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级联构造作为布尔函数的主要构造方法之一,具有结构简单、实现快速灵活等优点,被广泛用于构造实用的布尔函数。文中给出了一种通过迭代来构造密码学性质好的布尔函数的级联方法,详细测试了这类函数主要的密码学性质及代数正规型项数,并从理论上分析了构造的这类函数能够具有平衡性、最优的代数次数、高非线性度、高的代数免疫阶等多种好的密码性质。文中的结果表明,提出的级联构造方法能够用于构造密码学性质良好的布尔函数。 相似文献
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偶数变元代数免疫最优布尔函数的构造方法 总被引:1,自引:0,他引:1
提出了构造偶数变元代数免疫最优的布尔函数的方法,这是一个二阶的递归构造方法.分析表明,利用该方法构造而得到的布尔函数具有优良的密码学特性,比如具有较好的平衡性,较高的代数次数和非线性度等.最后,还对该构造方法进行了推广,进一步导出了递归构造偶数变元代数免疫最优布尔函数的一类方法. 相似文献
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From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity(AI) of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed. 相似文献
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Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity. 相似文献
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将导数和自定义的e-导数结合在一起作为新的研究工具,而这两者(导数和e-导数)结合在一起能直接明确反映布尔函数的重量,深入到布尔函数取值的内部结构中去,讨论相关免疫H布尔函数的代数免疫阶、代数次数等问题,即严格雪崩性质、相关免疫性、代数免疫性及最高代数次数的相容性问题,得出Hamming重量为2n-1+2n-2这类H布尔函数的最低代数次数和最高代数次数、最优代数免疫等结果。同时,也给出了一些求布尔函数代数次数和最优代数免疫的方法。 相似文献
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Algebraic immunity quantified the resistance of a Boolean function to the algebraic attack.Recently,Mesnager,et al showed that there were direct linked between the annihilators used in algebraic attacks and the coding theory.They showed that the lower bound of the algebraic immunity of Boolean functions could been derived from the minimum distance of the associated cyclic codes.An open problem proposed by Mesnager is settled with a detailed proof.Also,a lower bound of algebraic immunity of a class of Boolean functions will be introduced. 相似文献
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利用t+1个n元布尔函数(称为基函数)级联构造了一类n+t元布尔函数G(x,y),并给出了G(x,y)的Walsh循环谱和自相关系数。通过Krawtchouk多项式与Krawtchouk矩阵对G(x,y)和基函数的关系进行了研究。分析了G(x,y)的密码学性质:相关免疫性、扩散性和代数免疫性。特别地,当t=2时,分析了G(x,y)与基函数的具体关系。另外,一般化该构造方法构造了一类多输出布尔函数,给出了该类多输出布尔函数的广义Walsh循环谱,进而分析了该类多输出布尔函数的相关免疫性和代数免疫性。 相似文献