N. E. Hurt

Many Rational Points

Coding Theory and Algebraic Geometry

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Mathematics and Its Applications 564
• Verlag: Springer / Springer Netherlands
• Artikelnr. des Verlages: 978-90-481-6496-7
• 2003
• Seitenzahl: 368
• Erscheinungstermin: 8. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 20mm
• Gewicht: 564g
• ISBN-13: 9789048164967
• ISBN-10: 9048164966
• Artikelnr.: 32006739

Inhaltsangabe

Abelian Varieties.
Refined Bounds.
Codes and Curves.
Deligne
Lusztig Spaces.
Drinfeld Modules.
Shimura Curves.
Cryptography and Applications.
References.

Rezensionen

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)