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

Elliptic curve secp256k1 – the Bitcoin digital signature

ECDSA is the digital signature scheme used in Bitcoin architecture that adopts an elliptic curve called secp256k1, standardized by the Standards for Efficient Cryptography Group (SECG).

ECDSA suggests (a = 0) and (b = 7) as parameters in the following equation:

E: y2 = x3 + 7 

For a more formal presentation, you can read the document reported by the SECG at https://www.secg.org/sec2-v2.pdf, where you can find the recommended parameters for the 256 bits associated with a Koblitz curve and the other bit-length sister curves.

This is the representation of secp256k1 in the real plane:

Figure 7.7 – secp256k1 elliptic curve

As we know, the elliptic curve has a part visible in the real plane and another representation in the imaginary plane. The form of an elliptic curve can be represented in 3D by a torus when the points are defined in a finite field, just as you can see in the following...