Book Image

Cryptography Algorithms

By : Massimo Bertaccini
Book Image

Cryptography Algorithms

By: Massimo Bertaccini

Overview of this book

Cryptography Algorithms is designed to help you get up and running with modern cryptography algorithms. You'll not only explore old and modern security practices but also discover practical examples of implementing them effectively. The book starts with an overview of cryptography, exploring key concepts including popular classical symmetric and asymmetric algorithms, protocol standards, and more. You'll also cover everything from building crypto codes to breaking them. In addition to this, the book will help you to understand the difference between various types of digital signatures. As you advance, you will become well-versed with the new-age cryptography algorithms and protocols such as public and private key cryptography, zero-knowledge protocols, elliptic curves, quantum cryptography, and homomorphic encryption. Finally, you'll be able to apply the knowledge you've gained with the help of practical examples and use cases. By the end of this cryptography book, you will be well-versed with modern cryptography and be able to effectively apply it to security applications.
Table of Contents (15 chapters)
1
Section 1: A Brief History and Outline of Cryptography
3
Section 2: Classical Cryptography (Symmetric and Asymmetric Encryption)
7
Section 3: New Cryptography Algorithms and Protocols
12
Section 4: Homomorphic Encryption and the Crypto Search Engine

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 –...