03653nam 2200733 450 991046580770332120200520144314.03-11-041333-73-11-041632-810.1515/9783110413335(CKB)3710000000718425(SSID)ssj0001677765(PQKBManifestationID)16486985(PQKBTitleCode)TC0001677765(PQKBWorkID)14944418(PQKB)11270564(MiAaPQ)EBC4533883(DE-B1597)448720(OCoLC)951145267(OCoLC)953920693(DE-B1597)9783110413335(PPN)195103629(Au-PeEL)EBL4533883(CaPaEBR)ebr11214970(CaONFJC)MIL927184(OCoLC)951223219(EXLCZ)99371000000071842520160609h20162016 uy 0engurcnu||||||||txtccrDiscrete algebraic methods arithmetic, cryptography, automata, and groups /Volker Diekert [and three others]Berlin, Germany ;Boston, Massachusetts :De Gruyter,2016.©20161 online resource (354 pages) illustrationsDe Gruyter TextbookBibliographic Level Mode of Issuance: Monograph3-11-041332-9 Includes bibliographical references and index.Frontmatter -- Preface -- Contents -- 1. Algebraic structures -- 2. Cryptography -- 3. Number theoretic algorithms -- 4. Polynomial time primality test -- 5. Elliptic curves -- 6. Combinatorics on words -- 7. Automata -- 8. Discrete infinite groups -- Solutions to exercises -- Bibliography -- IndexThe 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 Ordered algebraic structuresTextbooksAlgorithmsTextbooksComputer scienceMathematicsTextbooksCryptographyTextbooksAlgebraTextbooksElectronic books.Ordered algebraic structuresAlgorithmsComputer scienceMathematicsCryptographyAlgebra511.3/3Diekert Volker1955-1044054Diekert VolkerMiAaPQMiAaPQMiAaPQBOOK9910465807703321Discrete algebraic methods2469445UNINA