Cryptography has crept into everything, from Web browsers and e-mail programs to cell phones, bank cards, cars and even into medical implants. In the near future we will see many new exciting applications for cryptography such as radio frequency identiﬁcation (RFID) tags for anti-counterfeiting or car-to-car communications (we’ve worked on securing both of these applications). This is quite a change from the past, where cryptography had been traditionally conﬁned to very speciﬁc applications, especially government communications and banking systems. As a consequence of the pervasiveness of crypto algorithms, an increasing number of people must understand how they work and how they can be applied in practice. This book addresses this issue by providing a comprehensive introduction to modern applied cryptography that is equally suited for students and practitioners in industry. Our book provides the reader with a deep understanding of how modern cryptographic schemes work. We introduce the necessary mathematical concepts in a way that is accessible for every reader with a minimum background in college-level calculus. It is thus equally well suited as a textbook for undergraduate or beginning graduate classes, or as a reference book for practicing engineers and computer scientists who are interested in a solid understanding of modern cryptography.