The protection of sensitive information against unauthorized access or fraudulent changes has been of prime concern throughout the centuries. Modern communication techniques, using computers connected through networks, make all data even more vulnerable to these threats. In addition, new issues have surfaced that did not exist previously, for example, adding a signature to an electronic document. Cryptology addresses the above issues - it is at the foundation of all information security. The techniques employed to this end have become increasingly mathematical in nature. This work serves as an introduction to modern cryptographic methods. After a brief survey of classical cryptosystems, it concentrates on three main areas. First, stream ciphers and block ciphers are discussed. These systems have extremely fast implementations, but sender and receiver must share a secret key. Second, the book presents public key cryptosystems, which make it possible to protect data without a prearranged key. Their security is based on intractable mathematical problems, such as the factorization of large numbers. The remaining chapters cover a variety of topics, including zero-knowledge proofs, secret sharing schemes and authentication codes. Two appendices explain all mathematical prerequisites in detail: one presents elementary number theory (Euclid’s Algorithm, the Chinese Remainder Theorem, quadratic residues, inversion formulas, and continued fractions) and the other introduces finite fields and their algebraic structure. The text is an updated and improved version of An Introduction to Cryptology, originally published in 1988. Apart from a revision of the existing material, there are many new sections, and two new chapters on elliptic curves and authentication codes, respectively. In addition, the book is accompanied by a full text electronic version on CD-ROM as an interactive Mathematica manuscript. Basic Concepts in Cryptology should be of interest to computer scientists, mathematicians, and researchers, students, and practitioners in the area of cryptography.