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 ScienceEnseñado por: Richard White, Assistant Research Professor
Computer ScienceEnseñado por: Sang-Yoon Chang, Assistant Professor
Computer Science
| Información básica | Curso 2 de 4 en Introduction to Applied Cryptography Specialization |
| Nivel | Principiante |
| Compromiso | This is Course 2 in a 4-course specialization. Estimated workload: 15-hours per week. |
| Idioma | Inglés (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 lecturas, 1 cuestionario de práctica
- Reading: Course Introduction
- Vídeo: Divisibility, Primes, GCD
- Reading: Lecture Slides - Divisibility, Primes, GCD
- Reading: Video - Adam Spencer: Why I fell in love with monster prime numbers
- Reading: L16: Additional Reference Material
- Vídeo: Modular Arithmetic
- Reading: Lecture Slides - Modular Arithmetic
- Reading: L17: Additional Reference Material
- Vídeo: Multiplicative Inverses
- Reading: Lecture Slides - Multiplicative Inverses
- Reading: L18: Additional Reference Material
- Vídeo: Extended Euclidean Algorithm
- Reading: Lecture Slides - Extended Euclidean Algorithm
- Reading: L19: Additional Reference Material
- Practice Quiz: Practice Assessment - Integer Foundation
- Discussion Prompt: 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 lecturas, 1 cuestionario de práctica
- Reading: Lecture Slides - Square-and-Multiply
- Reading: Video - Modular exponentiation made easy
- Reading: L20: Additional Reference Material
- Vídeo: Euler's Totient Theorem
- Reading: Lecture Slide - Euler's Totient Theorem
- Reading: L21: Additional Reference Material
- Vídeo: Eulers Totient Function
- Reading: Lecture Slide - Eulers Totient Function
- Reading: L22: Additional Reference Material
- Vídeo: Discrete Logarithms
- Reading: Lecture Slide - Discrete Logarithms
- Reading: L23: Additional Reference Material
- Practice Quiz: Practice Assessment - Modular Exponentiation
- Discussion Prompt: 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 lecturas, 1 cuestionario de práctica
- Reading: Lecture Slide - CRT Concepts, Integer-to-CRT Conversions
- Reading: L24: Additional Reference Material
- Vídeo: Moduli Restrictions, CRT-to-Integer Conversions
- Reading: Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions
- Vídeo: CRT Capabilities and Limitations
- Reading: Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions
- Reading: Video - How they found the World's Biggest Prime Number - Numberphile
- Practice Quiz: Practice Assessment - Chinese Remainder Theorem
- Discussion Prompt: 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 lecturas, 1 cuestionario de práctica
- Reading: Lecture Slide - Trial Division
- Reading: L27: Additional Reference Material
- Vídeo: Fermat's Primality
- Reading: Lecture Slide - Fermat's Primality
- Reading: L28: Additional Reference Material
- Vídeo: Miller-Rabin
- Reading: Lecture Slide - Miller-Rabin
- Reading: Video - James Lyne: Cryptography and the power of randomness
- Reading: L29: Additional Reference Material
- Practice Quiz: Practice Assessment - Primality Testing
- Discussion Prompt: What do you think?
- Reading: The Science of Encryption
Calificado: Graded Assessment - Primality Testing
Calificado: Course Project
Preguntas Frecuentes
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Coursework
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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
God, math, but the information is excelent
Good course, but would like some more exercises to implement the mathematics learnt.
Introduction assez complète aux mathématiques nécessaires à la cryptologie, avec des exemples précis en fin de cours autour de l'algorithme RSA.
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EG
Very interesting facts about number theory, the base of Cryptography. Although I'm mathematician, I've learnt new important facts in this course (especially those that refer to history or computation, including algorithms like trial division, Miller Rabin and RSA).
However, a couple mistakes were found in the correct answers of the graded assessments.
In my opinion, the slides are nice, but not enough. There should be a formal document to explain in more detail and more rigorously each step of the mathematical procedures, since several of them cannot be explained in a video or in a slide.
Also, the assessment should include more mathematical and programming exercises to put in practice the things we've learnt through the course.
To conclude, very nice and indispensable content, but not as excellent and well prepared as in the first course lessons.