Nonsingularity of grain-like cascade feedback shift registers subject to fault attacks

Feedback shift registers (FSRs) are pivotal in generating pseudorandom sequences for stream ciphers and play a crucial role in error detection and code correction. This paper investigates the resilience of grain-like cascade FSRs (GLC-FSRs) against two types of fault attacks: hard and soft. First, we introduce a new criterion for assessing the nonsingularity of GLC-FSRs using the structure matrices of feedback functions, which enable the measurement of the number of nonsingular GLC-FSRs. Second, we demonstrate that GLC-FSRs subject to hard fault attacks become singular as determined by this new criterion. Ultimately, by constructing a soft fault bit set, we discuss the resilience of GLC-FSRs to soft fault attacks. Results demonstrate that singular GLC-FSRs remain singular after being injected by soft fault attacks. Conversely, for nonsingular GLC-FSRs, suitable soft fault attacks are designed to maintain their nonsingular status.