Nonsingularity of grain-like cascade feedback shift registers subject to fault attacks over finite fields
Shilin Wang, Shihua Fu, Jianjun Wang, Xiaoyu Zhao · Nonlinear Analysis Hybrid Systems · 2026
This study investigates the nonsingularity of grain-like cascade feedback shift registers (GLC-FSRs) under fault attacks over finite fields. Firstly, a criterion which has low computational complexity than that of the state transition matrix method is proposed to detect the nonsingularity of GLC-FSRs. Secondly, the nonsingularity of GLC-FSRs under fault attacks is analyzed with respect to two attack types: hard fault attacks and soft fault attacks. And we prove that arbitrary GLC-FSR subject to hard fault attacks is always singular, whereas singular GLC-FSRs retain their singularity following soft fault attacks. For a nonsingular GLC-FSR, a condition for determining whether their nonsingularity can be preserved under soft fault attacks is presented. Additionally, a state feedback attack scheme is designed to ensure the system maintains its nonsingularity. Finally, the theoretical findings are verified through several numerical examples.