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Book

Cryptanalysis of Number Theoretic Ciphers

Book

Cryptanalysis of Number Theoretic Ciphers

DOI link for Cryptanalysis of Number Theoretic Ciphers

Cryptanalysis of Number Theoretic Ciphers book

Cryptanalysis of Number Theoretic Ciphers

DOI link for Cryptanalysis of Number Theoretic Ciphers

Cryptanalysis of Number Theoretic Ciphers book

BySamuel S. Wagstaff
Edition 1st Edition
First Published 2003
eBook Published 30 August 2019
Pub. Location Boca Raton
Imprint Chapman and Hall/CRC
DOI https://doi.org/10.1201/9781315275765
Pages 336
eBook ISBN 9781315275765
Subjects Mathematics & Statistics
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Wagstaff, Jr., S.S. (2003). Cryptanalysis of Number Theoretic Ciphers (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9781315275765

ABSTRACT

At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols.

First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it.

Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.

TABLE OF CONTENTS

part Part I|2 pages

Mathematical Foundations of Cryptanalysis

chapter Chapter 1|10 pages

Terminology of Cryptography

chapter Chapter 2|14 pages

Probability Theory

chapter Chapter 3|18 pages

Divisibility and Arithmetic

chapter Chapter 4|16 pages

Primes

chapter Chapter 5|14 pages

Congruences

chapter Chapter 6|18 pages

Euler’s Theorem and Its Consequences

chapter Chapter 7|18 pages

Second Degree Congruences

chapter Chapter 8|17 pages

Information Theory

chapter Chapter 9|18 pages

Groups, Rings and Fields

chapter Chapter 10|12 pages

Exponential Methods of Factoring Integers

chapter Chapter 11|16 pages

Finding Large Primes

chapter Chapter 12|14 pages

Elliptic Curves

chapter Chapter 13|18 pages

Subexponential Factoring Algorithms

chapter Chapter 14|8 pages

Computing Discrete Logarithms

chapter Chapter 15|8 pages

Random Number Generation

part Part II|2 pages

The Cryptographic Algorithms

chapter Chapter 16|10 pages

Private Key Ciphers

chapter Chapter 17|8 pages

Public Key Ciphers

chapter Chapter 18|6 pages

Signature Algorithms

chapter Chapter 19|8 pages

Key Exchange Algorithms

chapter Chapter 20|10 pages

Simple Protocols

chapter Chapter 21|12 pages

Complicated Protocols

chapter Chapter 22|4 pages

Complete Systems

part Part III|2 pages

Methods of Attack

chapter Chapter 23|8 pages

Direct Attacks

chapter Chapter 24|8 pages

Exploiting an Error

chapter Chapter 25|6 pages

Active Attacks

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