A Course in Number Theory and Cryptography

The purpose of this book is to introduce the reader to arithmetic topics, both ancient and modern, which have been at the center of interest in applications of number theory, particularly in cryptography. No background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory which is needed. The approach taken is algorithmic, emphasizing estimates of the efficiency of the techniques which arise from the theory. A special feature is the inclusion of recent application of the theory of elliptic curves. Extensive imaginative exercises and careful, revealing answers have been included in all of the chapters. The information society and the computer age have given rise to innumerable applications for cryptography besides the original motivation of secure communication. Thus, cryptography is a relatively fast-moving field. The new edition contains due to that fact substantial revisions and updated references.

Klappentext
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.

Inhalt
1: Some Topics in Elementary Number Theory. 2: Finite Fields and Quadratic Residues. 3: Cryptography. 4: Public Key. 5: Primality and Factoring. 6: Elliptic Curves.

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