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Master the RSA Public Key Cryptosystem in 9 short lessons
Rating: 4.7 out of 5(64 ratings)
286 students

Master the RSA Public Key Cryptosystem in 9 short lessons

Some have heard of RSA. Others use RSA. Most don't understand RSA. After this course - You can do RSA Encryption.
Created byDanie Brink
Last updated 4/2022
English

What you'll learn

  • After the 9 short lessons of this course you will be able to encrypt data using the unbreakable RSA Public Key Cryptosystem.

Course content

2 sections • 10 lectures • 1h 20m total length

  • Introduction3:44

    In this 4-minute introduction video we discuss

    - what the RSA Cryptosystem is and why it so powerful

    - the format of the course, who should do this course, why you would want to do this course,

    - what benefit you will get from the knowledge gained in this course and

    - what mathematics you need to know before you do this course (very little, in fact).   

  • Lesson 1: Factors, Multiples, Products, Prime Number and Rules for Divisibility.10:12

    This lesson might make you feel like you are back in your middle school classroom - well, at least the good part of it.

    We review the mathematical concepts of factors, multiples and products so that they are fresh and familiar when we use them in the lessons to come.

    We focus on the definition of prime numbers and emphasize their uniqueness and usefulness in RSA Cryptography. At this point you might have to admit that there actually was a good answer in middle school when you asked the question: "When will we ever use this math again?"

    We revise the rules of divisibility for 2 , 3, 4, 5, 6, 8, 9 and 10 because in RSA encryption it is important to know if certain numbers are divisible.

  • Lesson 2: Modular Arithmetic.9:12

    In this lesson...

    We introduce the concept of modular arithmetic. By the way - if you know that 22:00 means 10pm, you actually already know some modular arithmetic.

    We practice modular arithmetic until we are comfortable finding congruences (answers) of quite large numbers.

  • Lesson 3: The Binary Expansion of Positive Integers.8:08

    In this lesson, we get very familiar with how special the number 2 is.

    We look at the powers of 2 and we express positive integers as the sum of powers of two. This is called the number's binary expansion. Do not be intimidated - this is much easier than what it sounds.

  • Lesson 4: Successive Squaring.0:23

    In this lesson...

    We make use of the powers of two, a number's binary expansion and the concept of successive squaring to calculate huge powers very easily with a simple calculator.

    This skill could be a great party trick - very nerdy, but great nevertheless.

  • Lesson 5: The Euler Phi Function and Euler's Formula.7:23

    In this lesson...

    We get comfortable with the concept of two numbers that share no common factors other than 1. These pairs of numbers are called relatively prime.

    We learn about the Euler Phi Function - yet another mathematical concept that sounds much harder than it really is.

  • Lesson 6: The Euclidean Algorithm.10:40

    In this lesson...

    We determine the GCD between two positive integers using the Euclidean Algorithm.

    When you see this effective method you will be annoyed at everyone who taught you math before and who did not teach you this.

  • Lesson 7: The Extended Euclidean Algorithm.10:41

    In this lesson...

    We follow up on the Euclidean Algorithm and extend it in order to express the GCD of two numbers as a linear combination of those two numbers.

Requirements

  • You need a basic knowledge of middle- and early high school mathematics.

Description

The RSA Public Key Cryptosystem is one of the best and widely used cryptosystems in the world today. Some people can talk a little about some of what RSA Encryption entails, but very few people can actually encrypt (and decrypt) data from start to finish using the RSA Public Key Cryptosystem.

Other topics covered during the course: Number Theory, Multiples, Factors, Products, Modular Arithmetic, Divisibility of Integers, Prime Numbers, Prime Factorization, Exponents, Exponential Laws, Binary Expansion of Integers, The Euler Phi Function, Euler's Formula, Fermat's Little Theorem, The Euclidean Algorithm, The Extended Euclidean Algorithm, Relative Prime Pairs of Integers, Encryption of secret messages, Decryption of secret messages, Shift Cypher, Successive Squaring, Middle School Mathematics, High School Mathematics, Pre-Algebra, Algebra I, Algebra II, Real-life Mathematics.

After this course you will know exactly how to encrypt and decrypt data using the RSA Public Key Cryptosystem. In seven video lessons you will become familiar with all the mathematics that is needed. In the last two videos you will learn exactly how to put that knowledge together to encrypt (lesson 8) and decrypt (lesson 9) data.

The level of mathematics involved is going to be a pleasant surprise. As an experienced middle and high school mathematics teacher I can tell you with confidence that by the time you were done with 10th grade, you knew (or should have known) all the math in this course.

Who would ever wonder where the mathematics they took in Middle and High School ever gets used in real life?

I tried to be thorough but managed to keep the course short. I know you do not have much time to watch videos and I do not have much time to make videos. The average length of the videos is under 10 minutes and the worksheets should never take you more than 20 or 30 minutes.   

Who knows what new horizons you will see or what doors might open up for you after this course. I am excited for you.

Who this course is for:

  • Computer scientists
  • Data analysts
  • High school students interested in the power of mathematics
  • Anyone interested in the protection of their personal information and data
  • Mathematics students who wonder: "Where will I ever use this again?"
  • Public Key Cryptosystem Enthusiasts

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