Undergraduate resources for Number Theory and Cryptography

Question

For the absolute life of me, I cannot seem to wrap my head around the proofs given in my number theory and cryptography class. Maybe it's the teacher, or the textbook, both or neither, but this is causing me great concern for two reasons.

First is obvious, since I hate solving math without a full comprehensive understanding of the concepts. Second, I have the feeling I'll be asked to prove concepts in my exams.

So how do I go about this? Does anyone have any textbooks or something (or anything) that could help me grasp all this better? To clarify, the main concepts covered in class are GCDs, Euclidean algorithm, concepts of coprimes, Euler-Fermat theorem etc. Then these bleed into solving cryptosystems such as RSA, Chinese Remainder Theorem and others.

Thanks!

Answer 1

While Hardy and Wright is the standard reference I don't feel like this is very readable in general. Don't get me wrong, it's a great resource but maybe a book like Niven et al "Introduction to the theory of numbers" might be a book you would find useful.

Also another good introductory book is by Burton "Elementary Number Theory".

Answer 2

I took an elementary number theory course this past spring semester. The textbook we used for the course was "Elementary Number Theory" by Gareth A. Jones and J. Mary Jones. All of the topics you are looking to learn are covered in detail throughout the book. The book is heavily proof based but also does have questions worked out in detail. In my opinion, the best part of this book was the exercise portion of it. Every question in the textbook had a solution with work in the back of the book. I would definitely recommend looking at this book.

If you need any additional exercises to do, my professor has put up our problem sets on the course web page. The problem sets mostly follow the order of the textbook and at the beginning of each problem set it mentions the reading. This should allow you to follow along or get extra practice if you need it. Hope that helps!