Acerca de este curso: 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.
Para quién es esta clase: Learners with CS experience or education looking to: ○ Enhance/refresh critical skills; ○ Seeking to expand their opportunities. Learners undecided about pursuing a bachelor’s degree: ○ Seeking professional credit that may be applied towards a bachelor’s degree.
Creada por: University of Colorado System
Enseñado por: William Bahn, Lecturer
Computer Science
Enseñado por: Richard White, Assistant Research Professor
Computer Science
Enseñado por: Sang-Yoon Chang, Assistant Professor
Computer Science
| Información básica | Curso 2 de 4 en Introduction to Applied Cryptography Specialization |
| Nivel | Beginner |
| Compromiso | This is Course 2 in a 4-course specialization. Estimated workload: 15-hours per week. |
| Idioma | English |
| Cómo aprobar | Aprueba todas las tareas calificadas para completar el curso. |
| Calificaciones del usuario |
Programa
SEMANA 1
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 videos, 10 readings, 1 practice quiz
- Leitura: Course Introduction
- Vídeo: Divisibility, Primes, GCD
- Leitura: Lecture Slides - Divisibility, Primes, GCD
- Leitura: Video - Adam Spencer: Why I fell in love with monster prime numbers
- Leitura: L16: Additional Reference Material
- Vídeo: Modular Arithmetic
- Leitura: Lecture Slides - Modular Arithmetic
- Leitura: L17: Additional Reference Material
- Vídeo: Multiplicative Inverses
- Leitura: Lecture Slides - Multiplicative Inverses
- Leitura: L18: Additional Reference Material
- Vídeo: Extended Euclidean Algorithm
- Leitura: Lecture Slides - Extended Euclidean Algorithm
- Leitura: L19: Additional Reference Material
- Teste para praticar: Practice Assessment - Integer Foundation
- Prompt de discussão: What do you think?
Calificado: Graded Assessment - Integer Foundation
SEMANA 2
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 videos, 9 readings, 1 practice quiz
- Leitura: Lecture Slides - Square-and-Multiply
- Leitura: Video - Modular exponentiation made easy
- Leitura: L20: Additional Reference Material
- Vídeo: Euler's Totient Theorem
- Leitura: Lecture Slide - Euler's Totient Theorem
- Leitura: L21: Additional Reference Material
- Vídeo: Eulers Totient Function
- Leitura: Lecture Slide - Eulers Totient Function
- Leitura: L22: Additional Reference Material
- Vídeo: Discrete Logarithms
- Leitura: Lecture Slide - Discrete Logarithms
- Leitura: L23: Additional Reference Material
- Teste para praticar: Practice Assessment - Modular Exponentiation
- Prompt de discussão: What do you think?
Calificado: Graded Assessment - Modular Exponentiation
SEMANA 3
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 videos, 5 readings, 1 practice quiz
- Leitura: Lecture Slide - CRT Concepts, Integer-to-CRT Conversions
- Leitura: L24: Additional Reference Material
- Vídeo: Moduli Restrictions, CRT-to-Integer Conversions
- Leitura: Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions
- Vídeo: CRT Capabilities and Limitations
- Leitura: Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions
- Leitura: Video - How they found the World's Biggest Prime Number - Numberphile
- Teste para praticar: Practice Assessment - Chinese Remainder Theorem
- Prompt de discussão: What do you think?
Calificado: Graded Assessment - Chinese Remainder Theorem
SEMANA 4
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 videos, 8 readings, 1 practice quiz
- Leitura: Lecture Slide - Trial Division
- Leitura: L27: Additional Reference Material
- Vídeo: Fermat's Primality
- Leitura: Lecture Slide - Fermat's Primality
- Leitura: L28: Additional Reference Material
- Vídeo: Miller-Rabin
- Leitura: Lecture Slide - Miller-Rabin
- Leitura: Video - James Lyne: Cryptography and the power of randomness
- Leitura: L29: Additional Reference Material
- Teste para praticar: Practice Assessment - Primality Testing
- Prompt de discussão: What do you think?
- Leitura: The Science of Encryption
Calificado: Graded Assessment - Primality Testing
Calificado: Course Project
Preguntas Frecuentes
Cómo funciona
Trabalho
Cada curso é como um livro didático interativo, com vídeos pré-gravados, testes e projetos.
Ajuda dos seus colegas
Conecte-se com milhares de outros aprendizes, debata ideias, discuta sobre os materiais do curso e obtenha ajuda para dominar conceitos.
Certificados
Obtenha reconhecimento oficial pelo seu trabalho e compartilhe seu sucesso com amigos, colegas e empregadores.
Creadores
University of Colorado System
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.
Tarifa
| Comprar curso | |
|---|---|
| Accede a los materiales del curso | Disponible |
| Accede a los materiales con calificación | Disponible |
| Recibe una calificación final | Disponible |
| Obtén un Certificado de curso para compartir | Disponible |
Calificaciones y revisiones
Found this very useful. Thank you.
Excelent!
I love the way that this course presents the basic group theory and number theory concepts central to so much cryptography. For example, I've tried to teach myself about the the Chinese Remainder Theorem and its use through my own self-study, but never really grokked it until this course. The same is true of primality testing.
The lectures really are outstanding, and the practice and graded assessments are extremely well constructed to help one get a real sense of what the theorems and algorithms do. The numbers in many of the problems are chosen to make certain things clear if you do those problems "by hand".
My only criticisms are not about substance, and are things that may not apply to your sessions or have been addressed by the time you are reading this. There were some errors in the early problem sets, the course slides are distributed at powerpoint only (and not PDF), and during my session there was virtually no interaction with staff or fellow students on the forums. These are minor issues, probably specific to the session I was in, but in combination are why I'm rating this four stars instead of five.
It is hard for me to assess how accessible this course is for most of the people who might take it. I found it "easy", but I've been doing self-study of this sort of stuff for a while. I also think that this is a "what you get out of it depends on what you put into it" sort of things. I got a lot out of it, but that is because I did the exercises both by hand, and then also wrote code to solve those same sorts of problems with bigger numbers.
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AS
Introduction assez complète aux mathématiques nécessaires à la cryptologie, avec des exemples précis en fin de cours autour de l'algorithme RSA.