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The book studies modern concepts of Computer Security. It is selfcontained in the sense that it introduces the basic mathematical background necessary to follow computer security concepts. Next we examine modern developments in Cryptogra- phy 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, 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.