This book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem. It covers many of the familiar topics of elementary number theory, all with an algorithmic twist. The text also includes many interesting historical notes.
Table of Contents
1. Introduction 2. Fundamental algorithms 3. Unique factorization 4. Prime numbers 5. Modular arithmetic 6. Induction and Fermat 7. Pseudoprimes 8. Systems of Congruences 9. Groups 10. Mersenne and Fermat 11. Primality tests and primitive roots 12. The RSA cryptosystem