Number Theory for Computing

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 TheoryCh1. IntroductionCh2. Theory of DivisibilityCh3. Diophantine EquationsCh4. Arithmetic FunctionsCh5. Distribution of Prime NumbersCh6. Theory of Congruences Ch7. Arithmetic of Elliptic CurvesCh8. Bibliographic Notes and Further ReadingPART II Computational/Algorithmic Number TheoryCh9. Introduction Ch10. Algorithms for Primality Testing Ch11. Algorithms for Integer FactorizationCh12. Algorithms for Discrete LogarithmsCh13. Quantum Number-Theoretic AlgorithmsCh14. Miscellaneous Algorithms in Number TheoryCh15. Bibliographic Notes and Further Reading PART III Applied Number Theory in Computing/CryptographyCh16. Why Applied Number TheoryCh17. Computer Systems DesignCh18. Cryptography and Information Security Ch19. Bibliographic Notes and Further Reading