Chapter 7: Elliptic Curves

Elliptic curves are the new frontier for decentralized finance. Satoshi Nakamoto adopted a particular kind of elliptic curve to implement the transmission of digital currency in Bitcoin called secp256K1. Let's see how it works and what the main characteristics are of this very robust encryption.

In this chapter, we will learn the mathematical basics of elliptic curve cryptography. This topic involves geometry, modular mathematics, digital signatures, and logic.

Moreover, I will present the special kind of elliptic curve implemented for the digital signature of Bitcoin known as secp256K1.

Finally, we will discuss the possibility of an attack on elliptic curves.

So, in this chapter, we will cover the following topics:

• The genesis of cryptography on elliptic curves
• Mathematical and logical basics of elliptic curves
• The Diffie–Hellman key exchange based on elliptic curves
• An explanation of ECDSA on secp256K1 –...