Factoring integers: What to study?

Question

I want to learn everything related to factoring integers, I have no idea what should I study to learn about this, I want to learn and understand all the currently used algorithms, why a polynomial time algorithm seems so hard to find, etc.

Which books (cheap ones are better) cover the topics needed to get into factoring?

Answer 1

You can check out The Joy of Factoring by Samuel S. Wagstaff, Jr.

From the hyperlinked page:

This book is about the theory and practice of integer factorization 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.