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 forma parte de Programa Especializado - Introduction to Applied Cryptography
Mathematical Foundations for Cryptography
ofrecido por
Programa - Qué aprenderás en este curso
Semana
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 videos (Total 60 minutos), 10 readings, 2 quizzes
5 videos
Divisibility, Primes, GCD14m
Modular Arithmetic15m
Multiplicative Inverses12m
Extended Euclidean Algorithm13m
10 lecturas
Course Introduction10m
Lecture Slides - Divisibility, Primes, GCD10m
Video - Adam Spencer: Why I fell in love with monster prime numbers15m
L16: Additional Reference Material10m
Lecture Slides - Modular Arithmetic10m
L17: Additional Reference Material10m
Lecture Slides - Multiplicative Inverses10m
L18: Additional Reference Material10m
Lecture Slides - Extended Euclidean Algorithm10m
L19: Additional Reference Material10m
2 ejercicios de práctica
Practice Assessment - Integer Foundation18m
Graded Assessment - Integer Foundation16m
Semana
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 videos (Total 51 minutos), 9 readings, 2 quizzes
4 videos
Euler's Totient Theorem16m
Eulers Totient Function12m
Discrete Logarithms15m
9 lecturas
Lecture Slides - Square-and-Multiply10m
Video - Modular exponentiation made easy10m
L20: Additional Reference Material10m
Lecture Slide - Euler's Totient Theorem10m
L21: Additional Reference Material10m
Lecture Slide - Eulers Totient Function10m
L22: Additional Reference Material10m
Lecture Slide - Discrete Logarithms10m
L23: Additional Reference Material10m
2 ejercicios de práctica
Practice Assessment - Modular Exponentiation12m
Graded Assessment - Modular Exponentiation20m
Semana
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 videos (Total 25 minutos), 5 readings, 2 quizzes
3 videos
Moduli Restrictions, CRT-to-Integer Conversions10m
CRT Capabilities and Limitations8m
5 lecturas
Lecture Slide - CRT Concepts, Integer-to-CRT Conversions30m
L24: Additional Reference Material10m
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30m
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30m
Video - How they found the World's Biggest Prime Number - Numberphile12m
2 ejercicios de práctica
Practice Assessment - Chinese Remainder Theorem12m
Graded Assessment - Chinese Remainder Theorem20m
Semana
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 videos (Total 36 minutos), 8 readings, 3 quizzes
8 lecturas
Lecture Slide - Trial Division10m
L27: Additional Reference Material10m
Lecture Slide - Fermat's Primality10m
L28: Additional Reference Material10m
Lecture Slide - Miller-Rabin10m
Video - James Lyne: Cryptography and the power of randomness10m
L29: Additional Reference Material10m
The Science of Encryption10m
3 ejercicios de práctica
Practice Assessment - Primality Testing12m
Graded Assessment - Primality Testing20m
Course Project8m
Instructores
William Bahn
LecturerComputer Science
Richard White
Assistant Research ProfessorComputer Science
Sang-Yoon Chang
Assistant ProfessorComputer Science
Acerca de University of Colorado System
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Acerca del programa especializado 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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