An Introduction to Number Theory with Cryptography

✍ Scribed by Kraft, James S.; Washington, Lawrence C

• Publisher: CRC Press
• Year: 2013
• Tongue: English
• Leaves: 568
• Category: Library

✦ Synopsis

IntroductionDiophantine EquationsModular ArithmeticPrimes and the Distribution of PrimesCryptographyDivisibilityDivisibilityEuclid's Theorem Euclid's Original Proof The Sieve of Eratosthenes The Division Algorithm The Greatest Common Divisor The Euclidean Algorithm Other BasesLinear Diophantine EquationsThe Postage Stamp Problem Fermat and Mersenne Numbers Chapter Highlights Problems Unique FactorizationPreliminary Results The Fundamental Theorem of Arithmetic Euclid and the Fundamental Theorem of ArithmeticChapter Highlights Problems Applications of Unique Factorization A Puzzle Irrationality. Read more...

Abstract: IntroductionDiophantine EquationsModular ArithmeticPrimes and the Distribution of PrimesCryptographyDivisibilityDivisibilityEuclid's Theorem Euclid's Original Proof The Sieve of Eratosthenes The Division Algorithm The Greatest Common Divisor The Euclidean Algorithm Other BasesLinear Diophantine EquationsThe Postage Stamp Problem Fermat and Mersenne Numbers Chapter Highlights Problems Unique FactorizationPreliminary Results The Fundamental Theorem of Arithmetic Euclid and the Fundamental Theorem of ArithmeticChapter Highlights Problems Applications of Unique Factorization A Puzzle Irrationality

✦ Table of Contents

Content: Front Cover
Dedication
Contents
Preface
Chapter 0 Introduction
Chapter 1 Divisibility
Chapter 2 Unique Factorization
Chapter 3 Applications of Unique Factorization
Chapter 4 Congruences
Chapter 5 Cryptographic Applications
Chapter 6 Polynomial Congruences
Chapter 7 Order and Primitive Roots
Chapter 8 More Cryptographic Applications
Chapter 9 Quadratic Reciprocity
Chapter 10 Primality and Factorization
Chapter 11 Geometry of Numbers
Chapter 12 Arithmetic Functions
Chapter 13 Continued Fractions
Chapter 14 Gaussian Integers
Chapter 15 Algebraic Integers Chapter 16 Analytic MethodsChapter 17 Epilogue: Fermat's Last Theorem
Appendix A Supplementary Topics
Appendix B Answers and Hints for Odd-Numbered Exercises
Back Cover

✦ Subjects

Cryptography. Number theory.