Advances on Superelliptic Curves and Their Applications

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Editors
Beshaj, L., Shaska, T., Zhupa, E.
Pub. date
July 2015
Pages
388
Binding
hardcover
Volume
41 of NATO Science for Peace and Security Series - D: Information and Communication Security
ISBN print
978-1-61499-519-7
ISBN online
978-1-61499-520-3
Subject
Computer & Communication Sciences, Computer Science
 
This book contains a subject index
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This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves.

Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed.

The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.