An introduction to number theory with cryptography
著者
書誌事項
An introduction to number theory with cryptography
（Textbooks in mathematics）
CRC Press, c2018
2nd ed
- : hardback
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注記
"A Chapman & Hall book"
Includes index
内容説明・目次
内容説明
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.
目次
- 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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