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Reducible Polynomial over \(\mathbb{F}_{2}\) Constructed by Trinomial σ−LFSR

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Information Security and Cryptology (Inscrypt 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5487))

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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.

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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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, 450002, China

    Guang Zeng, Yang Yang, Wenbao Han & Shuqin Fan

Authors
  1. Guang Zeng
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  2. Yang Yang
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  3. Wenbao Han
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  4. Shuqin Fan
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Editor information

Editors and Affiliations

  1. Computer Science Department, Google Inc. and Columbia University, Room 464, S.W. Mudd Building, 10027, New York, NY, USA

    Moti Yung

  2. College of Information Sciences and Technology, Pennsylvania State University, PA 16802, University Park, USA

    Peng Liu

  3. SKLOIS, Institute of Software, Chinese Academy of Sciences, 100080, Beijing, China

    Dongdai Lin

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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

  • Print ISBN: 978-3-642-01439-0

  • Online ISBN: 978-3-642-01440-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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