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Author: Alasdair McAndrew
ISBN : 143982570X
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Format: PDF, EPUB
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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.
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- Series: Discrete Mathematics and Its Applications
- Hardcover: 461 pages
- Publisher: CRC Press (May 24, 2011)
- Language: English
- ISBN-10: 143982570X
- ISBN-13: 978-1439825709
- Product Dimensions: 1.1 x 6.5 x 9.8 inches
- Shipping Weight: 1.7 pounds (View shipping rates and policies)
Free Introduction to Cryptography with Open-Source Software
This is a well-written book on cryptography, suitable as a textbook for an undergraduate or graduate course in the topic. It is also useful for someone who just wants a reference book on how to do cryptographic computations in Sage. (Sage is a free and open-source mathematical software system, available from <...>.) Each chapter has an extensive set of exercises, as well as a glossary. The exercises are broken into four groups: Review Exercises, Beginning Exercises, Sage Exercises, and Further (or more advanced) Exercises. The text tries to be self-contained, with definitions and key ideas illustrated with examples, many of which are supported by corresponding Sage commands.
The chapters will be briefly summarized next.
The first chapter, Introduction to Cryptography, sketches basic ideas such as confidentiality, various types of attacks, cryptographic protocols, and computer security. Some simple ciphers are given as examples. Basic Number Theory is chapter 2. It covers some basic mathematical definitions in elementary number theory, talks about some of the commonly used computations such as the Euclidean algorithm and modular exponentiation. Also, primality testing is covered.
Chapter 3 is Classical Cryptosystems. This covers the Caesar cipher, the Vigenère cipher, the one-time pad, and several permutation ciphers and matrix ciphers. The fourth chapter, Introduction to Information Theory, introduces entropy and uncertainty, and illustrates the notions by estimating the entropy of typical English language text. Chapter 5, Public-Key Cryptosystems Based on Factoring, covers the RSA cryptosystem, Rabin's cryptosystem and ends with a discussion on the Pollard rho method of factoring large integers.
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