# Factoring Polynomials over Finite Fields

• Ian F. Blake
• XuHong Gao
• Ronald C. Mullin
• Scott A. Vanstone
• Tomik Yaghoobian
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 199)

## Abstract

A polynomial of degree n over a finite field F q is an expression in an indeterminate x having the form
$$f(x) = \sum\limits_{i = 0}^n {{a_i}{x^1}}$$
where n is a non-negative integer, a i F q , 0 ≤ in and a n ≠ 0. To be more precise, f (x) is called a univariate polynomial to distinguish the more general situation where more indeterminates are involved. Most of this chapter will deal with univariate polynomials but the multivariate case will be briefly mentioned at the end.

## Keywords

Finite Field Irreducible Polynomial Riemann Hypothesis Quadratic Residue Irreducible Factor
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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## Authors and Affiliations

• Ian F. Blake
• 1
• XuHong Gao
• 1
• Ronald C. Mullin
• 1
• Scott A. Vanstone
• 1
• Tomik Yaghoobian
• 1