James Kraft, Lawrence Washington

An Introduction to Number Theory with Cryptography

• Broschiertes Buch

Produktbeschreibung

Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory.

The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum.

Features of the second edition include

Over 800 exercises, projects, and computer explorations

Increased coverage of cryptography, including Vigenere, Stream, Transposition,and Block ciphers, along with RSA and discrete log-based systems

"Check Your Understanding" questions for instant feedback to students

New Appendices on "What is a proof?" and on Matrices

Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences

Answers and hints for odd-numbered problems

About the Authors:

Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School.

Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

Produktdetails

• Textbooks in Mathematics
• Verlag: CRC Press / Taylor & Francis
• 2. Aufl.
• Seitenzahl: 600
• Erscheinungstermin: 21. Januar 2023
• Englisch
• Abmessung: 155mm x 234mm x 36mm
• Gewicht: 901g
• ISBN-13: 9781032476353
• ISBN-10: 1032476354
• Artikelnr.: 67400553

Autorenporträt

Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School. Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

Inhaltsangabe

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

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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

Rezensionen

"... provides a fine history of number theory and surveys its applications. College-level undergrads will appreciate the number theory topics, arranged in a format suitable for any standard course in the topic, and will also appreciate the inclusion of many exercises and projects to support all the theory provided. In providing a foundation text with step-by-step analysis, examples, and exercises, this is a top teaching tool recommended for any cryptography student or instructor."
-California Bookwatch