Pseudorandom bit generators are essential components in many security applications. The security of the system relies on the security of its components. Feedback shift registers are commonly used to generate pseudorandom bits. Nonlinear feedback shift registers (NLFSRs) are known to be more secure than the linear ones. However, there is no mathematical foundation on how to construct NLFSR feedback functions with optimal periods. This article considers a new type of NLFSR capable of constructing feedback functions of degree 3 with optimal periods. Using their construction method, the authors propose new functions of this type.

The possibility of using decimation to the sequence generated by NLFSR is considered in this paper. The possibility of searching of sequence with maximal period by dint of the decimation is considered. The possibility of calculating the correlation for NLFSR based on the principle of group addition is considered. This correlation is used for calculating of the sequences with the predetermined shift.