# Free Bitcoin Programming Course: Programming Bitcoin – Learn How to Program Bitcoin from Scratch

## Who Is This Course For?

This book will teach you the technology of Bitcoin at a fundamental level. It doesn’t cover the monetary, economic, or social dynamics of Bitcoin, but knowing how Bitcoin works under the hood should give you greater insight into what’s possible. There’s a tendency to hype Bitcoin and blockchain without really understanding what’s going on; this book is meant to be an antidote to that tendency.

After all, there are lots of books about Bitcoin, covering the history and the economic aspects and giving technical descriptions. The aim of this book is to get you to under‐ stand Bitcoin by coding all of the components necessary for a Bitcoin library. The library is not meant to be exhaustive or efficient. The aim of the library is to help you learn.

This book is for programmers who want to learn how Bitcoin works by coding it themselves. You will learn Bitcoin by coding the “bare metal” stuff in a Bitcoin library you will create from scratch. This is not a reference book where you can look up the specification for a particular feature.

The material from this book has been largely taken from my two-day seminar where I teach developers all about Bitcoin. The material has been refined extensively, as I’ve taught this course more than 20 times, to over 400 people as of this writing.

By the time you’re done with the book, you’ll not only be able to create transactions, but also get all the data you need from peers and send the transactions over the network. It covers everything needed to accomplish this, including the math, parsing, network connectivity, and block validation.

## What Do I Need to Know?

A prerequisite for this book is that you know programming—Python, in particular. The library itself is written in Python 3, and a lot of the exercises can be done in a controlled environment like a Jupyter notebook. An intermediate knowledge of Python is preferable, but even a beginning knowledge is probably sufficient to get a lot of the concepts.

Some knowledge of math is required, especially for Chapters 1 and 2. These chapters introduce mathematical concepts probably not familiar to those who didn’t major in mathematics. Math knowledge around algebra level should suffice to understand the new concepts and to code the exercises covered in those chapters.

General computer science knowledge, for example, of hash functions, will come in handy but is not strictly necessary to complete the exercises in this book.

## How Is the Book Arranged?

This book is split into 14 chapters. Each is meant to build on the previous one as the Bitcoin library gets built from scratch all the way to the end.

Roughly speaking, Chapters 1–4 establish the mathematical tools that we need; Chapters 5–8 cover transactions, which are the fundamental unit of Bitcoin; and Chapters 9–12 cover blocks and networking. The last two chapters cover some advanced topics but don’t actually require you to write code.

Chapters 1 and 2 cover some math that we need. Finite fields and elliptic curves are needed to understand elliptic curve cryptography in Chapter 3. After we’ve established the public key cryptography at the end of Chapter 3, Chapter 4 adds parsing and serialization, which are how cryptographic primitives are stored and transmitted.

Chapter 5 covers the transaction structure. Chapter 6 goes into the smart contract language behind Bitcoin, called Script. Chapter 7 builds on all the previous chapters, showing how to validate and create transactions based on the elliptic curve cryptography from the first four chapters. Chapter 8 establishes how pay-to-script-hash (p2sh) works, which is a way to make more powerful smart contracts.

Chapter 9 covers blocks, which are groups of ordered transactions. Chapter 10 covers network communication in Bitcoin. Chapters 11 and 12 go into how a light client, or software without access to the entire blockchain, might request and broadcast data to and from nodes that store the entire blockchain.

Chapter 13 covers Segwit, a backward-compatible upgrade introduced in 2017, and Chapter 14 provides suggestions for further study. These chapters are not strictly necessary, but are included as a way to give you a taste of what more there is to learn.

Chapters 1–12 have exercises that require you to build up the library from scratch. The answers are in Appendix A and in the corresponding chapter directory in the GitHub repo. You will be writing many Python classes and building toward not just validating transactions/blocks, but also creating your own transactions and broad‐ casting them on the network.

The last exercise in Chapter 12 specifically asks you to connect to another node on the testnet network, calculate what you can spend, construct and sign a transaction of your devising, and broadcast that on the network. The first 11 chapters essentially prepare you for this exercise.

There will be a lot of unit tests that your code will need to pass. The book has been designed this way so you can do the “fun” part of coding. To aid your progress, we will be looking at a lot of code and diagrams throughout.

## CHAPTER 1 Finite Fields

One of the most difficult things about learning how to program Bitcoin is knowing where to start. There are so many components that depend on each other that learning one thing may lead you to have to learn another, which in turn may lead you to need to learn something else before you can understand the original thing.

This chapter is going to get you off to a more manageable start. It may seem strange, but we’ll start with the basic math that you need to understand elliptic curve cryptography. Elliptic curve cryptography, in turn, gives us the signing and verification algorithms. These are at the heart of how transactions work, and transactions are the atomic unit of value transfer in Bitcoin. By learning about finite fields and elliptic curves first, you’ll get a firm grasp of concepts that you’ll need to progress logically.

Be aware that this chapter and the next two chapters may feel a bit like you’re eating vegetables, especially if you haven’t done formal math in a long time. I would encourage you to get through them, though, as the concepts and code presented here will be used throughout the book.

## Learning Higher-Level Math

Learning about new mathematical structures can be a bit intimidating, and in this chapter, I hope to dispel the myth that high-level math is difficult. Finite fields, in particular, don’t require all that much more in terms of prior mathematical knowledge than, say, algebra.

Think of finite fields as something that you could have learned instead of trigonometry, except that the education system you’re a part of decided that trigonometry was more important for you to learn. This is my way of telling you that finite fields are not that hard to learn and require no more background than algebra.

This chapter is required if you want to understand elliptic curve cryptography. Elliptic curve cryptography is required for understanding signing and verification, which is at the heart of Bitcoin itself. As I’ve said, this chapter and the next two may feel a bit unrelated, but I encourage you to endure. The fundamentals here will not only make understanding Bitcoin a lot easier, but also make understanding Schnorr signatures, confidential transactions, and other leading-edge Bitcoin technologies easier.

## Finite Field Definition

Mathematically, a finite field is defined as a finite set of numbers and two operations + (addition) and ⋅ (multiplication) that satisfy the following:

- If a and b are in the set, a + b and a ⋅ b are in the set. We call this property closed.
- 0 exists and has the property a + 0 = a. We call this the additive identity.
- 1 exists and has the property a ⋅ 1 = a. We call this the multiplicative identity.
- If a is in the set, –a is in the set, which is defined as the value that makes a + (–a) = 0. This is what we call the additive inverse.
- If a is in the set and is not 0, a–1 is in the set, which is defined as the value that makes a ⋅ a–1 = 1. This is what we call the multiplicative inverse.

Let’s unpack each of these criteria.

We have a set of numbers that’s finite. Because the set is finite, we can designate a number p, which is how big the set is. This is what we call the order of the set.

#1 says we are closed under addition and multiplication. This means that we have to define addition and multiplication in a way that ensures the results stay in the set. For example, a set containing {0,1,2} is not closed under addition, since 1 + 2 = 3 and 3 is not in the set; neither is 2 + 2 = 4. Of course we can define addition a little differently to make this work, but using “normal” addition, this set is not closed. On the other hand, the set {–1,0,1} is closed under normal multiplication. Any two numbers can be multiplied (there are nine such combinations), and the result is always in the set.

The other option we have in mathematics is to define multiplication in a particular way to make these sets closed. We’ll get to how exactly we define addition and multi‐ plication later in this chapter, but the key concept here is that we can define addition and subtraction differently than the addition and subtraction you are familiar with.

#2 and #3 mean that we have the additive and multiplicative identities. That means 0 and 1 are in the set.

#4 means that we have the additive inverse. That is, if a is in the set, –a is in the set. Using the additive inverse, we can define subtraction.

#5 means that multiplication has the same property. If a is in the set, a–1 is in the set. That is a ⋅ a–1 = 1. Using the multiplicative inverse, we can define division. This will be the trickiest to define in a finite field.