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An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) 2008th Edition

4.5 out of 5 stars 13 customer reviews
ISBN-13: 978-0387779935
ISBN-10: 0387779930
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Editorial Reviews

Review

From the reviews:

"The book is devoted to public key cryptography, whose principal goal is to allow two or more people to exchange confidential information … . The material is very well organized, and it is self-contained: no prerequisites in higher mathematics are needed. In fact, everything is explained and carefully covered … . there is abundance of examples and proposed exercises at the end of each chapter. … This book is ideal as a textbook for a course aimed at undergraduate mathematics or computer science students." (Fabio Mainardi, The Mathematical Association of America, October, 2008)

"This book focuses on public key cryptography … . Hoffstein, Pipher, and Silverman … provide a thorough treatment of the topics while keeping the material accessible. … The book uses examples throughout the text to illustrate the theorems, and provides a large number of exercises … . The volume includes a nice bibliography. … Summing Up: Highly recommended. Upper-division undergraduate through professional collections." (C. Bauer, Choice, Vol. 46 (7), March, 2009)

"For most undergraduate students in mathematics or computer science (CS), mathematical cryptography is a challenging subject. … it is written in a way that makes you want to keep reading. … The authors officially targeted the book for advanced undergraduate or beginning graduate students. I believe that this audience is appropriate. … it could even be used with students who are just learning how to execute rigorous mathematical proofs. … I strongly believe that it finds the right tone for today’s students … ." (Burkhard Englert, ACM Computing Reviews, March, 2009)

"The exercises and text would make an excellent course for undergraduate independent study. … This is an excellent book. Hoffstein, Pipher and Silverman have written as good a book as is possible to explain public key cryptography. … This book would probably be best suited for a graduate course that focused on public key cryptography, for undergraduate independent study, or for the mathematician who wants to see how mathematics is used in public key cryptography." (Jintai Ding and Chris Christensen, Mathematical Reviews, Issue 2009 m)

From the Back Cover

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required.

The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:

* classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures;

* fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;

* an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.

This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.

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Product Details

  • Series: Undergraduate Texts in Mathematics
  • Hardcover: 524 pages
  • Publisher: Springer; 2008 edition (August 12, 2008)
  • Language: English
  • ISBN-10: 0387779930
  • ISBN-13: 978-0387779935
  • Product Dimensions: 6.1 x 1.2 x 9.2 inches
  • Shipping Weight: 2 pounds
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (13 customer reviews)
  • Amazon Best Sellers Rank: #1,039,526 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on December 17, 2009
Format: Hardcover Verified Purchase
At least for the chapters that were studied by this reviewer, the authors of this book give an effective introduction to the mathematical theory used in cryptography at a level that can be approached by an undergraduate senior in mathematics. The field of cryptography is vast of course, and a book of this size could not capture it effectively. The topics of primary importance are represented however, and the authors do a fine job of motivating and explaining the needed concepts.
The authors give an elementary overview of elliptic curves over the complex numbers, and most importantly over finite fields whose characteristic is greater than 3. The case where the characteristic is equal to 2 is delegated to its own section. In discussing the arithmetic of elliptic curves over finite fields, the authors give a good motivation for Hasse's formula, which gives a bound for the number of points of the elliptic curve (over a finite field), but they do not go into the details of the proof. The Hasse formula is viewed in some texts as a "Riemann Hypothesis" for elliptic curves over finite fields, and was proven by Hasse in 1934. This reviewer has not studied Hasse's proof, but a contemporary proof relies on the Frobenius map and its separability, two notions that the authors do not apparently want to introduce at this level of book (however they do introduce the Frobenius map when discussing elliptic curves over F2). Separability is viewed in some texts in elliptic curves as more of a technical issue, which can be ignored at an elementary level. It arises when studying endomorphisms of elliptic curves of fields of non-zero characteristic, and involves defining rational functions.
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By Stephen on March 15, 2014
Format: Hardcover Verified Purchase
I'm doing my honor's thesis on theoretical Cryptography as an undergrad at Colby College, and this book has been the perfect resource. It is so clear, and many time teaches by using easy to understand concrete examples. This book is the perfect place to start if you want to learn about Crypto.
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Format: Paperback Verified Purchase
Good start to this topic. The only hiccup was that I tried to work through the text example myself and came up with different answers. This is because the text was wrong. There is an extensive errata file that you can get online. May sure you get it before starting to work through text examples and end-of-chapter exercises. I hope that a revised version is issued that corrects these errata.
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Format: Paperback
This is a fantastic book. The writing is simple and clear. Even if I skipped class for a week, I could sit down and read this book, confident I would receive an explanation that was both complete and easy-to-follow. I couldn't recommend it more. Even though we didn't cover elliptic curves in my class, I read the chapter anyway and found that I was able to understand anything in the chapter that I committed to learning.
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Format: Hardcover Verified Purchase
Good introduction to intermediate level coverage of math-based crypto, however, I found the text hard to follow because the cross references were hard to look up. E.g. a back reference to proposition x.y is hard to look up bec propositions are somewhat sparse and each chapter x is very large -- so you find yourself thumbing through the chapter trying to find propositions to get your bearing. It really interferes with the reading process. Including a page number would help greatly. (For more purely math books, this isn't as large of an issue bec there are so many propositions and theorems that it's easy to isolate the back reference -- but for this text, it is quite difficult.)
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Format: Hardcover Verified Purchase
It is for undergrads, but useful at grad level to any student who didn't take the courses as an undergrad (i.e., fresh grad students discovering their love to cryptography)
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Format: Hardcover Verified Purchase
The text itself is decent and clear. However, I needed the 2nd edition for a class in which I was enrolled, and so rented the kindle version. Unfortunately, the kindle version linked is a reproduction of the first edition and as such is missing some of the exercises I need for the class.

Edit (followup):
By happy (from my perspective) accident it was the campus bookstore (and therefore the majority of my classmates) who had the wrong edition of the book. This does not alter my rating of the book, since the various formats linked together on a page ought (in my opinion) to be of the same edition of the text.
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