An Introduction to Number Theory with Cryptography

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CRC Press, Apr 19, 2016 - Mathematics - 572 pages
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Number theory has a rich history. For many years it was one of the purest areas of pure mathematics, studied because of the intellectual fascination with properties of integers. More recently, it has been an area that also has important applications to subjects such as cryptography. An Introduction to Number Theory with Cryptography presents number theory along with many interesting applications. Designed for an undergraduate-level course, it covers standard number theory topics and gives instructors the option of integrating several other topics into their coverage. The "Check Your Understanding" problems aid in learning the basics, and there are numerous exercises, projects, and computer explorations of varying levels of difficulty.

 

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Contents

Chapter 0 Introduction
1
Chapter 1 Divisibility
9
Chapter 2 Unique Factorization
59
Chapter 3 Applications of Unique Factorization
71
Chapter 4 Congruences
107
Chapter 5 Cryptographic Applications
167
Chapter 6 Polynomial Congruences
193
Chapter 7 Order and Primitive Roots
207
Chapter 11 Geometry of Numbers
337
Chapter 12 Arithmetic Functions
367
Chapter 13 Continued Fractions
383
Chapter 14 Gaussian Integers
427
Chapter 15 Algebraic Integers
453
Chapter 16 Analytic Methods
479
Fermats Last Theorem
503
Appendix A Supplementary Topics
513

Chapter 8 More Cryptographic Applications
241
Chapter 9 Quadratic Reciprocity
263
Chapter 10 Primality and Factorization
295
Appendix B Answers and Hints for OddNumbered Exercises
535
Back Cover
549
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