This book is about the theory and practice of integer factorisation
presented in a historic perspective. It describes about twenty
algorithms for factoring and a dozen other number theory algorithms
that support the factoring algorithms. Most algorithms are
described both in words and in pseudocode to satisfy both number
theorists and computer scientists. Each of the ten chapters begins
with a concise summary of its contents. The book starts with a
general explanation of why factoring integers is important. The
next two chapters present number theory results that are relevant
to factoring. Further on there is a chapter discussing, in
particular, mechanical and electronic devices for factoring, as
well as factoring using quantum physics and DNA molecules. Another
chapter applies factoring to breaking certain cryptographic
algorithms. Yet another chapter is devoted to practical vs.
theoretical aspects of factoring. The book contains more than 100
examples illustrating various algorithms and theorems. It also
contains more than 100 interesting exercises to test the reader's
understanding. Hints or answers are given for about a third of the
exercises. The book concludes with a dozen suggestions of possible
new methods for factoring integers. This book is written for
readers who want to learn more about the best methods of factoring
integers, many reasons for factoring, and some history of this
fascinating subject. It can be read by anyone who has taken a first
course in number theory.
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