Cryptographic methods are essential for the realization of electronic business processes. They secure billing in mobile networks and form a basis for security on the Internet and in end devices, as well as for the electronic awarding of licenses. This book introduces security services and security mechanisms conceptually and illustrates simple cryptographic mechanisms using historical methods. Modern cryptographic algorithms are based on discrete algebra, which can be intuitively understood through simple examples. The book also addresses newer areas with elliptic curves. In addition to the fundamental cryptographic mechanisms and protocols, it provides insights into applications such as recent security methods on the Internet and in mobile networks, operating systems of smart cards, trusted computing, and public key infrastructure.