Four Yuan Primitive Sequence And Its Maximum Power Sequence Of The Cryptographic Properties

The study of pseudorandom character of the primitive sequences and their highest-level sequences have very broad application foreground.The paper discuss the cipher features of the primitive sequences and their highest-level sequences over ring Z/(4), including the elements-distribution, linear-complexion, correlation function, and runs-distribution. First we give the proof of elements-distribution, which was presented by A.S.Kuzmin and A.A.Nechaev in 1992[21], but was not proved. Second we calculate the linear-complexity of the highest-level sequences, which was not presented by other papers. And then we give the all-possible correlation function values of the two sequences. At last we study the runs-distribution of these sequences. It is worth say, the calculation correlation function values of the highest-level sequences, and the descriptions of runs-distribution are the newest results, there are not the correlate results in the world.In this paper we have basically finished the depiction of the cipher features of the primitive sequences and their highest-level sequences over ring Z/(4). Which provides the study ways for the cipher features of the primitive sequences and their highest-level sequences over residue class ring Z/(2n).