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 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 applications 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 and it is due to this fact that this new edition contains substantial revisions and updated references.

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