Programming Bitcoin

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 ...