An introduction to number theory with cryptography

Author(s)

• Kraft, James S.
• Washington, Lawrence C.

Bibliographic Information

An introduction to number theory with cryptography

James S. Kraft, Lawrence C. Washington

（Textbooks in mathematics）

CRC Press, c2018

2nd ed

• : hardback

Note

"A Chapman & Hall book"

Includes index

Description and Table of Contents

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

by "Nielsen BookData"

Details

• NCID: BB25566997
• ISBN:
  • 9781138063471
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boca Raton
• Pages/Volumes: xxii, 578 p.
• Size: 24 cm
• Classification:
  • LCC : QA241
  • DC23 : 512.7
• Subject Headings:
  • LCSH : Number theory
  • LCSH : Cryptography
• Parent Bibliography ID:
  • BA83550953