A Note on "On the Construction of Boolean Functions with Optimal Algebraic Immunity"
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概要
- 論文の詳細を見る
In this note, we go further on the "basis exchange" idea presented in [2] by using Mobious inversion. We show that the matrix S1(ƒ)S0(ƒ)-1 has a nice form when ƒ is chosen to be the majority function, where S1(ƒ) is the matrix with row vectors υk(α) for all α ∈ 1ƒ and S0(ƒ)=S1(ƒ ⊕ 1). And an exact counting for Boolean functions with maximum algebraic immunity by exchanging one point in on-set with one point in off-set of the majority function is given. Furthermore, we present a necessary condition according to weight distribution for Boolean functions to achieve algebraic immunity not less than a given number.
- The Institute of Electronics, Information and Communication Engineersの論文
著者
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Kan Haibin
School Of Compute Science Fudan University
-
Li Yuan
School Of Computer Science Fudan University
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FUTATSUGI Kokichi
School of Information Science
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