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Item specifics
- Condition
- Good
- Seller Notes
- “Unread and unopened book.”
- Book Title
- Algebraic Aspects of Cryptography : With an Appendix on Hyperelli
- Features
- EX-LIBRARY
- ISBN
- 9783540634461
About this product
Product Identifiers
Publisher
Springer Berlin / Heidelberg
ISBN-10
3540634460
ISBN-13
9783540634461
eBay Product ID (ePID)
807648
Product Key Features
Number of Pages
IX, 206 Pages
Language
English
Publication Name
Algebraic Aspects of Cryptography : with an Appendix on Hyperelliptic Curves
Publication Year
1998
Subject
Communication Studies, Computer Science, Algebra / General, Number Theory, Databases / General, Geometry / Algebraic
Type
Textbook
Subject Area
Mathematics, Computers, Language Arts & Disciplines
Series
Algorithms and Computation in Mathematics Ser.
Format
Hardcover
Dimensions
Item Height
0.3 in
Item Weight
38.1 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
97-048779
Dewey Edition
21
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 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 , "... 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." P'ter 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 ?ffentlichem Schl'ssel" charakterisieren kann. ... Mit zunehmender Schwierigkeit des Material werden die Ausf'hrungen dabei skizzenhafter und beschr'nken sich immer st'rker 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 f'r "advanced undergraduates", wie es im Klappentext hei't, als Einstieg und erster ?berblick ?ber ein Gebiet, in dem sich in den letzten Jahren auf ?berraschende Weise praktische Anwendungsm'glichkeiten f'r tief innermathematische Themen ergeben haben." Hans-Gert Gr'be, Computeralgebra Rundbrief 1999, Issue 25 "... Es gelingt Koblitz, anschaulich und mit elementaren Mitteln auch Dinge zu erl'utern, die in vergleichbaren Texten kaum zu finden sind: z.B. den Hilbertschen Basis- und Nullstellensatz, sowie Gr'bnerbasen. ..." Franz Lemmermeyer, Mathematische Semesterberichte 1999, 46/1 , "... 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 , "... 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." Pter 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 ffentlichem Schlssel" charakterisieren kann. ... Mit zunehmender Schwierigkeit des Material werden die Ausfhrungen dabei skizzenhafter und beschrnken sich immer strker 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 fr "advanced undergraduates", wie es im Klappentext heit, als Einstieg und erster berblick ber ein Gebiet, in dem sich in den letzten Jahren auf berraschende Weise praktische Anwendungsmglichkeiten fr tief innermathematische Themen ergeben haben." Hans-Gert Grbe, Computeralgebra Rundbrief 1999, Issue 25 "... Es gelingt Koblitz, anschaulich und mit elementaren Mitteln auch Dinge zu erlutern, die in vergleichbaren Texten kaum zu finden sind: z.B. den Hilbertschen Basis- und Nullstellensatz, sowie Grbnerbasen. ..." Franz Lemmermeyer, Mathematische Semesterberichte 1999, 46/1 , "... 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 überraschendeWeise 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, "... 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." Pter 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 ffentlichem Schlssel" charakterisieren kann. ... Mit zunehmender Schwierigkeit des Material werden die Ausfhrungen dabei skizzenhafter und beschrnken sich immer strker 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 fr "advanced undergraduates", wie es im Klappentext heit, als Einstieg und erster berblick ber ein Gebiet, in dem sich in den letzten Jahren auf berraschende Weise praktische Anwendungsmglichkeiten fr tief innermathematische Themen ergeben haben." Hans-Gert Grbe, Computeralgebra Rundbrief 1999, Issue 25 "... Es gelingt Koblitz, anschaulich und mit elementaren Mitteln auch Dinge zu erlutern, die in vergleichbaren Texten kaum zu finden sind: z.B. den Hilbertschen Basis- und Nullstellensatz, sowie Grbnerbasen. ..." Franz Lemmermeyer, Mathematische Semesterberichte 1999, 46/1
Series Volume Number
3
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
005.8/2/01512
Table Of Content
1. Cryptography.- §1. Early History.- §2. The Idea of Public Key Cryptography.- §3. The RSA Cryptosystem.- §4. Diffie-Hellman and the Digital Signature Algorithm.- §5. Secret Sharing, Coin Flipping, and Time Spent on Homework.- §6. Passwords, Signatures, and Ciphers.- §7. Practical Cryptosystems and Useful Impractical Ones.- 2. Complexity of Computations.- §1. The Big-O Notation.- §2. Length of Numbers.- §3. Time Estimates.- §4. P, NP, and NP-Completeness.- §5. Promise Problems.- §6. Randomized Algorithms and Complexity Classes.- §7. Some Other Complexity Classes.- 3. Algebra.- §1. Fields.- §2. Finite Fields.- §3. The Euclidean Algorithm for Polynomials.- §4. Polynomial Rings.- §5. Gröbner Bases.- 4. Hidden Monomial Cryptosystems.- § 1. The Imai-Matsumoto System.- §2. Patarin's Little Dragon.- §3. Systems That Might Be More Secure.- 5. Combinatorial-Algebraic Cryptosystems.- §1. History.- §2. Irrelevance of Brassard's Theorem.- §3. Concrete Combinatorial-Algebraic Systems.- §4. The Basic Computational Algebra Problem.- §5. Cryptographic Version of Ideal Membership.- §6. Linear Algebra Attacks.- §7. Designing a Secure System.- 6. Elliptic and Hyperelliptic Cryptosystems.- § 1. Elliptic Curves.- §2. Elliptic Curve Cryptosystems.- §3. Elliptic Curve Analogues of Classical Number Theory Problems.- §4. Cultural Background: Conjectures on Elliptic Curves and Surprising Relations with Other Problems.- §5. Hyperelliptic Curves.- §6. Hyperelliptic Cryptosystems.- §1. Basic Definitions and Properties.- §2. Polynomial and Rational Functions.- §3. Zeros and Poles.- §4. Divisors.- §5. Representing Semi-Reduced Divisors.- §6. Reduced Divisors.- §7. Adding Reduced Divisors.- Exercises.- Answers to Exercises.
Synopsis
This book is intended as a text for a course on cryptography with emphasis on algebraic methods. It is written so as to be accessible to graduate or advanced undergraduate students, as well as to scientists in other fields. The first three chapters form a self-contained introduction to basic concepts and techniques. Here my approach is intuitive and informal. For example, the treatment of computational complexity in Chapter 2, while lacking formalistic rigor, emphasizes the aspects of the subject that are most important in cryptography. Chapters 4-6 and the Appendix contain material that for the most part has not previously appeared in textbook form. A novel feature is the inclusion of three types of cryptography - "hidden monomial" systems, combinatorial-algebraic sys- tems, and hyperelliptic systems - that are at an early stage of development. It is too soon to know which, if any, of these cryptosystems will ultimately be of practical use. But in the rapidly growing field of cryptography it is worthwhile to continually explore new one-way constructions coming from different areas of mathematics. Perhaps some of the readers will contribute to the research that still needs to be done. This book is designed not as a comprehensive reference work, but rather as a selective textbook. The many exercises (with answers at the back of the book) make it suitable for use in a math or computer science course or in a program of independent study., 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, This book is intended as a text for a course on cryptography with emphasis on algebraic methods. It is written so as to be accessible to graduate or advanced undergraduate students, as well as to scientists in other fields. The first three chapters form a self-contained introduction to basic concepts and techniques. Here my approach is intuitive and informal. For example, the treatment of computational complexity in Chapter 2, while lacking formalistic rigor, emphasizes the aspects of the subject that are most important in cryptography. Chapters 4-6 and the Appendix contain material that for the most part has not previously appeared in textbook form. A novel feature is the inclusion of three types of cryptography - "hidden monomial" systems, combinatorial-algebraic sys tems, and hyperelliptic systems - that are at an early stage of development. It is too soon to know which, if any, of these cryptosystems will ultimately be of practical use. But in the rapidly growing field of cryptography it is worthwhile to continually explore new one-way constructions coming from different areas of mathematics. Perhaps some of the readers will contribute to the research that still needs to be done. This book is designed not as a comprehensive reference work, but rather as a selective textbook. The many exercises (with answers at the back of the book) make it suitable for use in a math or computer science course or in a program of independent study.
LC Classification Number
QA75.5-76.95
Item description from the seller
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