Algebraic curves and finite fields : cryptography and other applications / edited by Harald Niederreiter [and three others].

Format:

Book

Contributor:

Niederreiter, Harald, editor.

Series:

Radon series on computational and applied mathematics ; Volume 16.

Radon Series on Computational and Applied Mathematics, 1865-3707 ; Volume 16

Language:

English

Subjects (All):

Curves, Algebraic.

Physical Description:

1 online resource (254 p.)

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, 2014.

Language Note:

English

Summary:

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.

Contents:

Front matter

Introduction

Contents

Generic Newton polygons for curves of given p-rank / Achter, Jeffrey D. / Pries, Rachel

Good towers of function fields / Bassa, Alp / Beelen, Peter / Nguyen, Nhut

Correlation-immune Boolean functions for easing counter measures to side-channel attacks / Carlet, Claude / Guilley, Sylvain

The discrete logarithm problem with auxiliary inputs / Cheon, Jung Hee / Kim, Taechan / Song, Yongsoo

Garden of curves with many automorphisms / Giulietti, Massimo / Korchmáros, Gábor

Nonlinear shift registers - A survey and challenges / Helleseth, Tor

Permutations of finite fields and uniform distribution modulo 1 / Pausinger, Florian / Topuzoğlu, Alev

Semifields, relative difference sets, and bent functions / Pott, Alexander / Schmidt, Kai-Uwe / Zhou, Yue

NTRU cryptosystem: Recent developments and emerging mathematical problems in finite polynomial rings / Steinfeld, Ron

Analog of the Kronecker-Weber theorem in positive characteristic / Villa-Salvador, Gabriel D.

Index

Backmatter

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on online resource; title from PDF title page (ebrary, viewed February 13, 2015).

ISBN:

3-11-037955-4

OCLC:

890071075