LEADER 04351nam 22006255 450 001 9910338255203321 005 20200703044234.0 010 $a3-030-15453-X 024 7 $a10.1007/978-3-030-15453-0 035 $a(CKB)4100000007992450 035 $a(DE-He213)978-3-030-15453-0 035 $a(MiAaPQ)EBC5926357 035 $a(PPN)235668222 035 $a(MiAaPQ)EBC31870632 035 $a(Au-PeEL)EBL31870632 035 $a(OCoLC)1099656760 035 $a(EXLCZ)994100000007992450 100 $a20190418d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCryptology and Error Correction $eAn Algebraic Introduction and Real-World Applications /$fby Lindsay N. Childs 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XIV, 351 p. 7 illus., 1 illus. in color.) 225 1 $aSpringer Undergraduate Texts in Mathematics and Technology,$x1867-5506 311 08$a3-030-15451-3 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1. Secure, Reliable Information -- 2. Modular Arithmetic -- 3. Linear Equations Modulo m -- 4. Unique Factorization in Z -- 5. Rings and Fields -- 6. Polynomials -- 7. Matrices and Hamming Codes -- 8. Orders and Euler's theorem -- 9. RSA Cryptography and Prime Numbers -- 10. Groups, Cosets, and Lagrange's theorem -- 11. Solving Systems of Congruences -- 12. Homomorphisms and Euler's Phi function -- 13. Cyclic Groups and Cryptography -- 14. Applications of Cosets -- 15. An Introduction to Reed?Solomon codes -- 16. Blum?Goldwasser Cryptography -- 17. Factoring by the Quadratic Sieve -- 18. Polynomials and Finite Fields -- 19. Reed-Solomon Codes II -- Bibliography. . 330 $aThis text presents a careful introduction to methods of cryptology and error correction in wide use throughout the world and the concepts of abstract algebra and number theory that are essential for understanding these methods. The objective is to provide a thorough understanding of RSA, Diffie?Hellman, and Blum?Goldwasser cryptosystems and Hamming and Reed?Solomon error correction: how they are constructed, how they are made to work efficiently, and also how they can be attacked. To reach that level of understanding requires and motivates many ideas found in a first course in abstract algebra?rings, fields, finite abelian groups, basic theory of numbers, computational number theory, homomorphisms, ideals, and cosets. Those who complete this book will have gained a solid mathematical foundation for more specialized applied courses on cryptology or error correction, and should also be well prepared, both in concepts and in motivation, to pursue more advanced study in algebra and number theory. This text is suitable for classroom or online use or for independent study. Aimed at students in mathematics, computer science, and engineering, the prerequisite includes one or two years of a standard calculus sequence. Ideally the reader will also take a concurrent course in linear algebra or elementary matrix theory. A solutions manual for the 400 exercises in the book is available to instructors who adopt the text for their course. 410 0$aSpringer Undergraduate Texts in Mathematics and Technology,$x1867-5506 606 $aAlgebra 606 $aData encryption (Computer science) 606 $aNumber theory 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aCryptology$3https://scigraph.springernature.com/ontologies/product-market-codes/I28020 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aAlgebra. 615 0$aData encryption (Computer science) 615 0$aNumber theory. 615 14$aAlgebra. 615 24$aCryptology. 615 24$aNumber Theory. 676 $a652.8 676 $a003.54 700 $aChilds$b Lindsay N$4aut$4http://id.loc.gov/vocabulary/relators/aut$041695 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910338255203321 996 $aCryptology and Error Correction$91732419 997 $aUNINA