Essential Maths for Zero Knowledge Proofs

Free Course 8 Modules Beginner Friendly Laurence Kirk

Master the mathematical foundations of zero-knowledge proofs. No advanced math background required—just curiosity and a desire to learn.

Enroll now and learn Essential Maths for ZKPs

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About This Course

This course is your gateway to mastering the essential mathematics that power zero knowledge proofs (ZKPs)—from modular arithmetic to elliptic curves. Whether you're a builder, auditor, or protocol engineer, you'll gain the real-world intuition and confidence needed to work with cutting-edge zk technology. No advanced math background required—just curiosity and a desire to learn.

What You'll Learn

  • Understand modular arithmetic and finite fields
  • Explore elliptic curves and pairings
  • Grasp the math behind zkSNARKs and zkSTARKs
  • Build mathematical intuition for proving systems

Course Modules

# Module Description
0IntroductionCourse intro
1Numbers and TerminologyCore terminology behind groups, fields, and modular arithmetic in ZK proofs
2Complexity TheoryAn intro to complexity theory and why it matters for ZK proofs
3Elliptic CurvesUnderstanding elliptic curves and why they matter in cryptography
4PolynomialsA powerful tool for encoding and verifying claims in ZK proofs
5Polynomail Commitment SchemesHow we commit to polynomials without revealing or transmitting them
6Further TechniquesSupporting techniques that add redundancy and structure to ZK proofs
7OutroFinal thoughts and curated resources to continue your ZK learning journey

Resources

Zero-Knowledge Concepts

  • Recursive Proofs: Key idea used in Mina Protocol
  • zkML: Machine learning + ZK primer resources
  • ZKP Use Cases: Identity, voting, and scalability

Foundational Maths

  • ZKMaths GitHub Repo: Core proofs, diagrams, and exercises
  • Number Theory: Primes, modular arithmetic, groups
  • Elliptic Curves: Introduction to ECC in cryptography

Further Learning

  • Bootcamps: Encode ZK Bootcamp, zkML workshops
  • Extropy Courses: Smart Contract Security, Cryptography, Agentic Web3
  • ZK Ecosystems: Mina, Starknet, zkSync — explore further

Community

  • Extropy Discord: Get updates & ask questions
  • ZK Communities: ZK Hack, Zero Knowledge Podcast, Mina Discord

Who This Is For

This course is built for developers, cryptography learners, auditors, protocol engineers, and anyone curious about the math behind zero knowledge proofs (ZKPs).

Whether you're a student, researcher, Web3 founder, product manager, or security professional, you'll find clear, accessible explanations and practical insights.

Perfect for those who want to:

  • Demystify the math behind ZKPs with clarity and confidence
  • Build, audit, or design zk-enabled protocols
  • Bridge the gap between theory and real-world applications
  • Gain practical intuition—no advanced math background required!

Enroll now and learn Essential Maths for ZKPs

Start the Course