The Cryptographic Analysis Of [d,k]-Self-Decimated Sequence Based On M-sequence

This paper based on the model of m-sequence's[d,k]-self-Decimated sequence,using the strings of proposed deletion's and quasi-reservation s patterns,finite field's and crypto-graphic's professional basic knowledge.In particular,translational equivalence of m[d,k]-self-Decimated sequence,the runs' distribution of m-sequence and properties of decimated sequence for m-sequence,determining the bounds of the period of m 2,1]-self-Decimated sequence.Through deeper exploration found that the model of[d,k]-self-Decimated se-quence all can be transformed into the type of m 1,k]or mq[k,1]-self-Decimated sequence,so giving the bounds of the period of m[2,1],[1,2]in GF(2).And extend this type of sequence to GF(3)and GF(q),the form of the sequence is (?),here k equals two,and obtain ideal periodic results.Then aimed at the model of m[2,1]-seif-Decimated sequence,also analysis cryptographic properties of k-tuple distribution and e-qnilibrium of sequences.In order to comprehensive determine the cryptographic properties of sequence,we need the further studies on run distribution and autocorrelation of m[1,2]-self-Decimated sequence and m[2,1]-self-Decimated sequence.Considering the allelism be-tween the above mentioned two types of sequences,we just.focus on the model of m 2,1].In addition,comparing the type of[2,1]with the type of[1,2]in run distribution.Then group-ing and comparing the correlated strings,we could received that when m-sequence's order is odd or even.the m 2,1-self-Decimated sequence's autocorrelation value is respective-ly-1,0,so the sequence autocorrelation is very well.Finally,a conjecture about the linear complexity of m[2,1]-self-Decimated sequence and m1[1,2]-self-Decimated are given,what's more,the results with a special example by matlab turns out the linear complexity is high and close to the period.