Number Theory and Cryptography

Course Curriculum

Chapter 1: Introduction

Lecture 1: Introduction

Lecture 2: Sets of numbers and roots of polynomials

Lecture 3: Number theory and Geometry : Lines

Lecture 4: Number theory and Geometry : The unit circle

Lecture 5: Number theory and Geometry : Hyperbolas

Lecture 6: Number theory and Geometry : Elliptic Curves

Lecture 7: Classical Encryption Schemes : The Caesar Cipher

Lecture 8: Classical Encryption Schemes : The Affine Ciphers

Lecture 9: Classical Encryption Schemes : The Vigenère Cipher

Chapter 2: Integers

Lecture 1: Induction

Lecture 2: Infinite descent of Fermat

Lecture 3: Prime numbers

Lecture 4: The Euclidean Algorithm and The Bézout Identity

Lecture 5: Congruences 1 (Part 1)

Lecture 6: Congruences 1 (Part 2)

Lecture 7: Congruences 1 (Part3)

Lecture 8: Fermat's little theorem (Part 1)

Lecture 9: Fermat's little theorem (Part 2)

Lecture 10: Euler the incredible genius I

Lecture 11: Euler the incredible genius II (Part I)

Lecture 12: Euler the incredible genius II (Part II)

Lecture 13: More on congruences : Cancellation and Linear equations

Lecture 14: Solving systems of linear congruences

Lecture 15: The famous Chinese Remainder Theorem

Lecture 16: Euler's theorem

Lecture 17: Euler's totient function