共查询到20条相似文献,搜索用时 15 毫秒
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在流密码和分组密码的设计中,所用布尔函数应该具有好的密码学性质来抵抗已知的各种有效攻击.布尔函数的低次零化子空间维数与其补函数低次零化子空间维数之和是评价该函数抵抗代数攻击能力的一个重要参数.根据Maiorana-McFarlands(M-M)Bent函数和布尔置换之间的一一对应关系,给出了一组布尔函数组并证明了它们是线性无关的.借助所给的线性无关布尔函数组和布尔置换中向量函数非零线性组合均是平衡函数的特性,给出了一类特殊M-M Bent函数低次零化子空间的维数与其补函数低次零化子空间的维数之和的一个上限.就这类特殊M-M Bent函数而言,该上限低于已知的限.进一步给出了适合所有M-M Bent函数的新上限. 相似文献
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本文讨论了向量值函数代数免疫度的定义,给出了向量值函数的代数免疫度与其非线性度之间的关系,研究了布尔函数的重量与其代数免疫度之间的关系,利用该关系,给出了达到最大代数免疫度的平衡布尔函数个数的一个下界。 相似文献
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《国际计算机数学杂志》2012,89(5):943-949
In this paper, we define a large class of almost balanced Boolean functions called nearly bent functions. These functions lie at large Hamming distance to all affine functions and preserve a high level of algebraic degree. Then a construction of nearly bent functions is described. It is shown that the constructed functions have good global avalanche characteristic properties. In the concluding remarks, we show that nearly bent functions have good stability. 相似文献
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布尔函数是在密码学、纠错编码和扩频通信等领域有着广泛应用的密码函数,寻找性能优良的布尔函数一直是密码学领域的重要问题之一。基于引力搜索算法设计了一种搜索布尔函数的新算法。该算法模仿万有引力定律,以n维空间中的质量点表示布尔函数,以布尔函数的密码特性作为目标适应度函数进行搜索。实验结果表明,算法使用新设计的目标适应度函数可以直接生成具有1阶弹性、1阶扩散准则和高非线性度、高代数次数以及低自相关指标等多种密码学指标的平衡布尔函数,并且进一步给出了直接生成2输出平衡布尔函数的计算机搜索算法。 相似文献
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该文介绍了一种关于一阶相关免疫布尔函数的计数方法,并由此给出了一些小重量的一阶相关免疲均衡布尔函数的计数。 相似文献
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针对密码学中布尔函数的代数免疫性和构造需求,通过选取适当次数的布尔函数,利用布尔函数的级联性质,提出了一种提高布尔函数代数免疫阶的递归构造法;同时证明了该构造法中所构造的布尔函数比原布尔函数的代数免疫阶高,利用该方法可以递归构造具有最优代数免疫阶平衡布尔函数,最后给出了一个具体实例。 相似文献
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平衡性,非线性,扩散性是具有高度密码特性的布尔函数要满足的最重 要的三个性质,本文给出了用Bent函数来构造满足高次扩散准则的,具有较高非线性度的平衡布尔函数的一些方法。 相似文献
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Yu ZHOU Weiguo ZHANG Juan LI Xinfeng DONG Guozhen XIAO 《Frontiers of Computer Science》2013,7(2):272-278
The global avalanche characteristics (the sum-of-squares indicator and the absolute indicator) measure the overall avalanche characteristics of a cryptographic Boolean function. Sung et al. (1999) gave the lower bound on the sum-of-squares indicator for a balanced Boolean function satisfying the propagation criterion with respect to some vectors. In this paper, if balanced Boolean functions satisfy the propagation criterion with respect to some vectors, we give three necessary and sufficient conditions on the auto-correlation distribution of these functions reaching the minimum the bound on the sum-of-squares indicator. And we also find all Boolean functions with 3-variable, 4-variable, and 5-variable reaching the minimum the bound on the sum-of-squares indicator. 相似文献
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本文利用线性复杂度相关理论,给出了布尔函数复杂系数的定义:得出任何布尔函数的线性复杂度均等于这个函数的复杂系数;给出了一种快速求解布尔函数多项式表示的算法;研究了Bent函数的线性复杂度特点,利用布尔函数的复杂系数,得出布尔函数为Bent函数的一个必要条件。 相似文献
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《国际计算机数学杂志》2012,89(9):1832-1839
Three of the most essential criteria for cryptographically strong Boolean functions are balancedness, high nonlinearity and high algebraic degree. In this paper, we give two methods for constructing balanced Boolean functions with high nonlinearity via modifying Maiorana–McFarland type bent functions. The algebraic immunity of the constructed functions is also considered. 相似文献
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Subhamoy Maitra 《Information Processing Letters》2002,83(5):281-286
Here we deal with an interesting subset of n-variable balanced Boolean functions which satisfy strict avalanche criteria. These functions achieve the sum-of-square indicator value (a measure for global avalanche criteria) strictly less than 22n+1 and nonlinearity strictly greater than 2n−1−2⌊n/2⌋. These parameters are currently best known. Moreover, these functions do not possess any nonzero linear structure. The technique involves a well-known simple construction coupled with very good initial functions obtained by computer search, which were not known earlier. 相似文献
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In this paper, we introduce the notion of models for quantified Boolean formulas. For various classes of quantified Boolean
formulas and various classes of Boolean functions, we investigate the problem of determining whether a model exists. Furthermore,
we show for these classes the complexity of the model checking problem, which is to check whether a given set of Boolean functions
is a model for a formula. For classes of Boolean functions, we establish some characterizations in terms of classes of quantified
Boolean formulas that have such a model.
This research has been supported in part by the Air Force Office of Scientific Research under grant FA9550-06-1-0050.
This research has been supported in part by the NSFC under grants 60573011 and 10410638. 相似文献
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Sheng Gao Wenping Ma Zepeng Zhuo Fenghe Wang 《Frontiers of Computer Science in China》2011,5(4):448-453
Substitution boxes (S-boxes) are often used as the most important nonlinear components in many symmetric encryption algorithms.
The cryptographic properties of an S-box directly affect the security of the whole cipher system. Recently, generalized global
avalanche characteristics (GGAC) were introduced to measure the correlation between two arbitrary Boolean functions. In this
paper, to better evaluate the security of an S-box, we present two cross-correlation indicators for it. In addition, by studying
the related properties of the cross-correlation between two balanced Boolean functions, we propose the lower bounds on the
sum-of-squares indicator related to GGAC for two balanced functions and also for an S-box. 相似文献
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互补对称布尔函数是一类特殊的对称布尔函数。在所有代数免疫最优的对称布尔函数中,有相当的比例均属此类函数。特别是当变元数量为2m元时,有2/3比例的代数免疫最优对称布尔函数都是互补对称布尔函数。通过布尔函数非线性度、Walsh谱和Krawtchouk多项式间的关系,计算出互补对称布尔函数的非线性度。结果表明,任意n元互补对称布尔函数的非线性度为2n-1-1/2[nn/2] 相似文献
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半bent函数是一类非线性度几乎最优且平衡的布尔函数,它弥补了bent函数的一些不足,如变元个数可以是奇数,具有平衡性.半bent函数可用于对称密码系统的设计和CDMA系统中的正交可变扩频码的构造.本文利用不相交线性码构造了一类新的半bent函数,设输入维度为n,当n=2k+1时,将F2^n划分为2^k+1个[n,k]线性码和1个[n,k+1]线性码,通过从该码集中选取合适线性码作支撑集来构造新的半bent函数.另一方面,多输出布尔函数(向量值函数)在应用中的效率更高,因此其使用场景更为广泛.本文同时利用不相交线性码构造了(n,n-k)平衡的多输出布尔函数,其中n/3相似文献
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A resynchronization attack is proposed on stream ciphers filtered by Maiorana-McFarland (M-M) functions and equipped with
a linear resynchronization mechanism. The proposed attack utilizes the linear weakness of the resynchronization mechanism,
the partial linearity of M-M functions, and applies the linear consistency test method to recover the secret key. It is shown
that an M-M function should not be implemented by itself but rather in combination with other nonlinear components in stream
ciphers using linear mechanisms to prevent the proposed attack. It is also shown that the use of linear resynchronization
mechanisms should be avoided despite their high efficiency in stream ciphers filtered by M-M functions. 相似文献