Cryptanalysis of Number Theoretic Ciphers 1st Edition by Samuel Wagstaff ISBN 1351991949 9781351991940

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Product details:

ISBN 10: 1351991949

ISBN 13: 9781351991940

Author:  Samuel S. Wagstaff 

Cryptanalysis of Number Theoretic Ciphers 1st Edition: 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.

 

Cryptanalysis of Number Theoretic Ciphers 1st Edition Table of 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
• Elliptic curves
• Subexponential factoring algorithms
• Computing discrete logarithms
• Random number generation

The Cryptographic Algorithms

• Private key algorithms
• Public key algorithms
• Signature algorithms
• Key exchange algorithms
• Simple protocols
• Complicated protocols
• Complete systems

Methods of Attack

• Direct attacks
• Exploiting a user error
• Active attacks

 

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Samuel Wagstaff,Cryptanalysis,Number,Theoretic,Ciphers