Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, etc. Therefore, users should not only know how its techniques work, but they must also be able to estimate their efficiency and security. Based on courses taught at Technical University in Darmstadt, Germany, this book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge that are interested in modern cryptographic algorithms and their mathematical foundation. Several exercises are included following each chapter. Johannes A. Buchmann is a Professor of Computer Science and Mathematics at the Technical University of Darmstadt, and the Associate Editor of the Journal of Cryptology. In 1985, he received the Feodor Lynen Fellowship of the Alexander vonHumboldt Foundation. Furthermore, he has received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation (Deutsche Forschungsgemeinschaft DFG).