This reference work looks at modern concepts of computer security. It introduces the basic mathematical background necessary to follow computer security concepts before moving on to modern developments in cryptography. The concepts are presented clearly and illustrated by numerous examples. Subjects covered include: private-key and public-key encryption, hashing, digital signatures, authentication, secret sharing, group-oriented cryptography, and many others. The section on intrusion detection and access control provide examples of security systems implemented as a part of operating system. Database and network security is also discussed. The final chapters introduce modern e- business systems based on digital cash.