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
MATHEMATICAL FOUNDATIONS OF CRYPTANALYSIS
Terminology of Cryptography
Divisibility and Arithmetic
Euler's Theorem and Its Consequences
Second Degree Congruences
Groups, Rings and Fields
Finding Large Primes
Exponential Methods of Factoring Integers
Subexponential Factoring Algorithms
Computing Discrete Logarithms
Random Number Generation
THE CRYPTOGRAPHIC ALGORITHMS
Private Key Algorithms
Public Key Algorithms
Key Exchange Algorithms
METHODS OF ATTACK
Exploiting a User Error
"This book contains a nice introduction to modern cryptography, with emphasis laid on the ciphers based on computational number theory. … The reader learns to deal with large numbers in a computer and to analyze the complexity of the most basic algorithms. … [T]he reader is not just confronted with a list of algorithms, but he/she is given the clues to assimilate the ideas behind the results … . The book contains more than 200 interesting exercises that test the reader's understanding of the text."
- Zentralblatt MATH, 1045
"The book provides an excellent text concerning cryptanalysis. … masterly and carefully written. As the proofs are given with full details … I can recommend it also to students."
- Monatshefte fur Mathematik