Discrete Algebraic Methods : Arithmetic, Cryptography, Automata and Groups
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| Title: | Discrete Algebraic Methods : Arithmetic, Cryptography, Automata and Groups |
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| Description: | 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. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups |
| Authors: | Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf |
| Resource Type: | eBook. |
| Subjects: | Ordered algebraic structures--Textbooks, Algorithms--Textbooks, Computer science--Textbooks--Mathematics, Cryptography--Textbooks |
| Categories: | MATHEMATICS / Discrete Mathematics, COMPUTERS / Computer Science, COMPUTERS / Information Theory, COMPUTERS / Programming / Algorithms, MATHEMATICS / Number Theory, MATHEMATICS / Combinatorics |
| Database: | eBook Collection (EBSCOhost) |
| Abstract: | 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. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups |
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| ISBN: | 9783110413328 9783110413335 9783110416329 |
