Reducible Polynomial over $\mathbb{F}_{2}$ Constructed by Trinomial σ-LFSR

Authors:
Guang Zeng;Yang Yang;Wenbao Han;Shuqin Fan
Affiliations:
Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, China 450002;Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, China 450002;Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, China 450002;Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, China 450002
Venue:
Information Security and Cryptology
Year:
2009

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Abstract

In the search for trinomial σ -LFSR over finite field $\mathbb{F}_{2^m}$, one type of binary polynomials which are always reducible with an even number of irreducible factors over binary field $\mathbb{F}_2$ were found. We prove this using the Stickelberger-Swan theorem and present one new of special pentanomials over $\mathbb{F}_2$ with the same property.