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This book presents modern concepts of computer security. It introduces the basic mathematical background necessary to follow computer security concepts. Modern developments in cryptography are examined, starting from private-key and public-key encryption, going through hashing, digital signatures, authentication, secret sharing, group-oriented cryptography, pseudorandomness, key establishment protocols, zero-knowledge protocols, and identification, and finishing with an introduction to modern e-business systems based on digital cash. Intrusion detection and access control provide examples of security systems implemented as a part of operating system. Database and network security is also discussed.