Research Project:
Nonlinear Feedback Shift Register Sequences

In the project on pseudorandom sequences generated by feedback shift registers, I have been studying sequences generated by nonlinear feedback shift registers because of their speed and ease of hardware implementation. Together with Dr. Games and Dr. Rushanan at the MITRE Corporation, we have started investigating maximal length sequences obtained from quadratic feedback functions. We have considered the construction of these quadratic m-sequences by adding simple quadratic devices to linear feedback shift registers. A mathematical model based on the shift operator and the product operator has been proposed and it is shown that such a model can be viewed as a left $GF(q)[x]$-module, where $GF(q)$ is the Galois field.


A. Chan, ``On Modeling Quadratic Feedback Shift Register Sequence'', Proceedings of 1996 IEEE International Symposium on Information Theory and Its Applications, (1996), pages 90-92.

A. Chan, R.A. Games and J.J.Rushanan, ``On Quadratic m-Sequences'', Fast Software Encryption, Springer Lecture Notes in Computer Science, No. 809, (1994), pages 166-173.