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.
Этот курс входит в специализацию ''Специализация Introduction to Applied Cryptography'
Mathematical Foundations for Cryptography
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Неделя
1Integer Foundations
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.
5 видео ((всего 60 мин.)), 10 материалов для самостоятельного изучения, 2 тестов
5 видео
Divisibility, Primes, GCD14мин
Modular Arithmetic15мин
Multiplicative Inverses12мин
Extended Euclidean Algorithm13мин
10 материала для самостоятельного изучения
Course Introduction10мин
Lecture Slides - Divisibility, Primes, GCD10мин
Video - Adam Spencer: Why I fell in love with monster prime numbers15мин
L16: Additional Reference Material10мин
Lecture Slides - Modular Arithmetic10мин
L17: Additional Reference Material10мин
Lecture Slides - Multiplicative Inverses10мин
L18: Additional Reference Material10мин
Lecture Slides - Extended Euclidean Algorithm10мин
L19: Additional Reference Material10мин
2 практического упражнения
Practice Assessment - Integer Foundation18мин
Graded Assessment - Integer Foundation16мин
Неделя
2Modular Exponentiation
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.
4 видео ((всего 51 мин.)), 9 материалов для самостоятельного изучения, 2 тестов
4 видео
Euler's Totient Theorem16мин
Eulers Totient Function12мин
Discrete Logarithms15мин
9 материала для самостоятельного изучения
Lecture Slides - Square-and-Multiply10мин
Video - Modular exponentiation made easy10мин
L20: Additional Reference Material10мин
Lecture Slide - Euler's Totient Theorem10мин
L21: Additional Reference Material10мин
Lecture Slide - Eulers Totient Function10мин
L22: Additional Reference Material10мин
Lecture Slide - Discrete Logarithms10мин
L23: Additional Reference Material10мин
2 практического упражнения
Practice Assessment - Modular Exponentiation12мин
Graded Assessment - Modular Exponentiation20мин
Неделя
3Chinese Remainder Theorem
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.
3 видео ((всего 25 мин.)), 5 материалов для самостоятельного изучения, 2 тестов
3 видео
Moduli Restrictions, CRT-to-Integer Conversions10мин
CRT Capabilities and Limitations8мин
5 материала для самостоятельного изучения
Lecture Slide - CRT Concepts, Integer-to-CRT Conversions30мин
L24: Additional Reference Material10мин
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30мин
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30мин
Video - How they found the World's Biggest Prime Number - Numberphile12мин
2 практического упражнения
Practice Assessment - Chinese Remainder Theorem12мин
Graded Assessment - Chinese Remainder Theorem20мин
Неделя
4Primality Testing
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.
3 видео ((всего 36 мин.)), 8 материалов для самостоятельного изучения, 3 тестов
8 материала для самостоятельного изучения
Lecture Slide - Trial Division10мин
L27: Additional Reference Material10мин
Lecture Slide - Fermat's Primality10мин
L28: Additional Reference Material10мин
Lecture Slide - Miller-Rabin10мин
Video - James Lyne: Cryptography and the power of randomness10мин
L29: Additional Reference Material10мин
The Science of Encryption10мин
3 практического упражнения
Practice Assessment - Primality Testing12мин
Graded Assessment - Primality Testing20мин
Course Project8мин
Преподавателя
William Bahn
LecturerComputer Science
Richard White
Assistant Research ProfessorComputer Science
Sang-Yoon Chang
Assistant ProfessorComputer Science
О Система университетов штата Колорадо
The University of Colorado is a recognized leader in higher education on the national and global stage. We collaborate to meet the diverse needs of our students and communities. We promote innovation, encourage discovery and support the extension of knowledge in ways unique to the state of Colorado and beyond.
О специализации ''Introduction to Applied Cryptography'
Cryptography is an essential component of cybersecurity. The need to protect sensitive information and ensure the integrity of industrial control processes has placed a premium on cybersecurity skills in today’s information technology market. Demand for cybersecurity jobs is expected to rise 6 million globally by 2019, with a projected shortfall of 1.5 million, according to Symantec, the world’s largest security software vendor. According to Forbes, the cybersecurity market is expected to grow from $75 billion in 2015 to $170 billion by 2020. In this specialization, students will learn basic security issues in computer communications, classical cryptographic algorithms, symmetric-key cryptography, public-key cryptography, authentication, and digital signatures. These topics should prove useful to those who are new to cybersecurity, and those with some experience.
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