RSA Algorithm Technique in Asymmetry Encryption 1st draft

This paper is about Asymmetric Encryption specifically the RSA Algorithm. Even though this is a computer science topic, the paper is for a math class so the main focus of the paper is the math involved in Asymmetric Encryption with main emphasis in the RSA Algorithm.

      The paper should be 10-15 pages, double-spaced in 12 pt. font with one-inch margins.
      The paper should be written for an audience of your peers, i.e. for senior mathematics majors.
      There should be an introduction that informs the reader of where the paper will take them and a conclusion that summarizes the work.
      You should make clear what your own contribution to the topic is.  That is, show how you relate or apply the material to an area of interest to you.
      Presentation and organization are major concerns.
      Style, grammar, and spelling are important and will be included in your grade.
      References must be cited within the paper.
      You should include complete bibliographic information, with several sources.

I included the 1st draft that is 6 pages. This is the feedback I received from my professor:

What you have so far makes sense, but I hoped to see more of the mathematics. Why are prime numbers used, and how? What does number theory have to do with the algorithm? I was also not clear on the difference between the public key and the private key. You call them “mathematically structured”; in what sense? You need to say a lot more about the mathematics behind the algorithm.

So the additional 5 pages need to be about the mathematics behind the algorithm.