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Cryptography Algorithms

You're reading from Cryptography Algorithms Explore New Algorithms in Zero-knowledge, Homomorphic Encryption, and Quantum Cryptography

Product type Paperback

Published in Aug 2024

Publisher Packt

ISBN-13 9781835080030

Length 410 pages

Edition 2nd Edition

Concepts

Cryptography

Author (1):

Massimo Bertaccini

View More author details

Table of Contents (17) Chapters

Preface

1. Section 1: A Brief History and Outline of Cryptography

2. Deep Dive into Cryptography FREE CHAPTER

3. Section 2: Classical Cryptography (Symmetric and Asymmetric Encryption)

4. Symmetric Encryption Algorithms

5. Asymmetric Encryption Algorithms

6. Hash Functions and Digital Signatures

7. Section 3: New Cryptography Algorithms and Protocols

8. Zero-Knowledge Protocols

9. New Inventions in Cryptography and Logical Attacks

10. Elliptic Curves

11. Homomorphic Encryption and Crypto Search Engine

12. Section 4: Quantum Cryptography

13. Quantum Cryptography

14. Quantum Search Algorithms and Quantum Computing

15. Other Books You May Enjoy

16. Index

An overview of elliptic curves

Around 1985, Victor Miller and Neal Koblitz pioneered elliptic curves for cryptographic uses. Later on, Hendrik Lenstra showed us how to use them to factorize an integer number.

Elliptic curves are essentially a geometrical representation of particular mathematical equations on the Cartesian plane. We will start to analyze their geometrical models in the 2D plane, conscious that their extended and deeper representation is in 3D or 4D, involving irrational and imaginary numbers. Don’t worry about these issues for now; they will become clearer later on in this chapter.

ECC is used as a valid alternative to some of the asymmetric algorithms we have seen in previous chapters, such as RSA and ElGamal. We will also see that is possible to implement Diffie–Hellman on a particular ECC algorithm.

Moreover, after the advent of the revolution in digital currency, a particular type of elliptic curve called secp256k1 and a digital signature...

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Authors (1)

Massimo Bertaccini

Massimo Bertaccini

Massimo Bertaccini, PhD, is a researcher, principal scientist, CEO, and co-founder at Cryptolab Inc. He holds several patents in cryptography, quantum cryptography, and AI. His career started as a professor of mathematics and statistics, following which he founded Cryptolab Inc., a start-up in the field of cryptography solutions for cybersecurity. With his team of engineers, he designed and implemented the first search engine in the world that can work with encrypted data. He has obtained several international prizes and awards, such as the Silicon Valley Inventors award, the Seal of Excellence from the EU, and Security Solutions Provider of the Year – USA, 2023. Currently, as a contract professor, he teaches cryptography for a cybersecurity course and has published many articles in the field of cryptography and blockchain. The first edition of Cryptography Algorithms was the tenth bestseller in its category on Amazon for 40 weeks and proclaimed by Book Authority as the best book of 2023 in homomorphic and quantum encryption.

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