The partial properties of a new pseudo-random sequence

The m subsequence proposed in this paper is a new sequence formed by changing state transition orders interactively according to the state transition characteristics of the m sequence. The m subsequence is validated using the random test software NIST for its similar randomness as an m sequence. Using the BM algorithm, it is shown that this type of pseudo-random sequences has very high linear complexity. Also, it is verified that its complementary sequence has very high linear complexity at the same time, which illustrates that m subsequences have a good linear complexity spectrum and strong abilities to resist linear attacks. The feedback functions that generate m subsequences are proved to have good algebraic immunity as well as comparatively strong capabilities to resist algebraic attacks. The m subsequences have nice cryptographic properties and a good prospect for applications.