## Cryptology ePrint Archive: Report 2013/760

On cross joining de Bruijn sequences

Johannes Mykkeltveit and Janusz Szmidt

Abstract: We explain the origins of Boolean feedback functions of nonlinear feedback shift registers (NLFSRs) of fixed order n generating de Bruijn binary sequences. They all come into existence by cross joining operations starting from one maximum period feedback shift register, e.g., a linear one which always exists for any order n. The result obtained yields some constructions of NLFSRs generating maximum period $2^n-1$ binary sequences.

Category / Keywords: secret-key cryptography / De Bruijn sequences, cross-join pairs, nonlinear feedback shift \mbox{registers}, maximum period, quadratic m-sequences.