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Many Rational Points: Coding Theory and Algebraic Geometry: 564 (Mathematics and Its Applications, 564) - Softcover
Synopsis
2 Triangle Groups: An Introduction 279 3 Elementary Shimura Curves 281 4 Examples of Shimura Curves 282 5 Congruence Zeta Functions 283 6 Diophantine Properties of Shimura Curves 284 7 Klein Quartic 285 8 Supersingular Points 289 Towers of Elkies 9 289 7. CRYPTOGRAPHY AND APPLICATIONS 291 1 Introduction 291 Discrete Logarithm Problem 2 291 Curves for Public-Key Cryptosystems 3 295 Hyperelliptic Curve Cryptosystems 4 297 CM-Method 5 299 6 Cryptographic Exponent 300 7 Constructive Descent 302 8 Gaudry and Harley Algorithm 306 9 Picard Jacobians 307 Drinfeld Module Based Public Key Cryptosystems 10 308 11 Drinfeld Modules and One Way Functions 308 12 Shimura's Map 309 13 Modular Jacobians of Genus 2 Curves 310 Modular Jacobian Surfaces 14 312 15 Modular Curves of Genus Two 313 16 Hecke Operators 314 8. REFERENCES 317 345 Index Xll Preface The history of counting points on curves over finite fields is very ex tensive, starting with the work of Gauss in 1801 and continuing with the work of Artin, Schmidt, Hasse and Weil in their study of curves and the related zeta functions Zx(t), where m Zx(t) = exp (2: N t ) m m 2': 1 m with N = #X(F qm). If X is a curve of genus g, Weil's conjectures m state that L(t) Zx(t) = (1 - t)(l - qt) where L(t) = rr~!l (1 - O'.
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Review
From the reviews:
"This book gives a nice overview of background and recent results on curves over finite fields. ... The main advantage of this book is that it provides a huge bibliography and takes into account even very recent results which are so far only presented at conferences or in preprints. So it serves well to get an update on recent results for the experienced reader and links to the original results for more details." (Tanja Lange, Zentralblatt MATH, Vol. 1072 (23), 2005)
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- PublisherSpringer
- Publication date2010
- ISBN 10 9048164966
- ISBN 13 9789048164967
- BindingPaperback
- LanguageEnglish
- Number of pages367
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Many Rational Points: Coding Theory and Algebraic Geometry (Mathematics and Its Applications)
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Abelian Varieties.- Refined Bounds.- Codes and Curves.- Deligne-Lusztig Spaces.- Drinfeld Modules.- Shimura Curves.- Cryptography and Applications.- References.From the reviews: This book gives a nice overview of background and recent r. Seller Inventory # 5820346
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Many Rational Points
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This monograph presents a comprehensive treatment of recent results on algebraic geometry as they apply to coding theory and cryptography, with the goal the study of algebraic curves and varieties with many rational points. They book surveys recent developments on abelian varieties, in particular the classification of abelian surfaces, hyperelliptic curves, modular towers, Kloosterman curves and codes, Shimura curves and modular jacobian surfaces. Applications of abelian varieties to cryptography are presented including a discussion of hyperelliptic curve cryptosystems. The inter-relationship of codes and curves is developed building on Goppa's results on algebraic-geometry cods. The volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators. 368 pp. Englisch. Seller Inventory # 9789048164967
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Many Rational Points : Coding Theory and Algebraic Geometry
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This monograph presents a comprehensive treatment of recent results on algebraic geometry as they apply to coding theory and cryptography, with the goal the study of algebraic curves and varieties with many rational points. They book surveys recent developments on abelian varieties, in particular the classification of abelian surfaces, hyperelliptic curves, modular towers, Kloosterman curves and codes, Shimura curves and modular jacobian surfaces. Applications of abelian varieties to cryptography are presented including a discussion of hyperelliptic curve cryptosystems. The inter-relationship of codes and curves is developed building on Goppa's results on algebraic-geometry cods. The volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators. Seller Inventory # 9789048164967
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Many Rational Points
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Springer Netherlands, Springer Netherlands Dez 2010, 2010
ISBN 10: 9048164966
ISBN 13: 9789048164967
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -2 Triangle Groups: An Introduction 279 3 Elementary Shimura Curves 281 4 Examples of Shimura Curves 282 5 Congruence Zeta Functions 283 6 Diophantine Properties of Shimura Curves 284 7 Klein Quartic 285 8 Supersingular Points 289 Towers of Elkies 9 289 7. CRYPTOGRAPHY AND APPLICATIONS 291 1 Introduction 291 Discrete Logarithm Problem 2 291 Curves for Public-Key Cryptosystems 3 295 Hyperelliptic Curve Cryptosystems 4 297 CM-Method 5 299 6 Cryptographic Exponent 300 7 Constructive Descent 302 8 Gaudry and Harley Algorithm 306 9 Picard Jacobians 307 Drinfeld Module Based Public Key Cryptosystems 10 308 11 Drinfeld Modules and One Way Functions 308 12 Shimura's Map 309 13 Modular Jacobians of Genus 2 Curves 310 Modular Jacobian Surfaces 14 312 15 Modular Curves of Genus Two 313 16 Hecke Operators 314 8. REFERENCES 317 345 Index Xll Preface The history of counting points on curves over finite fields is very ex tensive, starting with the work of Gauss in 1801 and continuing with the work of Artin, Schmidt, Hasse and Weil in their study of curves and the related zeta functions Zx(t), where m Zx(t) = exp (2: N t ) m m 2': 1 m with N = #X(F qm). If X is a curve of genus g, Weil's conjectures m state that L(t) Zx(t) = (1 - t)(l - qt) where L(t) = rr~!l (1 - O'.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 368 pp. Englisch. Seller Inventory # 9789048164967
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Many Rational Points: Coding Theory and Algebraic Geometry (Mathematics and Its Applications)
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Many Rational Points: Coding Theory and Algebraic Geometry (Mathematics and Its Applications)
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Many Rational Points: Coding Theory and Algebraic Geometry (Mathematics and Its Applications (564))
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