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Cryptography Algorithms

Cryptography Algorithms

By : Massimo Bertaccini
4.2 (18)
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Cryptography Algorithms

Cryptography Algorithms

4.2 (18)
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)
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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

Implementing the D-H algorithm on elliptic curves

In this section, we will implement the D–H algorithm on elliptic curves. We saw the D–H algorithm in Chapter 3, Asymmetric Encryption. You should remember that the problem underlying the D–H key exchange is the discrete logarithm. Here, we will demonstrate that the discrete logarithm problem could be transposed on elliptic curves too.

First of all, we are dealing with an elliptic curve (mod p). The base point or generator point is the first element in the D–H original algorithm represented by (g), and here we denote it by (G). Let's look at some elements to take into consideration:

  • G: This is a point on the curve that generates a cyclic group.

    Cyclic group means that each point on the curve is generated by a repeated addition (we have seen point addition in the previous section).

  • Another concept is the order of G denoted by (n):
    ord(G) = n 

    The order of (G) = (n) is the size of the group...

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