About this Course
최근 조회 17,142

다음 전문 분야의 1개 강좌 중 1번째 강좌:

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

초급 단계

완료하는 데 약 16시간 필요

권장: 4 weeks, 2-5 hours/week...

영어

자막: 영어, 그리스어

귀하가 습득할 기술

Number TheoryCryptographyModular Exponentiation

다음 전문 분야의 1개 강좌 중 1번째 강좌:

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

초급 단계

완료하는 데 약 16시간 필요

권장: 4 weeks, 2-5 hours/week...

영어

자막: 영어, 그리스어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 4시간 필요

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 videos (Total 90 min), 4 readings, 13 quizzes
10개의 동영상
Divisibility6m
Remainders9m
Problems6m
Divisibility Tests5m
Division by 212m
Binary System11m
Modular Arithmetic12m
Applications7m
Modular Subtraction and Division11m
4개의 읽기 자료
Python Code for Remainders5m
Slides1m
Slides1m
Slides1m
12개 연습문제
Divisibility15m
Remainders10m
Division by 45m
Four Numbers10m
Division by 10110m
Properties of Divisibility10m
Divisibility Tests8m
Division by 24m
Binary System8m
Modular Arithmetic8m
Remainders of Large Numbers10m
Modular Division10m
2
완료하는 데 4시간 필요

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 videos (Total 78 min), 4 readings, 7 quizzes
7개의 동영상
Euclid’s Algorithm15m
Extended Euclid’s Algorithm10m
Least Common Multiple8m
Diophantine Equations: Examples5m
Diophantine Equations: Theorem15m
Modular Division12m
4개의 읽기 자료
Greatest Common Divisor: Code15m
Extended Euclid's Algorithm: Code10m
Slides1m
Slides10m
7개 연습문제
Greatest Common Divisor10m
Tile a Rectangle with Squares20m
Least Common Multiple10m
Least Common Multiple: Code15m
Diophantine Equations15m
Diophantine Equations: Code20m
Modular Division: Code20m
3
완료하는 데 4시간 필요

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 videos (Total 91 min), 4 readings, 6 quizzes
14개의 동영상
Prime Numbers3m
Integers as Products of Primes3m
Existence of Prime Factorization2m
Euclid's Lemma4m
Unique Factorization9m
Implications of Unique Factorization10m
Remainders7m
Chinese Remainder Theorem7m
Many Modules5m
Fast Modular Exponentiation10m
Fermat's Little Theorem7m
Euler's Totient Function6m
Euler's Theorem4m
4개의 읽기 자료
Slides10m
Slides10m
Fast Modular Exponentiation7m
Slides10m
5개 연습문제
Integer Factorization20m
Remainders8m
Chinese Remainder Theorem: Code15m
Fast Modular Exponentiation: Code20m
Modular Exponentiation8m
4
완료하는 데 5시간 필요

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 videos (Total 67 min), 4 readings, 2 quizzes
9개의 동영상
One-time Pad4m
Many Messages7m
RSA Cryptosystem14m
Simple Attacks5m
Small Difference5m
Insufficient Randomness7m
Hastad's Broadcast Attack8m
More Attacks and Conclusion5m
4개의 읽기 자료
Many Time Pad Attack10m
Slides10m
Randomness Generation10m
Slides and External References10m
2개 연습문제
RSA Quiz: Code2h
RSA Quest - Quiz6m
4.6
28개의 리뷰Chevron Right

50%

이 강좌를 수료한 후 새로운 경력 시작하기

40%

이 강좌를 통해 확실한 경력상 이점 얻기

Number Theory and Cryptography의 최상위 리뷰

대학: 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.

대학: 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.

강사

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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

캘리포니아 샌디에고 대학교 정보

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....

국립 연구 고등 경제 대학 정보

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 전문 분야 정보

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

자주 묻는 질문

  • 강좌에 등록하면 바로 모든 비디오, 테스트 및 프로그래밍 과제(해당하는 경우)에 접근할 수 있습니다. 상호 첨삭 과제는 이 세션이 시작된 경우에만 제출하고 검토할 수 있습니다. 강좌를 구매하지 않고 살펴보기만 하면 특정 과제에 접근하지 못할 수 있습니다.

  • 강좌를 등록하면 전문 분야의 모든 강좌에 접근할 수 있고 강좌를 완료하면 수료증을 취득할 수 있습니다. 전자 수료증이 성취도 페이지에 추가되며 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 내용만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.

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