The combination of advanced mathematical techniques with the enormous growth of the possibilities for automatic data-processing has resulted in very strong systems of cryptography, that is systems that are powerful, sophisticated, and virtually impregnable. Cryptographers cannot design cryptosystems that are guaranteed to have no weaknesses or that are impervious to unforeseeable methods of attack. Cryptosystems make it very difficult but not impossible for an attacker to determine the decoding key and also protect information resources at less cost than the value of the information that is being protected. This book is aimed at solving a real life situation of encryption which uses cryptographic techniques for secure communication. At the end, a mathematical algorithm will be developed to produce a Key Generation and Exchange situation which will comprise of private key and public key. The general objective of this book is to contribute to the general body of knowledge in the area of cryptography and to support classification of top secret information. The following security requirements will be met: - authentication, confidentiality, Integrity, non-repudiation.