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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

Attacks on EDCSA and the security of elliptic curves

This attack on ECDSA can recover the private key, [d], if the random key (ephemeral key), [k], is not completely random or it is used multiple times for signing the hash of the message (z).

This attack, implemented to extract the signing key used for the PlayStation 3 gaming console in 2010, recovered the keys of more than 77 million accounts.

To better understand this disruptive attack (because it will recover not only the message but also the private key, [d]), we will divide it into two steps. In this example, we consider the case when two messages, [M] and [M1], are digitally signed using the same private keys, [k] and [d].

Step 1 – Discovering the random key, [k]

The signature (S = 47) generated at the time (t0) from the hash of the message, [M], as we know, is given by the following mathematical passages:

S ≡ (z + r*d )/k (mod p)

Here it is presented in numbers:

S ≡ (17 + 62 * 2)/3...

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