README_en.md

Outline

Chapter 1: Introduction to Number Theory

• Lecture 1: Basics of Integer Operations
  Code | Tutorial

• Lecture 2: Fundamentals of Prime Numbers
  Code | Tutorial

• Lecture 3: Euclidean Algorithm
  Code | Tutorial

• Lecture 4: Extended Euclidean Algorithm
  Code | Tutorial

• Lecture 5: Basics of Modular Arithmetic
  Code | Tutorial

• Lecture 6: Modular Arithmetic Division
  Code | Tutorial

• Lecture 7: Fermat's Little Theorem
  Code | Tutorial

• Lecture 8: Chinese Remainder Theorem
  Code | Tutorial

• Lecture 9: Euler's Totient Function
  Code | Tutorial

• Lecture 10: Euler's Theorem
  Code | Tutorial

• Milestone 01: RSA Algorithm
  Code | Tutorial | Paper

Chapter 2: Abstract Algebra: Group Theory

• Lecture 11: Groups
  Tutorial

• Lecture 12: Subgroups
  Tutorial

• Lecture 13: Cosets and Lagrange's Theorem
  Tutorial

• Lecture 14: Normal Subgroups and Quotient Groups
  Tutorial

• Lecture 15: Homomorphisms and Isomorphisms
  Tutorial

• Lecture 16: Abelian Groups
  Tutorial

• Lecture 17: Cyclic Groups
  Tutorial

• Lecture 18: Direct Product of Groups
  Tutorial

• Lecture 19: Discrete Logarithm Problem
  Tutorial

• Milestone 02: Diffie-Hellman Key Exchange Algorithm
  Code | Tutorial | Paper

• Milestone 03: ElGamal Encryption and Signature Algorithm
  Code | Tutorial | Paper

Chapter 3: Abstract Algebra: Rings and Fields

• Lecture 20: Rings
  Tutorial

• Lecture 21: Ideals and Quotient Rings
  Tutorial

• Lecture 22: Ring Homomorphisms and Isomorphisms
  Tutorial

• Lecture 23: Fields
  Tutorial

• Lecture 24: Basics of Polynomials
  Tutorial

• Lecture 25: Polynomial Rings
  Tutorial

• Lecture 26: Field Extensions

  Tutorial

• Lecture 27: Finite Fields
  Tutorial

• Lecture 28: Quadratic Residues
  Tutorial

• Milestone 04: Goldwasser-Micali (GM) Algorithm
  Code | Tutorial | Paper

• Milestone 05: Introduction to Zero-Knowledge Proofs
  Tutorial | Paper

Chapter 4: Elliptic Curves

• Lecture 29: Basics of Elliptic Curves
  Code | Tutorial

• Lecture 30: Elliptic Curves over Finite Fields
  Code | Tutorial