Cryptanalysis of Number Theoretic Ciphers

1. Auflage 2002
ISBN: 978-1-58488-153-7
Verlag: Taylor & Francis Inc

Buch, Englisch, 334 Seiten, Format (B × H): 172 mm x 231 mm, Gewicht: 640 g

Reihe: Computational Mathematics

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.

Zielgruppe

Undergraduate

Autoren/Hrsg.

Wagstaff Jr., Samuel S.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik EDV | Informatik Technische Informatik Computersicherheit Kryptographie, Datenverschlüsselung
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

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. References.

Über Autor(innen)

Samuel S. Wagstaff, Jr. is a professor at the Purdue University Center for Education and Research in Information Assurance and Security (CERIAS) in West Lafayette, Indiana.