Algebraic Aspects of Cryptography (Algorithms and Computation in Mathematics) [Hardcover]

Neal Koblitz (Author), A.J. Menezes (Contributor), Y.-H. Wu (Contributor), R.J. Zuccherato (Contributor)

Book Description

ISBN-10: 3540634460 | ISBN-13: 978-3540634461 | Publication Date: June 24, 2004 | Edition: 2nd Printing

From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews

Editorial Reviews

Review

"... This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. ... Overall, this is an excellent expository text, and will be very useful to both the student and researcher." M.V.D.Burmester, Mathematical Reviews 2002 "... I think this book is a very inspiring book on cryptography. It goes beyond the traditional topics (most of the cryptosystems presented here are first time in a textbook, some of Paturi's work is not published yet). This way the reader has the feeling how easy to suggest a cryptosystem, how easy to break a safe looking system and hence how hard to trust one. The interested readers are forced to think together with ther researchers and feel the joy of discovering new ideas. At the same time the importance of "hardcore" mathematics is emphasized and hopefully some application driven students will be motivated to study theory." Péter Hajnal, Acta Scientiarum Mathematicarum, 64.1998, p. 750 "... Overall, the book is highly recommended to everyone who has the requisite mathematical sophistication." E.Leiss, Computing Reviews 1998, p. 506 "... Der Autor, der ... vielen Lesern dieses Rundbriefs gut bekannt sein wird, hat hier ein kleines Werk vorgelegt, das man wohl am Besten als "Lesebuch zu algebraischen Aspekten der Kryptographie mit öffentlichem Schlüssel" charakterisieren kann. ... Mit zunehmender Schwierigkeit des Material werden die Ausführungen dabei skizzenhafter und beschränken sich immer stärker auf den Hinweis auf entsprechende Quellen, was den Charakter eines guten "Lesebuchs", wie ich es oben bezeichnet habe, ausmachen sollte. Das Buch eignet sich damit selbst für "advanced undergraduates", wie es im Klappentext heißt, als Einstieg und erster Überblick über ein Gebiet, in dem sich in den letzten Jahren auf überraschende Weise praktische Anwendungsmöglichkeiten für tief innermathematische Themen ergeben haben." Hans-Gert Gräbe, Computeralgebra Rundbrief 1999, Issue 25 "... Es gelingt Koblitz, anschaulich und mit elementaren Mitteln auch Dinge zu erläutern, die in vergleichbaren Texten kaum zu finden sind: z.B. den Hilbertschen Basis- und Nullstellensatz, sowie Gröbnerbasen. ..." Franz Lemmermeyer, Mathematische Semesterberichte 1999, 46/1     

From the Back Cover

This is a textbook for a course (or self-instruction) in cryptography with emphasis on algebraic methods. The first half of the book is a self-contained informal introduction to areas of algebra, number theory, and computer science that are used in cryptography. Most of the material in the second half - "hidden monomial" systems, combinatorial-algebraic systems, and hyperelliptic systems - has not previously appeared in monograph form. The Appendix by Menezes, Wu, and Zuccherato gives an elementary treatment of hyperelliptic curves. This book is intended for graduate students, advanced undergraduates, and scientists working in various fields of data security.   From the reviews: "... This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. ... Overall, this is an excellent expository text, and will be very useful to both the student and researcher." M.V.D.Burmester, Mathematical Reviews 2002 "... I think this book is a very inspiring book on cryptography. It goes beyond the traditional topics (most of the cryptosystems presented here are first time in a textbook, some of Patarin's work is not published yet). This way the reader has the feeling how easy to suggest a cryptosystem, how easy to break a safe looking system and hence how hard to trust one. The interested readers are forced to think together with their researchers and feel the joy of discovering new ideas. At the same time the importance of "hardcore" mathematics is emphasized and hopefully some application driven students will be motivated to study theory." P. Hajnal, Acta Scientiarum Mathematicarum 64.1998 "... Overall, the book is highly recommended to everyone who has the requisite mathematical sophistication." E.Leiss, Computing Reviews 1998

Product Details

• Hardcover: 215 pages
• Publisher: Springer; 2nd Printing edition (June 24, 2004)
• Language: English
• ISBN-10: 3540634460
• ISBN-13: 978-3540634461
• Product Dimensions: 9.6 x 6.4 x 0.7 inches
• Shipping Weight: 15.5 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,018,691 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

4.0 out of 5 stars Excellent, but only if you have extensive knowledge of math, June 28, 2004

By 

Ragnarok Books - See all my reviews

This review is from: Algebraic Aspects of Cryptography (Algorithms and Computation in Mathematics) (Hardcover)

The textbook is intended for students with extensive knowledge of number theory, field theory, and algebraic techniques. It is terse and runs through the material using the definition-lemma-proof-theorem-proof method, with almost no examples. For students without the aforementioned prerequisites, the book is almost impossible to understand.

The book can be great for students with the mathematical prerequisites and with sufficient mathematical maturity to understand elaborate definitions, theorems and proofs and who want to learn the material efficiently and quickly.

The beginning student is advised to look for other, more elementary textbooks.

The book contains many exercises with solutions at the end of the book.

1 of 21 people found the following review helpful:

4.0 out of 5 stars Excelent, May 25, 2000

By 

Kmacho (Madrid, Spain) - See all my reviews

This review is from: Algebraic Aspects of Cryptography (Algorithms and Computation in Mathematics) (Hardcover)

It's a very good book about cryptography and all the "stuff" about it. Neal Koblick is one of the invertor on ECC, so he knows about he talks.