Algebraic Curves and Finite Fields
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Edited by:
Harald Niederreiter
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With contributions by:
Jeffrey D. Achter
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 / Editor 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
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Frontmatter
i -
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Introduction
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Contents
vii -
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Generic Newton polygons for curves of given p-rank
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Good towers of function fields
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Correlation-immune Boolean functions for easing counter measures to side-channel attacks
41 -
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The discrete logarithm problem with auxiliary inputs
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Garden of curves with many automorphisms
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Nonlinear shift registers – A survey and challenges
121 -
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Permutations of finite fields and uniform distribution modulo 1
145 -
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Semifields, relative difference sets, and bent functions
161 -
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NTRU cryptosystem: Recent developments and emerging mathematical problems in finite polynomial rings
179 -
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Analog of the Kronecker–Weber theorem in positive characteristic
213 -
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Index
239 -
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Backmatter
241
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