ZK Algebra 0 - Introduction

Welcome to this blog! This is my first post, so I will look at it in some time and feel I could’ve done it way better. However, I will try my best!

If you arrived at this post, you want to understand how Zero Knowledge works; however, to do that, you will need some mathematical context first so that we will start there! I know that sometimes maths can feel challenging and overengineed. However, if you start simple and you understand all the concepts, you will really see that it’s straightforward to keep gaining knowledge; you will also notice that it’s actually easy to understand them if the maths are explained step by step.

This series of articles is for you if you are an engineer with the desire to understand Zero Knowledge. I don’t really care about your current level of maths, and the only prerequisite is knowing trivial things. I would recommend you stop here and take a look at these concepts if you are not used to them:

• Associativity $(a \cdot b) \cdot c = a \cdot (b \cdot c)$
• Commutativity $(a \cdot b) = (b \cdot a)$
• What rational, whole, integer and natural numbers are
• What a matrix is and what is it’s inverse

Even though the idea behind this series is to understand abstract algebra, you need to keep in mind that we won’t be going as deep as we could. You will learn the knowledge that will help you understand how it works to bring it to a practical level. We will be seeing a lot of topics, and you will be ending this series with knowledge of how they work, but you won’t end up as an M.sc. (basically, because you don’t really need it).

Let’s create a list of the topics that we will cover during this series. Don’t worry if you don’t even know something listed below, as the posts are done to learn this concept from scratch!

• Mathematical Notation
• Sets
• Magmas
• Semigroups
• Monoids
• Groups
• Fields
• Rings
• Modular Arithmetic
• Elliptic Curves
• Bilinear Pairings

Now that you have all that you will learn listed, I hope you don’t understand anything. That will put you through the wonderful path of learning that we all enjoy! Don’t get intimidated by the weird names. Go to the next article to learn about mathematical notation.