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Cryptography Algorithms

You're reading from   Cryptography Algorithms A guide to algorithms in blockchain, quantum cryptography, zero-knowledge protocols, and homomorphic encryption

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Product type Paperback
Published in Mar 2022
Publisher Packt
ISBN-13 9781789617139
Length 358 pages
Edition 1st Edition
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Author (1):
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Massimo Bertaccini Massimo Bertaccini
Author Profile Icon Massimo Bertaccini
Massimo Bertaccini
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Toc

Table of Contents (15) Chapters Close

Preface 1. Section 1: A Brief History and Outline of Cryptography
2. Chapter 1: Deep Diving into Cryptography FREE CHAPTER 3. Section 2: Classical Cryptography (Symmetric and Asymmetric Encryption)
4. Chapter 2: Introduction to Symmetric Encryption 5. Chapter 3: Asymmetric Encryption 6. Chapter 4: Introducing Hash Functions and Digital Signatures 7. Section 3: New Cryptography Algorithms and Protocols
8. Chapter 5: Introduction to Zero-Knowledge Protocols 9. Chapter 6: New Algorithms in Public/Private Key Cryptography 10. Chapter 7: Elliptic Curves 11. Chapter 8: Quantum Cryptography 12. Section 4: Homomorphic Encryption and the Crypto Search Engine
13. Chapter 9: Crypto Search Engine 14. Other Books You May Enjoy

A numerical exercise on a digital signature on secp256k1

In this section, we will deep dive into the digital signature of secp256k1 in order to understand the mechanism behind the operations of implementation and validation of the digital signature.

Suppose for instance that the parameters of the curve are the following:

p = 67 (modulo p)
G = (2,22)
Order n = 79
Private Key: [d]= 2

So, as we have chosen a very simple private key, it is just enough to perform a double point to obtain the public key (Q):

Q = d*G

In this case, we proceed to calculate the public key (Q). First, we will be using the following formula to calculate the double point:

t = (3XP^2 + a)/ 2YP
t = (3*2^2 + 0)/ 2*22= 12/ 44 = Reduce[44*x == 12, x, Modulus -> (67)] = 49
t = 49

Calculating Q = d * G using numbers implies replacing [d] and (G) with numbers:

Q = 2 *(2,22) 

Relying on the formula of the double point, let's find the coordinates of Q (x and y), starting with x:

xQ...
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