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.
Este curso faz parte do Programa de cursos integrados Introduction to Applied Cryptography
Mathematical Foundations for Cryptography
oferecido por
Programa de cursos integrados Introduction to Applied CryptographySistema de Universidades do ColoradoUniversidade do Colorado
Programa - O que você aprenderá com este curso
Semana
13 horas para concluir
Integer 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 vídeos (total de (Total 60 mín.) min), 10 leituras, 2 testes
5 videos
Divisibility, Primes, GCD14min
Modular Arithmetic15min
Multiplicative Inverses12min
Extended Euclidean Algorithm13min
10 leituras
Course Introduction10min
Lecture Slides - Divisibility, Primes, GCD10min
Video - Adam Spencer: Why I fell in love with monster prime numbers15min
L16: Additional Reference Material10min
Lecture Slides - Modular Arithmetic10min
L17: Additional Reference Material10min
Lecture Slides - Multiplicative Inverses10min
L18: Additional Reference Material10min
Lecture Slides - Extended Euclidean Algorithm10min
L19: Additional Reference Material10min
2 exercícios práticos
Practice Assessment - Integer Foundation18min
Graded Assessment - Integer Foundation16min
Semana
23 horas para concluir
Modular 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 vídeos (total de (Total 51 mín.) min), 9 leituras, 2 testes
4 videos
Euler's Totient Theorem16min
Eulers Totient Function12min
Discrete Logarithms15min
9 leituras
Lecture Slides - Square-and-Multiply10min
Video - Modular exponentiation made easy10min
L20: Additional Reference Material10min
Lecture Slide - Euler's Totient Theorem10min
L21: Additional Reference Material10min
Lecture Slide - Eulers Totient Function10min
L22: Additional Reference Material10min
Lecture Slide - Discrete Logarithms10min
L23: Additional Reference Material10min
2 exercícios práticos
Practice Assessment - Modular Exponentiation12min
Graded Assessment - Modular Exponentiation20min
Semana
33 horas para concluir
Chinese 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 vídeos (total de (Total 25 mín.) min), 5 leituras, 2 testes
3 videos
Moduli Restrictions, CRT-to-Integer Conversions10min
CRT Capabilities and Limitations8min
5 leituras
Lecture Slide - CRT Concepts, Integer-to-CRT Conversions30min
L24: Additional Reference Material10min
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30min
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30min
Video - How they found the World's Biggest Prime Number - Numberphile12min
2 exercícios práticos
Practice Assessment - Chinese Remainder Theorem12min
Graded Assessment - Chinese Remainder Theorem20min
Semana
43 horas para concluir
Primality 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 vídeos (total de (Total 36 mín.) min), 8 leituras, 3 testes
8 leituras
Lecture Slide - Trial Division10min
L27: Additional Reference Material10min
Lecture Slide - Fermat's Primality10min
L28: Additional Reference Material10min
Lecture Slide - Miller-Rabin10min
Video - James Lyne: Cryptography and the power of randomness10min
L29: Additional Reference Material10min
The Science of Encryption10min
3 exercícios práticos
Practice Assessment - Primality Testing12min
Graded Assessment - Primality Testing20min
Course Project8min
Instrutores
William Bahn
LecturerComputer Science
Richard White
Assistant Research ProfessorComputer Science
Sang-Yoon Chang
Assistant ProfessorComputer Science
Sobre Sistema de Universidades do ColoradoUniversidade do Colorado
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.
Sobre o Programa de cursos integrados 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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