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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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