In this chapter we describe, at an elementary level, some of the applications of the Group Theory and Number Theory we have developed so far to Cryptology. We emphasise that these “textbook versions” of the applications do not do justice to the complexities that arise in practice, and warn the reader that implementing the mechanisms that we discuss in the form given here would lead to severe vulnerabilities of the schemes. The reader is encouraged to start by reading the paper on Why textbook ElGamal and RSA encryption are insecure.