Cryptanalysis of Number Theoretic Ciphers

Samuel S. Wagstaff, Jr

334 pages, parution le 08/01/2003

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Résumé

Provides a thorough analysis of the modern ciphers that are based on number
theory
Decribes various known ways to break certain ciphers and other cryptosystems - including some private key ciphers, some signatures, and some protocols - and assesses their effectiveness
Lists and explains each pitfall you may encounter
Provides numerous examples of ciphers in use today and describes many algorithms in pseudocode for easy programming
Presents cryptosystems as practical, workable algorithms, not just as oversimplified mathematical objects
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, through the inner workings of ciphers and protocols, to their strengths and weaknesses.
The first part of 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. Part Two 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. If a problem can be avoided, he tells how to avoid 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.

Contents

Mathematical Foundations of Cryptanalysis

Terminology of Cryptography
Probability Theory
Divisibility and Arithmetic
Primes
Congruences
Euler's Theorem and Its Consequences
Second Degree Congruences
Information Theory
Groups, Rings and Fields
Finding Large Primes
Exponential Methods of Factoring Integers
Finding Large Primes
Elliptic Curves
Subexponential Factoring Algorithms
Computing Discrete Logarithms
Random Number Generation

The Cryptographic Algorithms

Private Key Ciphers
Public Key Ciphers
Signature Algorithms
Key Exchange Algorithms
Simple Protocols
Complicated Protocols
Complete Systems

Methods of Attack

Direct Attacks
Exploiting an Error
Active Attacks

L'auteur - Samuel S. Wagstaff, Jr

Purdue University, West Lafayette, Indiana, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Samuel S. Wagstaff, Jr
Parution	08/01/2003
Nb. de pages	334
Format	16 x 24
Couverture	Relié
Poids	633g
Intérieur	Noir et Blanc
EAN13	9781584881537
ISBN13	978-1-58488-153-7