Algebraic Curves and Finite Fields

Published by De Gruyter 2014

Algebraic Curves and Finite Fields

Cryptography and Other Applications

With contributions by: Jeffrey D. Achter , Alp Bassa , Peter Beelen , Jung Hee Cheon , Carlet Claude , Massimo Giulietti , Sylvain Guilley , Tor Helleseth , Taechan Kim , Gabor Korchmaros , Nhut Nguyen , Florian Pausinger , Alexander Pott , Rachel Pries , Kai-Uwe Schmidt , Yongsoo Song , Ron Steinfeld , Alev Topuzoglu , Gabriel D. Villa-Salvador and Yue Zhou
Edited by: Harald Niederreiter , Alina Ostafe , Daniel Panario and Arne Winterhof

Volume 16 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110317916

Overview
Contents

About this book

Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples.

This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.

Author information

Harald Niederreiter, JKU Linz, Austria; Alina Ostafe, Macquarie University, NSW, Australia; Daniel Panario, Carleton University, Ottawa, Ontario, Canada; Arne Winterhof, JKU Linz, Austria.

Topics

Frontmatter Publicly Available Download PDF	i
Introduction Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	vii
Generic Newton polygons for curves of given p-rank Jeffrey D. Achter and Rachel Pries Requires Authentication Unlicensed Licensed Download PDF	1
Good towers of function fields Alp Bassa, Peter Beelen and Nhut Nguyen Requires Authentication Unlicensed Licensed Download PDF	23
Correlation-immune Boolean functions for easing counter measures to side-channel attacks Claude Carlet and Sylvain Guilley Requires Authentication Unlicensed Licensed Download PDF	41
The discrete logarithm problem with auxiliary inputs Jung Hee Cheon, Taechan Kim and Yongsoo Song Requires Authentication Unlicensed Licensed Download PDF	71
Garden of curves with many automorphisms Massimo Giulietti and Gábor Korchmáros Requires Authentication Unlicensed Licensed Download PDF	93
Nonlinear shift registers – A survey and challenges Tor Helleseth Requires Authentication Unlicensed Licensed Download PDF	121
Permutations of finite fields and uniform distribution modulo 1 Florian Pausinger and Alev Topuzoğlu Requires Authentication Unlicensed Licensed Download PDF	145
Semifields, relative difference sets, and bent functions Alexander Pott, Kai-Uwe Schmidt and Yue Zhou Requires Authentication Unlicensed Licensed Download PDF	161
NTRU cryptosystem: Recent developments and emerging mathematical problems in finite polynomial rings Ron Steinfeld Requires Authentication Unlicensed Licensed Download PDF	179
Analog of the Kronecker–Weber theorem in positive characteristic Gabriel D. Villa-Salvador Requires Authentication Unlicensed Licensed Download PDF	213
Index Requires Authentication Unlicensed Licensed Download PDF	239
Backmatter Requires Authentication Unlicensed Licensed Download PDF	241

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers in Mathematics and Computer Science; Academic libraries.
Pages
- Front matter: 11
- Main content: 240
Keywords: Algebraische Kurven; Endliche Felder

eBook

Published: August 20, 2014
ISBN: 9783110317916

Hardcover

Published: June 30, 2014
ISBN: 9783110317886