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

An overview of elliptic curves

Around 1985, Victor Miller and Neal Koblitz pioneered elliptic curves for cryptographic uses. Later on, Hendrik Lenstra showed us how to use them to factorize an integer number.

Elliptic curves are essentially a geometrical representation of particular mathematical equations on the Cartesian plane. We will start to analyze their geometrical models in the 2D plane, conscious that their extended and deeper representation is in 3D or 4D, involving irrational and imaginary numbers. Don't worry now about these issues; it will become clearer later on in this chapter.

Elliptic Curves Cryptography (ECC) is used to implement some algorithms we have seen in previous chapters, such as RSA, Diffie–Hellman (D–H), and ElGamal.

Moreover, after the advent of the revolution in digital currency, a particular type of elliptic curve called secp256K1 and a digital signature algorithm called Elliptic Curve Digital Signature Algorithm (ECDSA) have...