Algebraic Aspects of Cryptography (Algorithms and Computation in Mathematics, Vol. 3) by Neal Koblitz (PDF)

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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

User’s 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

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐on time and as described

⭐In part four of my favorite book reviews, I recommended Neil’s A Course in Number Theory and Cryptography. I said “I love two of his books. This is one of them. I’ll keep the other book secret until the next part of the series.” Well here it is.Koblitz is my favorite author. He’s not only a badass and inventor of elliptic curve cryptography but also a great writer. As I said early in the series, I hate textbooks. But not Koblitz’s textbooks. His textbooks are not really textbooks. Koblitz knows exactly what to explain and how to explain and always gives good and relevant examples. This book gives brief refresher to algebra and then introduces hidden monomial cryptosystems, combinatorial-algebraic cryptosystems, and hyperelliptic cryptosystems (as well as elliptic-cruve systems). I hadn’t heard about these systems before and that’s what also made me excited about this book. It’s not like some other boring stupid cryptography books that derive RSA for the 5000th time.This book is also written mostly in definition-theorem-proof-example-exercise-answer style, which is one of the quickest ways to learn something.I’ve placed this book #34 in my all time 100 most favorite cryptography books. Google for >>catonmat favorite cryptography books<< to find my list and other reviews. My reviews have no affiliate links or garbage. Just awesome books that I truly enjoy. ⭐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. ⭐An excellent introductory text to some of the key mathematics of cryptography. The math here is fairly elementary, and everything that's needed is developed well. I've referred to this text many times. ⭐

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