Kraft / Washington An Introduction to Number Theory with Cryptography, Second Edition

2. Auflage 2018
ISBN: 978-1-351-66410-3
Verlag: Taylor & Francis
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 602 Seiten

Reihe: Textbooks in Mathematics

An undergraduate textbook for the sophomore/junior mathematics course on number theory, this book adds the very hot topic of cryptography and integrates the coverage. The book also offers the traditional topics found in all successful number theory texts. Includes many interesting cryptographic applications. Three new chapters, Linear Diophantine Equations; Fermat, Euler, and Wilson, and RSA and five new sections expand the coverage of cryptography and improve the structure of topics. "What is a Proof ,' a new Appendix offers basic ideas of what a proof is and strategies for constructing one. Over 200 new exercises in this edition.

Autoren/Hrsg.

Kraft, James

Washington, Lawrence

Fachgebiete

• Mathematik | Informatik EDV | Informatik Technische Informatik Computersicherheit Kryptographie, Datenverschlüsselung
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

20 1. Introduction; 2 Divisibility; 3. Linear Diophantine Equations; 4. Unique Factorization; 5. Applications of Unique Factorization; 6. Conguences; 7. Classsical Cryposystems; 8. Fermat, Euler, Wilson; 9. RSA; 10. Polynomial Congruences; 11. Order and Primitive Roots; 12. More Cryptographic Applications; 13. Quadratic Reciprocity; 14. Primality and Factorization; 15. Geometry of Numbers; 16. Arithmetic Functions; 17. Continued Fractions; 18. Gaussian Integers; 19. Algebraic Integers; 20. Analytic Methods, 21. Epilogue: Fermat's Last Theorem; Appendices; Answers and Hints for Odd-Numbered Exercises; Index

Über Autor(innen)

James S. Kraft teaches mathematics at the Gilman School. He has previously taught at the University of Rochester, St. Mary’s College of California, and Ithaca College. He has also worked in communications security. Dr. Kraft has published several research papers in algebraic number theory. He received his Ph.D. from the University of Maryland.

Lawrence C. Washington is a professor of mathematics and Distinguished Scholar-Teacher at the University of Maryland. Dr. Washington has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. He received his Ph.D. from Princeton University.