Current version: 9th edition, July 2008
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In this script delivered with the CrypTool application you will find predominantly mathematically oriented information on using cryptographic procedures. The main chapters have been written by various authors and are therefore independent from one another. At the end of each chapter you will find bibliographical references and web links.

• The first chapter explains the principles of symmetric and asymmetric encryption and describes shortly the current decryption records of modern symmetric algorithms.
• Because of didactical reasons, the second chapter gives an exhaustive overview about paper and pencil encryption methods.
• Chapter three is dedicated to the fascinating topic of prime numbers.
• In chapter 4, modular arithmetic and elementary number theory are introduced, and applied in an exemplary manner for the RSA procedure.
• By reading chapter 5 you will gain an insight into the mathematical ideas and concepts behind modern cryptography.
• Chapter 6 gives an overview about the status of attacks against modern hash algorithms and is then shortly devoted to digital signatures, which are an essential component of e-business applications.
• Chapter 7 describes elliptic curves: Compared to RSA, they provide a very efficient alternative for the hardware based generation of digital signatures.
• Chapter 8 discusses the threats for existing cryptographic methods and introduces the current alternative research approaches to achieve long-term security of cryptographic schemes.

Additionally the appendix contains a list of movies and novels where cryptography plays a role.