摘要
M序列由于具有良好的统计特性经常被应用在信息安全领域.这使得寻找F_2中M序列反馈函数成为一项有意义的工作.给出了由已知M序列反馈多项式得出新的与已知函数同次数的M序列反馈多项式的新方法.主要工作如下:1)用图形简单的给出了并圈法的逆过程所实现的操作过程.2)将并圈法的逆运算与并圈法先后应用在已有M序列状态图交叉排列的两对前共轭顶点对上,得到了由已知M序列反馈多项式生成新M序列反馈多项式的算法.3)证明了上述给出算法在二阶有限域F_2中的正确性.4)用C语言实现了算法.实验结果表明当移位寄存器的阶不是很大时算法是有效的.
M sequences are used in secure communication due to their good statistical properties.Hence,seeking new M sequence feedback polynomials in F_2 becomes a meaningful work.In this paper,we put forward a new method for generating M sequence feedback polynomials in F_2 from the given M sequence feedback polynomials with the same order.Our main work is as follows：Firstly,we present the main operation realized by the converse of amalgamating-circles method using graphs.Secondly,we apply the converse of amalgamatingcircles method and itself alternately on two pairs of front-conjugate and intersecting vertexes on the state graph of the known M-sequences,and thus give an algorithm for generating new M sequence feedback polynomials from the given M sequence feedback polynomials.Then we prove that the given algorithm is correct in F_2.Finally,we implement the algorithm in C language.Experimental results indicate that the algorithm is efficient when the order n of the shift register is moderate.
出处
《系统科学与数学》
CSCD
北大核心
2012年第3期310-318,共9页
Journal of Systems Science and Mathematical Sciences
关键词
M序列
安全通信
并圈法
反馈多项式
M sequences
secure communication
amalgamating-circles method
feedback polynomial
