International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

On the order of the polynomial $x^p-x-a$

Authors:
Xiwang Cao
Download:
URL: http://eprint.iacr.org/2010/034
Search ePrint
Search Google
Abstract: In this note, we prove that the order of $x^p-x-1\in \F_p[x]$ is $\frac{p^p-1}{p-1}$, where $p$ is a prime and $\mathbb{F}_p$ is the finite field of size $p$. As a consequence, it is shown that $x^p-x-a\in \mathbb{F}_p[x]$ is primitive if and only if $a$ is a primitive element in $\mathbb{F}_p$.
BibTeX
@misc{eprint-2010-22935,
  title={On the order of the polynomial $x^p-x-a$},
  booktitle={IACR Eprint archive},
  keywords={foundations /},
  url={http://eprint.iacr.org/2010/034},
  note={ xwcao@nuaa.edu.cn 14630 received 21 Jan 2010},
  author={Xiwang Cao},
  year=2010
}