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On semi-bent functions with Niho exponents

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Abstract

Semi-bent functions are a kind of Boolean functions with high nonlinearity. They have important applications in cryptography and communications. In this paper, two classes of semi-bent functions with Niho exponents are proposed. It is shown that all semi-bent functions of the first class attain the maximum algebraic degree, and there exists one subclass of semi-bent functions with maximum algebraic degree in the second class. Furthermore, two examples of semi-bent functions in a small field are given by using the zeros of some Kloosterman sums. Based on the result given by Kim et al., two examples of infinite families of semi-bent functions are also obtained. These results provide more available Boolean functions with high nonlinearity and high algebraic degrees for designing the filter generators of stream ciphers.

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Authors and Affiliations

  1. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China

    YeFeng He & WenPing Ma

  2. School of Telecommunications and Information Engineering, Xi’an Institute of Posts and Telecommunications, Xi’an, 710121, China

    YeFeng He

  3. Lean Engineering Research Group Faculty of Technology, The Gateway, De Monfort University, Leicester, LE1 9BH, UK

    Parminder Kang

Authors
  1. YeFeng He
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  2. WenPing Ma
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  3. Parminder Kang
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Correspondence to YeFeng He.

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He, Y., Ma, W. & Kang, P. On semi-bent functions with Niho exponents. Sci. China Inf. Sci. 55, 1624–1630 (2012). https://doi.org/10.1007/s11432-011-4522-2

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  • DOI: https://doi.org/10.1007/s11432-011-4522-2

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