Nowadays, I spend most of my time studying on Nonlinear Feedback Shift Registers (NFSRs). Especially the ones with Maximum period.
A feedback shift register is a device that shifts its contents into adjacent positions within the register and fills the position on the other end with a new value generated by the feedback function. If the feedback function is linear, everything is easy! :)But when you start to work on nonlinear feedback functions, things start to get a little bit harder.
There are some important unsolved problems and conjectures related to the selection of feedback function of a NFSR. There is no efficient method that finds feedback function with maximum period and also, given a feedback function it is hard to predict the period.
If you want to learn more about NFSRs, you can start with the following papers and books.
- H. Fredricksen. A survey of full length nonlinear shift register cyclealgorithms. Siam Review, 24(2):195–221, 1982
- S. W. Golomb. Shift Register Sequences. Aegean Park Press, LagunaHills, CA, USA, 1981
- A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone. Handbook ofapplied cryptography. CRC Press, Boca Raton, Florida, 1996.
If you want to discuss anything about NFSRs, please feel free :)