代数数论 meaning in English
algebraic number theory
Examples
- It has developed from two sources: algebraic geometry and algebraic member theory .
它由两个方面发展而来，代数几何和代数数论。 - As an important algebraic subject , rings are the base of algebraic geometry and algebraic theory . rings are concerned about many other subjects
环作为一门重要的代数学科是代数几何和代数数论的基础，有许多其它相关学科领域都涉及到环。 - 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。