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On the equal-weight symmetric Boolean functions

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Abstract

Two important classes of symmetric Boolean functions are the equal-weight Boolean functions and the elementary (or homogeneous) symmetric Boolean functions. In this paper we studied the equal-weight symmetric Boolean functions. First the Walsh spectra of the equal-weight symmetric Boolean functions are given. Second the sufficient and necessary condition on correlation-immunity of the equal-weight symmetric Boolean function is derived and other cryptology properties such as the nonlinearity, balance and propagation criterion are taken into account. In particular, the nonlinearity of the equal-weight symmetric Boolean functions with n (n ≥ 10) variables is determined by their Hamming weight. Considering these properties will be helpful in further investigations of symmetric Boolean functions.

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Authors and Affiliations

  1. National Key Lab of Integrated Service Networks, Xidian University, Xi’an, 710071, China

    Yu Zhou & Guozhen Xiao

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  1. Yu Zhou
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  2. Guozhen Xiao
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Correspondence to Yu Zhou.

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Zhou, Y., Xiao, G. On the equal-weight symmetric Boolean functions. Front. Comput. Sci. China 3, 485–493 (2009). https://doi.org/10.1007/s11704-009-0002-x

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  • DOI: https://doi.org/10.1007/s11704-009-0002-x

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