This second edition is a solid introduction to classical and modern number theory and its applications in computer science. It introduces basic concepts, results and methods, and discusses their application in the design of hardware and software, cryptography, and security. It is aimed at those in computing and information technology, including electrical engineering but will also be valuable to mathematics students interested in applications. Proofs of many theorems have been added in this new edition.
PART I Elementary Number Theory
Ch1. Introduction
Ch2. Theory of Divisibility
Ch3. Diophantine Equations
Ch4. Arithmetic Functions
Ch5. Distribution of Prime Numbers
Ch6. Theory of Congruences
Ch7. Arithmetic of Elliptic Curves
Ch8. Bibliographic Notes and Further Reading
PART II Computational/Algorithmic Number Theory
Ch9. Introduction
Ch10. Algorithms for Primality Testing
Ch11. Algorithms for Integer Factorization
Ch12. Algorithms for Discrete Logarithms
Ch13. Quantum Number-Theoretic Algorithms
Ch14. Miscellaneous Algorithms in Number Theory
Ch15. Bibliographic Notes and Further Reading
PART III Applied Number Theory in Computing/Cryptography
Ch16. Why Applied Number Theory
Ch17. Computer Systems Design
Ch18. Cryptography and Information Security
Ch19. Bibliographic Notes and Further Reading