
An Introduction to Number Theory with Cryptography
CRC Press
2nd Edition
Published on 31. January 2018
Book
Hardback
578 pages
978-1-138-06347-1 (ISBN)
Description
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.
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.
Reviews / Votes
"... 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
More details
Series
Edition
2nd edition
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Illustrations
28 s/w Abbildungen, 18 s/w Tabellen
18 Tables, black and white; 28 Illustrations, black and white
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 37 mm
Weight
1060 gr
ISBN-13
978-1-138-06347-1 (9781138063471)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

James Kraft | Lawrence Washington
An Introduction to Number Theory with Cryptography
Book
01/2023
2nd Edition
Chapman & Hall/CRC
€74.90
Shipment within 10-20 days

James Kraft | Lawrence Washington
An Introduction to Number Theory with Cryptography
E-Book
01/2018
2nd Edition
Chapman & Hall/CRC
€65.99
Available for download

James Kraft | Lawrence Washington
An Introduction to Number Theory with Cryptography
E-Book
01/2018
2nd Edition
Chapman & Hall/CRC
€65.99
Available for download
Persons
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.
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.
Content
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