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Other titles in the Discrete Mathematics and Its Applications series:
Discrete Mathematics and Its Applications #65: Introduction to Cryptography with Open-Source Softwareby Alasdair Mcandrew
Synopses & Reviews
Once the privilege of a secret few, cryptography is now taught at universities around the world. Introduction to Cryptography with Open-Source Software illustrates algorithms and cryptosystems using examples and the open-source computer algebra system of Sage. The author, a noted educator in the field, provides a highly practical learning experience by progressing at a gentle pace, keeping mathematics at a manageable level, and including numerous end-of-chapter exercises.
Focusing on the cryptosystems themselves rather than the means of breaking them, the book first explores when and how the methods of modern cryptography can be used and misused. It then presents number theory and the algorithms and methods that make up the basis of cryptography today. After a brief review of classical cryptography, the book introduces information theory and examines the public-key cryptosystems of RSA and Rabin's cryptosystem. Other public-key systems studied include the El Gamal cryptosystem, systems based on knapsack problems, and algorithms for creating digital signature schemes.
The second half of the text moves on to consider bit-oriented secret-key, or symmetric, systems suitable for encrypting large amounts of data. The author describes block ciphers (including the Data Encryption Standard), cryptographic hash functions, finite fields, the Advanced Encryption Standard, cryptosystems based on elliptical curves, random number generation, and stream ciphers. The book concludes with a look at examples and applications of modern cryptographic systems, such as multi-party computation, zero-knowledge proofs, oblivious transfer, and voting protocols.
Book News Annotation:
Intended as an introduction to cryptography and accessible to readers with modest college level mathematic experience, this text provides a comprehensive overview of the basic principles, practices and technologies of modern encryption. Beginning with sections on the basic cryptographic theory and historical cyphers, the volume cover such topics as public key encryption, block cyphers, hash functions and random numbers and stream cyphers. The work includes technical examples and equations throughout, all of which can be simulated by the reader with the open source Sage computer algebra system. McAndrew is a professor of engineering and science at Victoria University, Australia. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
Presenting both mathematical and security perspectives, this text reviews basic theory and discusses cryptographic protocols and systems. With an emphasis on experimentation and exploration, the text offers a wealth of practical examples and numerous exercises using the open source software Sage. An accompanying CD-ROM includes the necessary codes. The author covers private and public key cryptosystems, knapsack cryptosystems, digital signatures, random number generators, elliptic curves, block ciphers, hash functions, the DES and AES, finite fields, and message authentication codes.
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