Zero Knowledge Bootcamp
Conquer the fearsome math and code zk algorithms from scratch.
Nine weeks of live online classes.
According to Vitalik Buterin, Ethereum’s inventor,
“I expect ZKSNARKs to be a significant revolution as they permeate the mainstream world over the next 1020 years.” (source)
Zero knowledge proofs (ZK proofs) have two incredible properties: one is they allow privacy preservation in ways that were previously impossible, and they allow the computation to be verified faster than the original computation. This allows for the Ethereum blockchain to scale up because validators don’t have to rerun all the transactions to ensure they are valid — they just need to check the proofs.
Unfortunately, like all new technologies, learning zero knowledge is not easy. But that’s what this Zero knowledge course is for!
This course is not simply about writing applications in zero knowledge programming languages, but acquiring such a comprehensive understanding of the subject that you can write a zero knowledge proof algorithm from scratch.
We will cover applied zero knowledge programming, of course, but the real value of this course is deeply understanding the foundations that have stumped learners for years.
What makes this course different
Throughout the course, we are careful to stay within the prerequisites that we set at the beginning and not wander into other fields of mathematics, no matter how interesting they may be.
Where many zero knowledge courses go astray is they do not make strong assumptions about the mathematical background of the learner and introduce the prerequisite math as they go. We believe this gets in the way of the student understanding the bigger picture, and it makes the algorithms seem like a long sequence of arbitrary steps.
Our course takes the opposite approach. We lean heavily on a small subset of abstract algebra and linear algebra and make sure the student understands those fields sufficiently well before we begin. Armed with these powerful abstractions, you will cut through zero knowledge proofs like a hot knife through butter.
Throughout this course, we will speak in the language of abstract algebra. Despite the scary name, abstract algebra behaves like a wrapper API that hides a lot of complexity and motivates the relationship between seemingly unrelated concepts. Abstract algebra gives us the special ability to jump between universes with ease and unites the seemingly bizarre collection of mathematical theorems that zk proofs rely on.
Rather than try to avoid mathematics, we pick the most useful subset, stay within that subset, and lean heavily into it. Counterintuitively, this makes the subject of zero knowledge proofs very easy.
Although we expect you to be comfortable with math, we don’t expect you to already know abstract algebra. We’ll teach you the parts you need to know well.
Our waxon waxoff approach will serve you well through the rest of your programming career as what you learn in this course is generalizable evergreen knowledge — useful beyond zkp.
Zero knowledge proofs are an extremely easy subject to learn — if you have the right mathematics background. If you do not have the right mathematical training, zero knowledge proofs are nightmarishly hard.
Isn’t abstract algebra hard to learn?
We don’t think so. If you have a STEM major or taught yourself how to code, you’ll be able to learn the parts you need. Abstract algebra isn’t useful because of its complexity (it’s not complex), but because of its generalizability. We will only cover elementary abstract algebra, equivalent to two or three chapters in a lightweight textbook.
Don't zk proofs require moon math?
No, only bilinear pairings can rightfully be considered moon math. The rest requires math every 1st year undergraduate STEM major knows (or can easily learn). But armed with abstract algebra, you’ll be able to literally abstract away the complexity and focus on the practical aspects.
Prerequisites
You should be familiar with the following before starting.
Python and numpy. Basic experience with Jupyter Notebooks is highly recommended.
You should know what Z.K.S.N.A.R.K. stands for and what each term means. We will not waste time explaining to you why zksnarks are important, hopefully, you know that already.
You need to have taken a course on linear algebra before. It’s okay if you’ve forgotten it, we will give you some refresher materials, but to really appreciate abstract algebra, you need to have seen at least two fields of “traditional” algebra. We will also take it for granted that you know how matrix multiplication and the dot product works.
Being familiar with Solidity, yul assembly, and ABI encoding will be helpful for completing the assignments. If you do not come from a smart contract programming background, we have a separate set of assignments for you to enforce the concepts as a replacement for the Solidity ones. The course is taught from the perspective of a Solidity developer, but blockchain developers from other chains like Solana can benefit too, even those from a nonweb3 technical background such as machine learning engineers.
9 Week Curriculum
9 Weeks + 1 Week Precourse Study
9 Weeks
1. Set Theory and Abstract Algebra
Topics: sets, groups, cyclic groups, rings, fields, finite fields, binary operators, bijective, injective, and surjective functions, isomorphisms, homomorphisms, dot product, linear combinations
2. Ellipitc curves and ECDSA
Topics: Homomorphic addition, elliptic curve addition, elliptic curve digital signature algorithm
3. Elliptic curves in Solidity
Topics: EIP 196, Homomorphic encryption with elliptic curve points
4. Bilinear Pairings
Topics: EIP 197, bn128, symmetric and asymmetric pairings
5. Arithmetization and Rank 1 Constraint Systems
Topics: Ring homomorphisms, lagrange interpolation, schwartzzippel lemma, polynomial commitments, interactive proofs, column vectors, Hadamard product
6. Quadratic Arithmetic Programs (part 1)
Topics: Ring homomorphisms, lagrange interpolation, schwartzzippel lemma, polynomial commitments, interactive proofs, column vectors
7. Quadratic Arithmetic Programs (part 2)
Topics: Evaluation of Polynomials over elliptic curves, trusted setups
8. Groth16
Topics: Groth16, endtoend ZKSNARKS
By the end of this week, you will have built a fully functional prover and verifier in Python and Solidity using the Groth16 algorithm.
9. Circom
Topics: Circom and Circomlib
You will write circom circuits with a full understanding of what is going on from the powers of tau ceremony to completing the Solidity verifier. You’ll understand why for loops in zero knowledge are strange and why implementing comparison operators (<=, >=) are surprisingly hard.
FAQs
Your topics section has a lot of scary math terminology, are you sure this doesn’t require moon math?
Although mathematicians often use unnecessarily complex vocabulary to describe simple concepts, we opt to use their lingo because it will help you study the literature on your own later. You’ll get used to it pretty quickly.
I want to get started right now. What should I do?
Please read our article Elementary Set Theory and Abstract Algebra for Programmers and do the exercises in it.
Is this course selfpaced?
No. If you are just looking to casually understand the subject, check out our blog topics tagged zero knowledge proof. This course is intended for serious learners who are not satisfied with going halfway.
What is the course structure?
If you purchase the basic plan, you get access to weekly live lectures (eight total), study materials, and the RareSkills community. If you purchase the premium plan, you also get a weekly oneonone meeting (8 in total) with one of the instructors to review your code and make sure you really understand the material. The hard commitments are 1 hour per week, plus an optional 30minute meeting.
How many hours per week?
This will strongly depend on your background. If you’ve already taken an abstract algebra course, you might be able to do the course in as little as 6 hours a week. If you’re newer to the fields of math we’ve listed above, you should set aside 20 hours to be on the safe side, as it will take more time for the concepts to sink in and complete the homework satisfactorily.
I don’t care how zero knowledge works, I just want to use it
This isn’t advisable because without a deeper understanding, you won’t be able to design applications, and you’ll have a harder time understanding vulnerabilities. Additionally, there seem to be far more jobs in the infrastructure layer than the application layer. That said, our zero knowledge puzzles (in Circom) and Noir puzzles are opensourced, so check them out to start writing code right away.
How good do I need to be at Python?
Beginner is good enough. We use Python as it has some handy math libraries that we will explicitly teach. You are free to use another language, but you’ll need to find the equivalent libraries on your own. If you prefer to use math software like Matlab, you can do that also, but we won’t offer support for other languages. That said, you need to be proficient at coding in general. If you are completely new to Python, we will provide some precourse study materials for you to go over.
Is this in person or online?
100% online. Everything will be done through Google meets.
Basic

9 x Weekly lectures

Tailored homework

Community access
$2,100
(or two payments of $1150)
Premium

Everything in basic and

9 x Weekly 1on1 with the instructor
$2,900
(or two payments of $1,600)