This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Chapter Ⅰ Some Topics in Elementary Number Theory
Chapter Ⅱ Finite Fields and Quadratic Residues
Chapter Ⅲ Cryptography
Chapter Ⅳ Public Key
Chapter Ⅴ Primality and Factoring
Chapter Ⅵ Elliptic Curves
Answers to Exercises

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