Model Design Of The Jump Self-Shrinking Sequences And Property Analysis

This paper proposed the idea of the jump self-shrinking sequences in accordance with the model of self-shrinking sequences on GF（2）.The new model use the triple pair which is a more complex one to control the bit output instead of using the binary pair.Furthermore,the detailed value of output bits is controlled by the sum of two nonadjacent bits.In this paper,the main consideration is the case that the base sequence is m—sequence which is generated by an LFSR of length n.Let a^∞（a₀,a₁,a₂,…）be the sequence produced by an LFSR of length n.This a^∞ can be written as the sequence of triple pair,so a^∞ =（a₀,a₁,a₂）,（a3,a4,a5）….The output way about the model of the jump self-shrinking sequences is as follows.Considering the positive integer k in turn,the output bits of triple pair(a_3k,a_3k+1,a_3k+2)is determined by the value of a_3k（?）a_3k+2.If a_3k（?）a_3k+2=0,discard this triple pair and go to the next adjacent triple pair.If a_3k（?）a_3k+2=1,output a_3k+1 and go to the next adjacent triple pair.According to the model design of the jump self-shrinking sequences,this paper analyzed the period,linear complexity,run distribution and self-correction of the jump self-shrinking sequences.The results showed that the jump self-shrinking sequences have better properties of the period and linear complexity.Moreover,when the minimal polynomial of base sequences are primitive trinomials or pentanomials,the period and linear complexity about the jump self-shrinking sequences which are produced by this base sequences is twice as much as common case.At the end of GF（2）part,through practical examples studies by Matlab,not only find out that the theory accords with practice,but notice that the jump self-shrinking sequences have the similar properties with m—sequences.The last part of this paper,we extend the case from GF（2）to GF（3）,and analyze the cryptology properties of the GF（3）case.