Discrete Algebraic Methods: Arithmetic, Cryptography, Automata and Groups

by Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger

The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups

354 pages, Paperback

Published May 24, 2016

Reviews

[James Swenson · Rating 5 out of 5]

Excellent! Perfect for well-prepared math majors, or graduate students in math or related fields, interested in applications of abstract algebra to computer science. Suitable for independent study.

I wrote a longer review for MAA Reviews, which you can read
here.