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, called secp256k1. Elliptic Curve Cryptography (ECC) is highly used in embedded devices because of its smaller keys and reduced power consumption for private key operations. 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 ECC. I will explain what we are doing, but it’s worth understanding from the beginning that elliptic curve cryptography is a complex topic, involving geometry, modular mathematics, digital signatures, and logic.

To help demonstrate the mathematics, I will present how secp256k1 is implemented for the digital signature of Bitcoin.

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

In this chapter, we will cover the following...