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Alasdair McAndrew

Introduction to Cryptography with Open-Source Software (Discrete Mathematics and Its Applications) 1st Edition

by Alasdair McAndrew (Author)

4.6 4 ratings

Part of: Discrete Mathematics and Its Applications (80 books)

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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.

ISBN-10

143982570X
ISBN-13

978-1439825709
Edition

1st
Publication date

June 17, 2011
Part of series

Discrete Mathematics and Its Applications
Language

English
Dimensions

6.14 x 1.23 x 9.21 inches
Print length

462 pages
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Editorial Reviews

Review

"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

About the Author

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

Product details

Publisher ‏ : ‎ CRC Press; 1st edition (June 17, 2011)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 462 pages
ISBN-10 ‏ : ‎ 143982570X
ISBN-13 ‏ : ‎ 978-1439825709
Item Weight ‏ : ‎ 1.7 pounds
Dimensions ‏ : ‎ 6.14 x 1.23 x 9.21 inches

Best Sellers Rank: #4,451,104 in Books (See Top 100 in Books)
- #720 in Combinatorics (Books)
- #873 in Discrete Mathematics (Books)
- #1,707 in Computer Graphics

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ransona

A wonderful introduction or perhaps something more.

Reviewed in the United States on December 9, 2011

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It's a very good book if not excellent. Extremely educational allows any person to understand the framework of security from the point of view of cryptography. Concepts are presented in a simple way and combining this with the ability to experiment with them in the Sage mathematical simulation tool, makes the learning experience motivating.

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David Joyner

well-written book on cryptography

Reviewed in the United States on July 4, 2011

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. Public-Key Cryptosystems Based on Logarithms and Knapsacks, the sixth chapter, covers the discrete logarithm problem, El Gamal's cryptosystem, the Diffie-Hellman key exchange, and Knapsack cryptosystems. Chapter 7, Digital Signatures, talks about the RSA signature scheme, Rabin digital signatures, and the El Gamal digital signature scheme. The eighth chapter, Block Ciphers and the Data Encryption Standard, discusses Block ciphers, the Data Encryption Standard (DES), and Feistel ciphers. Chapter 9 is a review of finite fields. The Advanced Encryption Standard is chapter 10. This chapter covers both the usual AES but also a simplified Rijndael cipher. Both of these are implemented in Sage and Sage examples illiustrate the computations. Chapter 11 is on Hash Functions. Their security, construction, and uses are discussed. Chapter 12 is on Elliptic Curve Cryptosystems.About half the chapter sketches background on elliptic curves. This is a very technical topic, but one which Sage has a great deal of computational functionality implemented. The rest of the chapter covers elliptic curve cryptosystems, elliptic curve signature schemes, and related topics.
Random Numbers and Stream Ciphers is chapter 13. It covers such topics as pseudo-random number generators, Stream ciphers, RC4, and the Blum-Goldwasser cryptosystem. The last chapter is Advanced Applications and Protocols. It covers topics such as zero knowledge proofs, digital cash and voting protocols.

There are two appendices: one is an introduction to the mathematical software system Sage and the other summarizes some more advanced aspects of computational number theory. The book also has a good index.

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Peter

Very comprehensive book for a beginner in cryptography.

Reviewed in the United Kingdom on December 28, 2013

Verified Purchase

The concept of modular maths was new to me, so takes some getting used to.
In conjunction with this book I use The Code Book by Simon Singh. The 'Very Brief Guide to Cryptography' (or similar title) is also a useful source book. With these books and Excel I hope to find out more about the mechanics of PGP.

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Introduction to Cryptography with Open-Source Software (Discrete Mathematics and Its Applications) 1st Edition

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