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Construction of Boolean functions with maximum algebraic immunity and count of their annihilators at lowest degree

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Abstract

Boolean functions used in stream ciphers against algebraic attacks are required to have a necessary cryptographic property-high algebraic immunity (AI). In this paper, Boolean functions of even variables with the maximum AI are investigated. The number of independent annihilators at the lowest degree of Boolean functions of even variables with the maximum AI is determined. It is shown that when n is even, one can get an (n + 1)-variable Boolean function with the maximum AI from two n-variable Boolean functions with the maximum AI only if the Hamming weights of the two functions satisfy the given conditions. The nonlinearity of the Boolean functions obtained in this way is computed. Similarly, one can get an (n + 2)-variable Boolean function with the maximum AI from four n-variable Boolean functions with the maximum AI. The nonlinearity of a class of Boolean functions with the maximum AI is determined such that their Hamming weights are either the maximum or the minimum.

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  1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China

    YuSong Du & DingYi Pei

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  1. YuSong Du
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  2. DingYi Pei
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Correspondence to YuSong Du.

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Du, Y., Pei, D. Construction of Boolean functions with maximum algebraic immunity and count of their annihilators at lowest degree. Sci. China Inf. Sci. 53, 780–787 (2010). https://doi.org/10.1007/s11432-010-0064-2

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