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Once the privilege of a secret few, cryptography is now taught at universities around the world. Introduction to Cryptography with OpenSource Software illustrates algorithms and cryptosystems using examples and the opensource 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 endofchapter 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 publickey cryptosystems of RSA and Rabins cryptosystem. Other publickey 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 bitoriented secretkey, 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 multiparty computation, zeroknowledge proofs, oblivious transfer, and voting protocols.
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