| Boolean functions of an odd number of variables with maximum algebraic immunity |
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| 作者单位： | LI Na（Department of Applied Mathematics, Zhengzhou Information Engineering University, Zhengzhou 450002,China） ;
QI WenFeng（Department of Applied Mathematics, Zhengzhou Information Engineering University, Zhengzhou 450002,China） ; |
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| 基金项目： | 国家自然科学基金;国家高技术研究发展计划(863计划) |
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| 摘 要： | In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity. We identify three classes of such functions, and give some necessary conditions of such functions, which help to examine whether a Boolean function of an odd number of variables has the maximum algebraic immunity. Further, some necessary conditions for such functions to have also higher nonlinearity are proposed, and a class of these functions are also obtained. Finally, we present a sufficient and necessary condition for Boolean functions of an odd number of variables to achieve maximum algebraic immunity and to be also 1-resilient.
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Boolean functions of an odd number of variables with maximum algebraic immunity |
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| Authors: | Li Na Qi WenFeng |
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| Affiliation: | Department of Applied Mathematics, Zhengzhou Information Engineering University, Zhengzhou 450002,China |
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| Abstract: | In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity. We identify three classes of such functions, and give some necessary conditions of such functions, which help to examine whether a Boolean function of an odd number of variables has the maximum algebraic immunity. Further, some necessary conditions for such functions to have also higher nonlinearity are proposed, and a class of these functions are also obtained. Finally, we present a sufficient and necessary condition for Boolean functions of an odd number of variables to achieve maximum algebraic immunity and to be also 1-resilient. |
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| Keywords: | algebraic attacks algebraic immunity nonlinearity correlation immunity |
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