
Fast Modular Exponentiation10 分
Fermat's Little Theorem7 分
Euler's Totient Function6 分
Euler's Theorem4 分
4件の学習用教材
Slides10 分
Slides10 分
Fast Modular Exponentiation7 分
Slides10 分
5の練習問題
Integer Factorization20 分
Remainders8 分
Chinese Remainder Theorem: Code15 分
Fast Modular Exponentiation: Code20 分
Modular Exponentiation8 分
4
5時間で修了

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!

...
9件のビデオ (合計67分), 4 readings, 2 quizzes
9件のビデオ
One-time Pad4 分
Many Messages7 分
RSA Cryptosystem14 分
Simple Attacks5 分
Small Difference5 分
Insufficient Randomness7 分
Hastad's Broadcast Attack8 分
More Attacks and Conclusion5 分
4件の学習用教材
Many Time Pad Attack10 分
Slides10 分
Randomness Generation10 分
Slides and External References10 分
2の練習問題
RSA Quiz: Code2 時間
RSA Quest - Quiz6 分
4.6
28件のレビューChevron Right

50%

コース終了後に新しいキャリアをスタートした

40%

コースが具体的なキャリアアップにつながった

Number Theory and Cryptography からの人気レビュー

by 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.

by 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.

講師

Avatar

Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering
Avatar

Michael Levin

Lecturer
Computer Science
Avatar

Vladimir Podolskii

Associate Professor
Computer Science Department

カリフォルニア大学サンディエゴ校について

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....

ロシア国立研究大学経済高等学院(National Research University Higher School of Economics)について

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 communicamathematics, engineering, and more. Learn more on www.hse.ru...

Introduction to Discrete Mathematics for Computer Scienceの専門講座について

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

よくある質問

  • 修了証に登録すると、すべてのビデオ、テスト、およびプログラミング課題(該当する場合)にアクセスできます。ピアレビュー課題は、セッションが開始してからのみ、提出およびレビューできます。購入せずにコースを検討することを選択する場合、特定の課題にアクセスすることはできません。

  • コースに登録する際、専門講座のすべてのコースにアクセスできます。コースの完了時には修了証を取得できます。電子修了証が成果のページに追加され、そこから修了証を印刷したり、LinkedInのプロフィールに追加したりできます。コースの内容の閲覧のみを希望する場合は、無料でコースを聴講できます。

さらに質問がある場合は、受講者向けヘルプセンターにアクセスしてください。