An Introduction to Number Theory with Cryptography: 2nd Edition (Hardback) book cover

An Introduction to Number Theory with Cryptography

2nd Edition

By James Kraft, Lawrence Washington

Chapman and Hall/CRC

578 pages | 28 B/W Illus.

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Hardback: 9781138063471
pub: 2018-01-31
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pub: 2018-01-29
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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.

Table of Contents

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

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.

About the Series

Textbooks in Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
COM083000
COMPUTERS / Security / Cryptography
MAT022000
MATHEMATICS / Number Theory