Finite Fields And Applications
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Finite Fields and Applications
Thisvolumerepresentstherefereedproceedingsofthe7thInternationalC- ference on Finite Fields and Applications (F 7) held during May 5-9, q 2003, in Toulouse, France. The conference was hosted by the Pierre Baudis C- gress Center, downtown, and held at the excellent conference facility. This event continued a series of biennial international conferences on Finite Fields and - plications, following earlier meetings at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University of Glasgow (UK) in July 1995, the University of Waterloo (Canada) in August 1997, the Univ- sity of Augsburg (Germany) in August 1999, and the Universidad Aut ́ onoma Metropolitana-Iztapalapa, in Oaxaca (Mexico) in 2001. The Organizing Committee of F 7 consisted of Claude Carlet (INRIA, Paris, q France), Dieter Jungnickel (University of Augsburg, Germany), Gary Mullen (Pennsylvania State University, USA), Harald Niederreiter (National University of Singapore, Singapore), Alain Poli, Chair (Paul Sabatier University, Toulouse, France), Henning Stichtenoth (Essen University, Germany), and Horacio Tapia- Recillas (Universidad Aut ́ onoma Metropolitan-Iztapalapa, Mexico). The program of the conference consisted of four full days and one half day of sessions, with eight invited plenary talks, and close to 60 contributed talks.
Applications of Finite Fields
Author: Alfred J. Menezes
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-17
The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good error-correcting codes. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references.