How to Embed Short Cycles into Large Nonlinear Feedback-Shift Registers

Abstract

We construct nonlinear feedback shift registers with short cycles. Our method is to embed nonlinear feedback shift registers with small state spaces into nonlinear feedback shift registers with large state spaces. Algebraic analysis of our embedding indicates that detecting the embedded ‘small' feedback shift register in the large feedback register is infeasible without additional information. As an application we propose a low-cost group-identification scheme.