How to 𝒫𝔩𝔬𝔫𝒦Zero-Knowledge Proof Protocol

Interactive tutorial exploring the mathematical foundations of 𝒫𝔩𝔬𝔫𝒦

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Download Notebook

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Mathematical Foundation

Deep dive into the cryptographic math behind 𝒫𝔩𝔬𝔫𝒦 zero-knowledge proofs

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Interactive Examples

Sage/Python code examples with exercises to build understanding

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Complete Protocol

Full implementation from circuit constraints to verification

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Visual Learning

Diagrams and visualizations of complex cryptographic concepts

About This Tutorial

This interactive tutorial walks you through the 𝒫𝔩𝔬𝔫𝒦 zero-knowledge proof protocol, providing both theoretical understanding and practical implementation. You'll learn:

Circuit Constraints: How to encode computational problems
Polynomial Commitments: Using KZG commitments for efficiency
Schwartz-Zippel: Probabilistic polynomial equality testing
Permutation Arguments: Handling copy constraints elegantly
Fiat-Shamir: Making the protocol non-interactive

Each section builds progressively, with exercises to reinforce learning and Sage code examples you can run locally.

Getting Started

Introduction - Start here for an overview
Download the Notebook - Interactive Sage version
Follow Along - Implement solutions as you read

Credits

Authors: Martín Ochoa and David Wong, zkSecurity

Acknowledgements: Thanks to Jorge Cuellar, Katat Choi and Jaehun Kim for their valuable feedback to this tutorial.

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