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Paper 2013/252

On the Primitivity of some Trinomials over Finite Fields

LI Yujuan, WANG Huaifu, 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
Creative Commons Attribution
CC BY
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