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.
Supported by the National Natural Science Foundation of China (60503011, 90704003), the National High Technology Research and Development Program of China (863 Program) (2006AA01Z425) and the National Basic Research Program of China (937 Program) (2007CB807902).
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Zeng, G., Yang, Y., Han, W., Fan, S. (2009). Reducible Polynomial over \(\mathbb{F}_{2}\) Constructed by Trinomial σ−LFSR. In: Yung, M., Liu, P., Lin, D. (eds) Information Security and Cryptology. Inscrypt 2008. Lecture Notes in Computer Science, vol 5487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01440-6_16
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DOI: https://doi.org/10.1007/978-3-642-01440-6_16
Publisher Name: Springer, Berlin, Heidelberg
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