一类k阶拟Bent函数密码性质的矩阵特征  

The Matrix Characteristics of the Cryptographic Properties of a Special Kind of k-Order Quasi-Bent Functions

作　　者：滕吉红[1] 张文英[1] 李世取[1] 黄晓英[1] 

机构地区：[1]解放军信息工程大学信息工程学院信息研究系,郑州450002

出　　处：《计算机学报》2004年第4期543-547,共5页Chinese Journal of Computers

摘　　要：由于非线性组合函数的密码性质通常可以由函数的Walsh谱和自相关函数来刻划 ,因而对函数的密码性质的分析通常要计算大量的Walsh循环谱值和自相关函数值来验证 .该文利用一类k阶拟Bent函数的特殊性质 ,把对这类函数的密码性质的研究转化为对矩阵性质的研究 ,如平衡性、相关免疫性、扩散性、最高代数次数等 .这种转化避开了大量的计算 ,同时为构造密码性质好的k阶拟Bent函数提供了一种更为简洁且易于实现的方法 .In this paper, the cryptographic properties of a special kind of k -order quasi-Bent functions are studied by a new kind of method, which is denoted by the matrix method. The cryptographic properties of the k -order quasi-Bent functions, such as balancedness, correlation immunity, propagation criterion and the highest algebraic degree can all be easily decided only by the distributions of 0 and 1 in the character matrix, which is different from the spectrum method and the auto-correlation method. The method proposed here can also be used to construct the k -order quasi-Bent functions with good cryptographic properties, which is more effective and much simpler than the spectrum method and can be carried out easily.

关 键 词：部分BENT函数 k阶拟Bent函数 特征矩阵 相关免疫性 代数次数 

分 类 号：TN918[电子电信—通信与信息系统]