README.md

WTF zk tutorials

中文版本

WTF zk is intro-level Zero-Knowledge Proofs (ZKP) tutorial: The goal is to make ZKP accessible to individuals with only a high school math background. We will replicate some algorithms using Python, so you will need to learn Python as well.

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: Ring and Field

• Lecture 20: Ring Tutorial

• Lecture 21: Ideal and Quotient Ring Tutorial

• Lecture 22: Homomorphisms and Isomorphisms of Ring Tutorial

• Lecture 23: Field Tutorial

• Lecture 24: Polynomial Basics Tutorial

• Lecture 25: Polynomial Ring Tutorial

• Lecture 26: Field Extension Tutorial

• Lecture 27: Finite Field Tutorial

• Lecture 28: Quadratic Residue 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: Introduction to Elliptic Curves Code | Tutorial

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

• Lecture 31: Elliptic Curve Discrete Logarithm Problem: Code | Tutorial

• Lecture 32: Elliptic Curve Cryptography: Code | Tutorial

• Lecture 33: Elliptic Curves over Extension Fields: Tutorial

• Lecture 34: Bilinear Pairing Basics: Tutorial

• Lecture 35: Torsion Groups and Divisors: Code | Tutorial

• Lecture 36: Weil Pairing: Tutorial

• Lecture 37: Miller Algorithm: Code | Tutorial

• Lecture 38: Tate Pairing: Code | Tutorial

• Lecture 39: Weil Pairing over Extension Fields: Tutorial

• Lecture 40: Common Elliptic Curves: Code | Tutorial

Milestone 06: Hash Functions Code | Tutorial

Milestone 07: Identity-Based Encryption (IBE) Code | Tutorial

WTF zk contributors

Contributors are the Basis of WTF Academy

WTF zk Sponsor

Reference

1. Moonmath Manual by LeastAuthority

2. zk-learning MOOC

3. The RareSkills Book of Zero Knowledge

4. Number Theory Notes

5. 密码学的数学基础

6. Cryptography 101 for Blockchain Developers by OpenZeppelin

7. Vitalik's blogs: Weil Pairing