CS260: More Immersion into Congruences modulo n | Saylor Academy

This video takes you through the arithmetic operations necessary for understanding the RSA cryptosystem. The main takeaway is that our congruences need a set of algebraic rules similar to what you are used to from basic high school algebra.

Source: Steven Gordon, https://www.youtube.com/watch?v=UCzdAtE-AnQ
This work is licensed under a Creative Commons Attribution 3.0 License.

COURSE INTRODUCTION

Course Syllabus

Unit 1: Introduction to Cryptography

Unit 1 Learning Objectives

1.1: Introduction to Encryption and Computational Security

Key Concepts of Cryptography

How Cryptography Works

Key Terms for Network Security

1.2: Block Ciphers vs. Stream Ciphers

Overview

More on Stream Ciphers

1.3: Substitution Cipher

Basic Techniques

Python Exercise

1.4: Transposition Cipher

Basic Techniques

1.5: Random Numbers

The Basics of PRNGs

Python Example

1.6: Perfect Secrecy and the One-Time Pad

Perfect Secrecy a La Shannon

The Main Idea behind the One-Time Pad

More on the One-Time Pad

Unit 1 Assessment

Unit 1 Assessment

Unit 2: Hash Functions

Unit 2 Learning Objectives

2.1: What Is a Hash Function?

Overview

One Way Functions

Hash Functions

Python Exercise

2.2: Collision Resistance

The Importance of Collision Resistance

The Vulnerabilities of MD5

2.3: Merkle-Damgard Construction

Overview

Recipes for Hash Functions

2.4: SHA (Secure Hash Algorithm)

Overview

The Security of SHA

Python Exercise

2.5: Application: Blockchain

Introduction to Blockchain

Proof of Work

Python Exercise

Unit 2 Assessment

Unit 2 Assessment

Unit 3: Symmetric Encryption

Unit 3 Learning Objectives

3.1: Introduction to Symmetric Encryption

Key Concepts

3.2: Feistel Cipher

Combining Transposition and Substitution

The Elegance of the Feistel Cipher

3.3: Data Encryption Standard (DES)

Overview

Applying the Feistel Cipher

3.4: Advanced Encryption Standard (AES)

Beyond DES

Python Implementations

3.5: Triple DES (3DES)

Introduction to 3DES

Contrasting 3DES with AES

A Performance Comparison of DES, AES, and DES

Unit 3 Assessment

Unit 3 Assessment

Unit 4: Asymmetric Encryption

Unit 4 Learning Objectives

4.1: Asymmetric Cryptosystems

Introduction to Public Key Cryptography

4.2: The RSA Cryptosystem

The RSA Cryptosystem

4.3: Integer Factorization

Prime Factorization

Factoring Techniques

Python Exercise

4.4: Congruences Modulo n

Modular Arithmetic

More Immersion into Congruences modulo n