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Strategies for Polynomial Systems

  • Gregory V. Bard
Chapter

Abstract

Before we devote numerous pages to the topic of polynomial systems of equations over finite fields, we should pause and ask why one would want to do this. This will give us an opportunity to highlight the several applications of this interesting area.

Before that, however, an important distinction must be made. In this book, when one has a system of equations over the finite field \(\mathbb{G}\mathbb{F}\)(p n ), we assume that one is interested only in those solutions which are also elements of \(\mathbb{G}\mathbb{F}\)(pn). If one is also interested in solutions in some extension field, (e.g. \(\mathbb{G}\mathbb{F}\)(p m ) with n|m), then since \(\mathbb{G}\mathbb{F}\)(p n ) is a subfield of \(\mathbb{G}\mathbb{F}\)(p m ), it is safe to consider the system of equations as if it were over \(\mathbb{G}\mathbb{F}\)(p n ), or at worse the splitting field.

Keywords

Polynomial Time Graph Coloring Advance Encryption Standard Polynomial System Quadratic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of MathematicsFordham UniversityBronxUSA

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