Teaching & Academics
Math
Cryptography
Mathematical Cryptography - Crack The Code
4.1 (509 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
20,756 students enrolled

Mathematical Cryptography - Crack The Code

Learn Every Cryptosystem Including RSA, AES and Even Elliptic Curve Cryptography, and See the Math that Secures Us.
4.1 (509 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
20,756 students enrolled
Created by Kody Amour
Last updated 10/2017
English
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Mathematical Cryptography - Crack The Code
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This course includes
  • 5 hours on-demand video
  • 9 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll learn
  • Crack any security system
  • Understand and crack the modern AES cryptosystem
  • Understand and crack the modern RSA cryptosystem
  • Understand the new cryptosystem on Elliptic Curves
  • Understand modern 21st century security
  • Learn why old cryptosystems are vulnerable to attacks
  • Create unique cryptosystems that are completely secure
  • Learn number theoretic mathematics
Requirements
  • Basic Algebra
  • For AES (which can be skipped), a good idea of how to multiply matrices is helpful
  • Motivation
Description

In this course, you will learn all of the old and modern security systems that have been used and are currently being used. You also learn how to crack each one and understand why certain security systems are weak and why others are strong. We will even go into RSA, AES and ECC which are the three main modern cryptography systems used today. 

Learn How to Crack the Code! 

  • Advanced Encryption Standard

  • Public Key Cryptosystems (ie RSA)

  • Elliptic Curve Cryptography

  • Modern Cryptographic Security

  • Advanced Mathematical Techniques

Master the Art of Security! 

                     Security is a very important tool, and the ability to use mathematics to hide information is vital to the world. See how our banks and even the National Security Agency (NSA) keeps their data secure. With the knowledge of this course, you can even apply for security jobs at places like the NSA! This is a course that is rarely taught in Universities, so take advantage and start today! 

                  Most of today's security is based upon RSA, and AES but the NSA is trying to push Elliptic Curve Cryptography since it is more secure than RSA. In this course, we learn all of these cryptosystems and their weaknesses. We give examples of every cipher that we cover. Only a small number of people currently understand these systems, and you can join them. The best part of this course is the fun in breaking the codes. We offer many examples of each cryptosystem and how to break each one. 

                  Even as you are reading this, your https:// at the top says that the RSA Algorithm is successfully keeping your information from flooding the internet. You can find out how it all works and the mathematical structures that keep it secure in this course. So what are you waiting for? 

Who this course is for:
  • Anyone interested in computers and security
  • Anyone who wants to work at the National Security Agency
  • Anyone who understands a little about mathematics
  • Anyone who wants to understand why certain systems are secure
Course content
Expand all 39 lectures 05:09:29
+ – Introduction
2 lectures 11:54
Introduction
03:08

Learn and understand the common terminology behind cryptography such as "Key" and "Ciphertext"

Terminology
08:46
+ – Number Theory Lectures That Might Help
12 lectures 02:19:23
Introduction to Congruences
19:33
Equivalence Classes
07:26
Introduction to Linear Congruences
08:14
Systems of Residues
14:13
Linear Congruences
08:40
Euclidean Algorithm
09:42
Extended Euclidean Algorithm
13:30
Linear Congruences Example
05:01
Euler's Generalization of Fermat's Little Theorem
13:57
Successive Squaring
16:56
The Euler-Phi Function Part 1
16:13
The Euler-Phi Function Part 2
05:58
+ – Old Cryptography
15 lectures 01:05:28

Learn how to encrypt and decrypt the Ceaser Cipher and learn why it is a weak cryptosystem

Caeser Cipher (Shift Cipher)
10:00

See some examples on the Shift Cipher and learn how to hack it without knowing the key

Examples of the Ceaser Cipher and How to Crack
06:03
Shift Cipher Reading and Exercises
2 pages

Learn how to encrypt and decrypt the Affine Cipher and why it is so much stronger than the shift cipher and learn about frequency analysis and why it is so useful in attacking old cryptography

Affine Cipher
09:31

Learn how to use online calculators for frequency analysis and how to use that to crack the Affine cipher without the key

Examples of the Affine Cipher and How to Crack
07:25
Affine Cipher Reading and Exercises
3 pages

Learn what a block cipher is and why they are so much more secure, and learn how to crack the Vigenere cipher without the key

Vigenere Cipher
Preview 06:34

See some examples of encrypting and decrypting the Vigenere cipher and see how to find the key length (which would then crack the system entirely)

Examples of the Vigenere Cipher and How to Crack
09:06
Vigenere Cipher Reading and Exercises
1 page

Understand how the Playfair cipher works and why it is so fun and secure

Playfair Cipher
10:38

Watch a more visually appealing lecture on the Playfair cipher and examine the weaknesses

Examples of Playfair Cipher and How to Crack
06:11
Playfair Cipher Reading and Exercises
2 pages
Rail Fence Reading and Exercises
1 page
Hill Cipher Reading and Exercises
2 pages
Trifid Cipher Reading and Exercises
2 pages
+ – Modern Cryptography
8 lectures 01:12:01

Completely understand the AES Cryptosystem (each step) and learn why it is so secure and used today. Learn how to encrypt a message

The AES Cryptosystem
Preview 13:05
AES RoundKey Addition
16:01

Watch a more visually appealing lecture on how to encrypt using the AES cryptosystem and see applications of it on your wireless router and wireless connection (we will show using Windows 7)

How to Encrypt/Decrypt AES and Where to Find AES on Your Computer
10:17

Understand the most modern cryptosystem today: the RSA cryptosystem. Learn how to encrypt, decrypt and attack it without the key. Understand what a public key cryptosystem is and why it is so secure. Learn the strength behind factorization and why it is a problem that we can bet our crpytosystems on. Find out why knowing how to attack the cryptosystem still makes it secure.

The RSA Cryptosystem and How to Crack
12:40

Learn the ins and outs of the RSA cryptosystem and where it is used on the internet (We use a Bank of America example and see their RSA cryptosystem) and see how big security is today

Where to Find RSA Cryptosystems on Your Computer
09:28
RSA Cryptosystem Reading and Exercises
3 pages
El Gamal Reading and Exercises
2 pages

In this lecture, we introduce the most modern cryptosystem: elliptic curve cryptography. See where its applied today and why it is not as widely used yet (but likely will be within the next decade).

Introduction to Elliptic Curve Cryptography (Extremely Modern)
10:30