仿射函数 meaning in English
affine function
Examples
- This paper revealed an optimized strategy to search for systolic array transformations for nested loops , when the upper and lower bound of inner index was affine functions of there outer loop indexes
对于多重循环中,当内层迭代的上下界为外层迭代的仿射函数时,介绍了搜索脉动变换的一个优化策略和相应的自动化算法。 - This paper revealed an optimized strategy to search for systolic array transformations for nested loops , when the upper and lower bound of inner index was affine functions of there outer loop indexes
摘要对于多重循环中，当内层迭代的上下界为外层迭代的仿射函数时，介绍了搜索脉动变换的一个优化策略和相应的自动化算法。 - The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field , with the help of the properties of trace functions , and that of p - polynomials , as well as the permutation theory over finite field : the new definition of chrestenson linear spectrum is given and the relation between the new chrestenson linear spectrum and the chrestenson cyclic spectrum is presented , followed by the inverse formula of logical function over finite field ; the distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested , which leads to the conception of the extended affine functions over finite field , whose cryptographic properties is similar to that of the affine functions over field gf ( 2 ) and prime field fp ; the relationship between the degeneration of logical functions and the linear structures , the degeneration of logical functions and the support of chrestenson spectrum , as well as the relation between the nonlinearity and the linear structures are discussed ; using the relation of the logical functions over finite field and the vector logical functions over its prime field , we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized bent functions over its prime field ; the existence or not of the perfect nonlinear functions with any variables over any finite fields is offered , and some methods are proposed to construct the perfect nonlinear functions by using the balanced p - polynomials over finite field
重新定义了有限域上逻辑函数的chrestenson线性谱，考察了新定义的chrestenson线性谱和原来的chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的“泛仿射函数”的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相信息工程大学博士学位论文应素域上向量逻辑函数的关系，揭示了有限域上的广义bent函数与相应素域上的广义bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义bent函数之间的关系;给出了任意有限域上任意。 - Using the theories of probability , algebra and number theory comprehensively , we investigate a class of boolean functions with three - valued walsh spectrum in the first part of this dissertation : the properties of the extended semi - bent functions , which are constructed from any two bent functions , are studied , followed by the structure characteristics of the boolean functions satisfying propagation criterion with respect to all but two vectors ; the definition and cryptographic properties of k - order quasi - bent functions are proposed whose walsh spectrum takes on only three values . some sufficient and necessary conditions are offered to decide whether a boolean function is a k - order quasi - bent function ; a special method is presented to construct the k - order quasi - bent functions , whose cryptographic properties are explored by the matrix method , which is different from the method of walsh spectrum and that of autocorrelation of boolean functions ; the application of this kind of boolean functions in the fields of stream cipher , communications and block ciphers is discussed , which shows the great importance of the fc - order quasi - bent functions ; some methodology are proposed to construct the k - order quasi - bent functions , including the complete construction by using the characteristic matrices of boolean functions , and the recursive method by two known k - order quasi - bent functions we further extend our investigation to the ring zp , where p is a prime , and the similar results are presented as far as the p - valued quasi - generalized - bent functions are considered
本文首先综合运用概率论、代数学、数论等基础学科的理论知识，并以频谱理论作为主要研究工具，对一类谱值分布相对均匀的函数? ?广半bent函数、 k阶拟bent函数和p值k阶拟广义bent函数进行了系统、深入的研究，给出了广半bent函数定义，并探讨了广半bent函数的密码学性质；给出了k阶拟bent函数和p值k阶拟广义bent函数的定义及等价判别条件；讨论了k阶拟bent函数和p值k阶拟广义bent函数与部分bent函数和p值广义部分bent函数的关系，探讨了它们的密码学性质；给出了k阶拟bent函数和p值k阶拟广义bent函数的典型构造方法，并将对k阶拟bent函数的密码性质的研究转化到对一类特殊的矩阵的研究上；利用布尔函数的特征矩阵原则上给出了k阶拟bent函数的一种完全构造方法，还给出了从已有的p值k阶拟广义bent函数出发，递归构造变元个数更多的p值k阶拟广义bent函数的方法；初步探讨了k阶拟bent函数在序列密码、分组密码以及通信中的应用；给出了一类布尔函数walsh谱的分解式，并利用这类布尔函数的walsh谱分解式给出了一类近似稳定的布尔函数的构造，特殊情形下为k阶拟bent函数；利用代数数论的知识考察了p值k阶拟广义bent函数的谱特征，并给出了k阶拟广义bent函数与所有仿射函数的符合率特征等等。