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

Introducing the MB09 algorithm

First, we will start with some considerations regarding the algorithm and reintroduce Fermat's Last Theorem. The first time I presented MB09, it was as an encryption algorithm, but effectively it is much more a protocol for digital payments. As I have already mentioned, while blockchain and cryptocurrency were not yet well known, I developed MB09 as an encryption/decryption algorithm to exchange a message between two actors. Many years later, I worked on the algorithm, taking it as the basis for a fully homomorphic encryption system and creating MB23, which was a fully homomorphic algorithm. Eventually, in 2020, it was turned into a new version, called MBXX, to overcome the consensus problem proposed by Satoshi Nakamoto.

Let's examine how the first version of MB09 worked. To do that, we'll recall Fermat's Last Theorem:

a^n + b^n = z^n 

Here, the (n) exponents represent all the sets of positive integers.

This equation,...