Introduction to Cryptography with Open-Source Software

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.

"This very well-written book is recommended to graduate or final-year undergraduate students intended to start research work on both theoretical and experimental cryptography. Most of the cryptographic protocols are illustrated by various examples and implemented using the open-source algebra software Sage. The book provides a rigorous introduction to the mathematics used in cryptography and covers almost all modern practical cryptosystems. Also, the book is certainly a valuable resource for practitioners looking for experimental cryptography with a computer algebra system."—Abderrahmane Nitaj (LMNO, Université de Caen Basse Normandie), IACR book reviews, February 2014"It would make a great first course in cryptography but it is also easy enough to read to make it suitable for solitary study. … Overall this is an excellent book. It is far from the theorem-proof format and it does try to explain the ideas and motivate the reader. The pattern of mixing some theory followed by some practice is good at keeping the less theory-minded reader rolling along as the need for the theory becomes all too apparent. … this is a really good book. If you want to master cryptography, this is a great place to start."—Mike James, IProgrammer, August 2011

Alasdair McAndrew is a senior lecturer in the School of Engineering and Science at Victoria University in Melbourne, Australia.