Paper 2013/252 Original: eprint.iacr.org/2013/252 ↗
On the Primitivity of some Trinomials over Finite Fields
Abstract
In this paper, we give conditions under which the trinomials of the form $x^{n}+ax+b$ over finite field ${\mathbb{F}}_{p^{m}}$ are not primitive and conditions under which there are no primitive trinomials of the form $x^{n}+ax+b$ over finite field ${\mathbb{F}}_{p^{m}}$. For finite field ${\mathbb{F}}_{4}$, We show that there are no primitive trinomials of the form $x^{n}+x+\alpha$, if $n\equiv1\mod 3$ or $n\equiv0\mod 3$ or $n\equiv4\mod 5$.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2013-05-03: last updated
- 2013-05-03: published
- Short URL
- https://ia.cr/2013/252
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2013/252,
author = {LI Yujuan and WANG Huaifu and ZHAO Jinhua},
title = {On the Primitivity of some Trinomials over Finite Fields},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/252},
year = {2013},
url = {https://eprint.iacr.org/2013/252}
}