Study On The Construction Of A New Self-shrinking Control Sequence On GF(2)and Its Pseudo-random Properties

This thesis based on the primitive LFSRs of length n on GF(2)and pro-pose the model of the new self-shrinking control generator in accordance with the model of modified self-shrinking generator.The new model use the the modu-lar addition of adjacent bits to control the output of specific bits.Let a? is a primitive LFSRs of length n,and a? can be written as the sequence of ternary pair,so a??(a0,a1,a2),…,(a3k,a3k+1,a3k+2),….The output way about the model of new self-shrinking control generator is as follows:for k?0,the specific output bits of the ternary pair(a3k,a3k+1,a3k+2)are determined by the value of a3k?a3k+1,specifically,if a3k ? a3k+l=0,then the whole ternary pair does not make any output and transfers to the next adjacent ternary pair;if a3k?a3k+1=1,then output a3k+1,a3k+2.Then,in this thesis,we uses the finite field theory,ana-lyze and study the period,linear complexity,autocorrelation and run distribution of the new self-shrinking control sequences which are produced by the primitive LFSRs of length n.Obtained such sequences have good autocorrelation proper-ties,and the upper bound of the period is 2n;The lower bound of the period is 22·[n/3];the upper bound of the linear complexity is 2n-(n-3);the lower bound of the linear complexity is 22·[n/3J]-1.Those results show that the new self-shrinking control sequences have better periodic and linear complexity properties.