Title: Constructing Boolean Functions with Maximum Algebraic Immunity
Abstract:Because of the recent algebraic attacks, a high algebraic immunity is now an absolutely necessary property for Boolean functions used in stream ciphers. For a n-variable Boolean function f, the algebr...Because of the recent algebraic attacks, a high algebraic immunity is now an absolutely necessary property for Boolean functions used in stream ciphers. For a n-variable Boolean function f, the algebraic immunity AI(f) is no more than n/2. If AI(f) equals n/2, the immune of f resisting algebraic attack is optimal. In this paper, focusing on algebraic normal form and the construction requirements of Boolean function, the conditions that Boolean function f does not exists annihator with deg(f)≤m are analysed. The sufficient conditions that Boolean function f reaches the maximum algebraic immunity are obtained¡DTherefore a new class of Boolean functions with optimal algebraic immunity are constructed, and the balanceness and count of the constructed functions are discussed.Read More
Publication Year: 2011
Publication Date: 2011-08-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2
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Title: $Constructing Boolean Functions with Maximum Algebraic Immunity
Abstract: Because of the recent algebraic attacks, a high algebraic immunity is now an absolutely necessary property for Boolean functions used in stream ciphers. For a n-variable Boolean function f, the algebraic immunity AI(f) is no more than n/2. If AI(f) equals n/2, the immune of f resisting algebraic attack is optimal. In this paper, focusing on algebraic normal form and the construction requirements of Boolean function, the conditions that Boolean function f does not exists annihator with deg(f)≤m are analysed. The sufficient conditions that Boolean function f reaches the maximum algebraic immunity are obtained¡DTherefore a new class of Boolean functions with optimal algebraic immunity are constructed, and the balanceness and count of the constructed functions are discussed.