Group Theory and the RSA Encryption Algorithm

This is another large group of postings, focusing on the culmination of three year's private study – I finally understand the RSA Encryption Algorithm. I'm one of those people that finds mathematical concepts baffling and confusing unless I understand all aspects of it. If there's any vagueness or ambiguity anywhere, it niggles at my mind and drives me up the wall. No I don't have Aspergers', I'm just very pedantic. :-)

Anyway, I will be presenting my understanding of RSA in the following sections:

• Introduction to Group Theory
  
• Mod Multiplication
• Coprimes and Totients.
• Lagrange's Theorem in Group Theory and the Euler-Fermat Theorem
  
• Prime-Testing
  
• The Euclidean and Extended Euclidean Algorithms
  
• RSA Two-Key Encryption