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 applicationsof number theory, particularly in cryptography. No background in algebraor number theory is assumed, and the book begins with a discussion of thebasic number theory needed. The approach taken is algorithmic, emphasizingestimates of the efficiency of the techniques which arise from the theory.A special feature is the inclusion of recent applications of the theoryof elliptic curves. Extensive imaginative exercises and careful, revealinganswers have been included in all of the chapters. The information societyand the computer age have given rise to innumerable applications for cryptographybesides the original motivation of secure communication. Thus, cryptographyis a relatively fast-moving field and it is due to this fact that thisnew edition contains substantial revisions and updated references.
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