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Australasian Conference on Information Security and Privacy

ACISP 2011: Information Security and Privacy pp 47–60Cite as

Finding More Boolean Functions with Maximum Algebraic Immunity Based on Univariate Polynomial Representation

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6812))

Abstract

Algebraic immunity is an important cryptographic property for Boolean functions against algebraic attacks. Constructions of Boolean functions with the maximum algebraic immunity (MAI Boolean functions) by using univariate polynomial representation of Boolean functions over finite fields have received more and more attention. In this paper, how to obtain more MAI Boolean functions from a known MAI Boolean function under univariate polynomial representation is further investigated. The sufficient condition of Boolean functions having the maximum algebraic immunity obtained by changing a known MAI Boolean function under univariate polynomial representation is given. With this condition, more balanced MAI Boolean functions under univariate polynomial representation can be obtained. The algebraic degree and the nonlinearity of these Boolean functions are analyzed.

This work is supported by National Natural Science Foundation of China (Grant No. 61070168, Grant No. 10971246, Grant No. 10871222) and Research Fund for the Doctoral Program of Higher Education of China (20094410110001).

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Authors and Affiliations

  1. School of Information Science and Technology, Sun Yat-sen University, 510006, Guangzhou, China

    Yusong Du & Fangguo Zhang

Authors
  1. Yusong Du
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  2. Fangguo Zhang
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Software Engineering, The University of Melbourne, 3010, Victoria, Australia

    Udaya Parampalli

  2. Qualcomm Incorporated, Suite 301, Level 3, 77 King Street, NSW 2000, Sydney, Australia

    Philip Hawkes

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Du, Y., Zhang, F. (2011). Finding More Boolean Functions with Maximum Algebraic Immunity Based on Univariate Polynomial Representation. In: Parampalli, U., Hawkes, P. (eds) Information Security and Privacy. ACISP 2011. Lecture Notes in Computer Science, vol 6812. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22497-3_4

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  • DOI: https://doi.org/10.1007/978-3-642-22497-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22496-6

  • Online ISBN: 978-3-642-22497-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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