For multi-output boolean functions, we give out the definition of correlation permissibility . by investigating some properties of the balanced multi-output boolean functions, a feasible strategy of evolvement of function is presented . based on the method of simulated annealing and using the strategy presented in the 3rd section of capter four, a method is described to tell us how we can get some multi-output boolean functions with low correlation permissibility and high nonlinearity 对于多输出布尔函数,本文提出了相关容许度的概念,针对平衡的多输出布尔函数,研究了这类函数的分量函数之间的关系和性质,在不改变部分分量函数的情况下,分析了相邻函数演化的可行性和演化策略,基于simulatedannealing算法,本文分别提出了具有高非线性度的一阶相关免疫平衡函数的优化设计算法,以及具有高非线性度和低相关容许度的布尔函数或多输出布尔函数的优化设计算法。
It gives a detailed study on the non-degenerated boolean functions with correlation immunity and presents a better bound for such functions . it provides the analytic equation of g ( k ) in bibliography [ 5 ]; by analyzing linear structures of cib, it proves that the concept of linear structure and degeneration of cib for the case of weight 4k + 2 are equivalent; provides a sufficient condition on which cib functions are non-degenerated for the case of weight 4k; based on these results, a method of constructing non-degenerated cib is given 得到了文献[5]中g(k)的解析式;通过分析函数的线性结构,证明了重量为4k+2的相关免疫布尔函数的非退化性和非线性结构是等价的;给出了重量为4k的相关免疫布尔函数非退化的一个充分条件;在此基础上,给出了重量为4k+2、4k的非退化的相关免疫布尔函数的构造方法。
This paper has studied propagation criterion of boolean functions and boolean permutation and has gained results as following : 1 ) in the first chapter, the main study achievements and results of boolean functions satisfying propagation criterion have been summarized . 2 ) in the first section of the second chapter, the propagation properties of boolean functions have been studied 本文对布尔函数的扩散性和布尔置换进行了研究,取得了下列成果:1)综述了国内外关于满足扩散准则布尔函数的主要研究成果,即第一章;2)对满足k次扩散准则的布尔函数进行了研究,即第二章第一节。
This paper has studied propagation criterion of boolean functions and boolean permutation and has gained results as following : 1 ) in the first chapter, the main study achievements and results of boolean functions satisfying propagation criterion have been summarized . 2 ) in the first section of the second chapter, the propagation properties of boolean functions have been studied 本文对布尔函数的扩散性和布尔置换进行了研究,取得了下列成果:1)综述了国内外关于满足扩散准则布尔函数的主要研究成果,即第一章;2)对满足k次扩散准则的布尔函数进行了研究,即第二章第一节。
This paper has studied propagation criterion of boolean functions and boolean permutation and has gained results as following : 1 ) in the first chapter, the main study achievements and results of boolean functions satisfying propagation criterion have been summarized . 2 ) in the first section of the second chapter, the propagation properties of boolean functions have been studied 本文对布尔函数的扩散性和布尔置换进行了研究,取得了下列成果:1)综述了国内外关于满足扩散准则布尔函数的主要研究成果,即第一章;2)对满足k次扩散准则的布尔函数进行了研究,即第二章第一节。
3 ) in the second section of the second chapter, the relationship of boolean permutation and propagation properties is studied . by the boolean permutation, the sufficient and necessary condition on which boolean functions with high degrees satisfy pc ( n ) is derived . and boolean functions satisfying sac are constructed under the transformation of boolean permutation 当n为偶数时,利用布尔置换定出了一类高次布尔函数满足n次扩散准则的充要条件;利用布尔置换给出了一类满足严格雪崩准则的布尔函数;构造了一类新的布尔置换;最后给出了求布尔置换(x_0,…,x_(n-1))~(2~n-2)的算法和源程序。
3 ) in the second section of the second chapter, the relationship of boolean permutation and propagation properties is studied . by the boolean permutation, the sufficient and necessary condition on which boolean functions with high degrees satisfy pc ( n ) is derived . and boolean functions satisfying sac are constructed under the transformation of boolean permutation 当n为偶数时,利用布尔置换定出了一类高次布尔函数满足n次扩散准则的充要条件;利用布尔置换给出了一类满足严格雪崩准则的布尔函数;构造了一类新的布尔置换;最后给出了求布尔置换(x_0,…,x_(n-1))~(2~n-2)的算法和源程序。
A subtle synthesis algorithm for nonlinear shift register by using characteristics of the binary neural network and its learning algorithm and mapping to boolean function is developed . the algorithm can obtain both nonlinear complexity of the given sequence and feedback boolean function of the shift register . furthermore it is simple, reliable and has small burden of storage and computation 本文利用二进神经网络及其学习算法特点和对布尔函数的映射能力,设计了一个精巧的非线性移位寄存器的综合算法,同时得到序列非线性复杂度的移位寄存器的反馈布尔函数.此综合算法简单可靠,所需存储运算量小
A subtle synthesis algorithm for nonlinear shift register by using characteristics of the binary neural network and its learning algorithm and mapping to boolean function is developed . the algorithm can obtain both nonlinear complexity of the given sequence and feedback boolean function of the shift register . furthermore it is simple, reliable and has small burden of storage and computation 本文利用二进神经网络及其学习算法特点和对布尔函数的映射能力,设计了一个精巧的非线性移位寄存器的综合算法,同时得到序列非线性复杂度的移位寄存器的反馈布尔函数.此综合算法简单可靠,所需存储运算量小
In this paper, the general structure of block cipher together with its related properties is firstly discussed, then the main non-linear component of s-boxes in block cipher is analyzed . as to the boolean function in binary field, we studied its non-linearity, linearity structure, output bit independence criterion ( big ), balance, completeness, strict avalanche criterion, propagation criterion, correlation immunity, linear approximation table and xor distribution table . we also discussed the pile-up lama used to compute the combination linear probability and showed an instance of its application 本文首先讨论了分组密码的一般结构及其相关特性,此外还有分组密码主要的非线性组成部分s盒。对于二元域上的布尔函数主要讨论了其非线性性、线性结构、比特独立准则、平衡性、完整性、雪崩准则、传播准则、相关免疫性、线性分布表及异或分布表等特性。对计算组合线性概率的迭加定理我们也进行了具体的讨论,并给出了运用事例。