A Scalable Method for Constructing Galois NLFSRs With Period $2^n-1$ Using Cross-Join Pairs

Abstract

A method for constructing n-stage Galois NLFSRs with period 2n-1 from n-stage maximum length LFSRs is presented. Nonlinearity is introduced into state cycles by adding a nonlinear Boolean function to the feedback polynomial of the LFSR. Each assignment of variables for which this function evaluates to 1 acts as a crossing point for the LFSR state cycle. The effect of nonlinearity is cancelled and state cycles are joined back by adding a copy of the same function to a later stage of the register. The presented method requires no extra time steps and it has a smaller area overhead compared to the previous approaches based on cross-join pairs. It is feasible for large n.