Generation of nonlinear feedback shift registers with special-purpose hardware

The nonlinear feedback shift registers (NLFSR) are used as primitives in cryptographic algorithms. Their theory is not so complete as that of the linear feedback shift registers (LFSR). In general, it is not known how to construct NLFSRs with maximum period. The direct method is to search for such registers with suitable properties. We used the implementation of NLFSRs in Field Programmable Gate Arrays (FPGA) to perform a corresponding search. We also investigated local statistical properties of the binary sequences generated by NLFSRs of order 25 and 27.