ZK Notes

A structured curriculum map for learning Zero-Knowledge Proofs, from the underlying math to production zkVMs.

ZK Notes is not a textbook. It's a set of topics that guide you through learning ZK from discrete math and linear algebra all the way to STARKs, PLONK, folding schemes, and real-world zkVMs like Cairo and Plonky3. Each brief tells you where to study a topic from, how deep to go, and what you should be able to answer once you're done. Nothing here assumes you already know cryptography: each phase builds on the last.

This repo doesn't try to re-teach material that's already taught well elsewhere. Every file follows the same shape:

1. Study sources (top of the file): the best free resource(s) to actually learn the topic from, e.g. an MIT OCW course, a textbook, or a foundational paper.
2. Depth level: one of SKIM / SOLID / DEEP (see below), telling you what level of understanding is expected for this topic before moving on.
3. Self-check questions (end of the file): the questions you should be able to answer once you've studied the topic, so you can confirm you actually learned it rather than just skimmed it.

Think of each file as a syllabus entry plus a comprehension check, not a substitute for the source material it points to.

Every topic is tagged with one of three target depths. This tells you how far to take the source material before moving on. Going deeper than the tag is never wrong, but going shallower means you'll likely hit gaps later.

• SKIM: Know it exists, know the one-sentence definition, know when to look it up. You should be able to recognize the term in a paper and not be lost, but you won't use it hands-on.
• SOLID: Can explain it correctly to someone else, can use it in code/practice, can reason about it without a reference open. This is "competent working developer" level.
• DEEP: Can derive it, can explain why it's sound (not just that it is), can compare it against alternatives with real tradeoffs, could teach it, could spot a subtle bug in someone else's implementation of it. This is "the people hiring you would trust your judgment on this" level.

Most ZK learning material assumes you already have a strong crypto or math background, or it jumps straight into "here's how Groth16 works" without ever explaining why a QAP exists or what a commitment scheme actually commits to. ZK Notes is an attempt to fix that: a linear, dependency-aware path that tells you exactly where to learn each prerequisite and how to know when you've actually learned it.

1. Start at Phase 1 even if you think you know the math. The later topics assume this vocabulary.
2. For each topic: read the linked source(s) first, study to the stated depth, then answer the self-check questions at the end before moving on.
3. Work through the phases roughly in order. Within a phase, topics are largely independent.
4. Once you hit Phase 6+, start reading real implementations (Halo2, Plonky3, Cairo) side by side with the topic briefs.

Every topic file opens with a link to the best free resource for that subject: MIT OpenCourseWare lecture series, Victor Shoup's A Computational Introduction to Number Theory and Algebra, foundational papers on arXiv/eprint.iacr.org, and similar. These are where you should actually study from; the file itself is the scope and the self-check, not the lesson.

The language everything else is written in.

The primitives ZK protocols are built out of.

Where "ZK" actually starts.

The constructions everything downstream builds on.

Where current research and production zkVMs live.

Building this stuff for real.

Where ZK meets the real world.

For when you've cleared everything above.

Better source links, sharper scope/depth guidance, and improved self-check questions are all welcome. Open an issue or PR. Please keep the sources, depth, questions structure and the phase/file-naming convention intact so the learning path stays navigable.

Add a license (MIT or CC-BY-4.0 are common for educational content) so people know how they're allowed to reuse and share these topic briefs.

If this helped you learn ZK, a ⭐ helps other people find it.