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

This paper presents a method for constructing n-stage Galois NLFSRs with period 2n − 1 from n-stage maximum length LFSRs. We introduce nonlinearity 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. By adding a copy of the same function to a later stage of the register, we cancel the effect of nonlinearity and join the state cycles back. 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. However, it has a number of limitations. One is that the resulting NLFSRs can have at most ⌊n/2⌋-1 stages with a nonlinear update. Another is that feedback functions depend only on state variables which are updated linearly. The latter implies that sequences generated by the presented method can also be generate...

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Elena Dubrova
• Keywords: Feedback Functions, IACR 2011, State Cycles, State Variables