Paper 2013/252
On the Primitivity of some Trinomials over Finite Fields
LI Yujuan, WANG Huaifu, and ZHAO Jinhua
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
- Published elsewhere. Unknown where it was published
- Keywords
- LFSRprimitive polynomialfinite field
- Contact author(s)
- wanghf @ mmrc iss ac cn
- History
- 2013-05-03: received
- Short URL
- https://ia.cr/2013/252
- License
-
CC BY
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},
note = {\url{https://eprint.iacr.org/2013/252}},
url = {https://eprint.iacr.org/2013/252}
}
