Paper 2021/504

A Generic Method for Investigating Nonsingular Galois NFSRs

Xiao-Juan Wang, Tian Tian, and Wen-Feng Qi


Let n be a positive integer. An n-stage Galois NFSR has n registers and each register is updated by a feedback function. Then a Galois NFSR is called nonsingular if every register generates (strictly) periodic sequences, i.e., no branch points. In this paper, a generic method for investigating nonsingular Galois NFSRs is provided. Two fundamental concepts that are standard Galois NFSRs and the simplified feedback function of a standard Galois NFSR are proposed. Based on the new concepts, a sufficient condition is given for nonsingular Galois NFSRs. In particular, for the class of Galois NFSRs with linear simplified feedback functions, a necessary and sufficient condition is presented. Hopefully, some new insights are provided on determining nonsingular Galois NFSRs.

Available format(s)
Publication info
Preprint. MINOR revision.
Stream ciphersnonlinear feedback shift registersGalois configurationperiodic sequences
Contact author(s)
tiantian_d @ 126 com
Xiaojuan_Wang0 @ 163 com
wenfeng qi @ 263 net
2021-04-19: received
Short URL
Creative Commons Attribution


      author = {Xiao-Juan Wang and Tian Tian and Wen-Feng Qi},
      title = {A Generic Method for Investigating Nonsingular Galois NFSRs},
      howpublished = {Cryptology ePrint Archive, Paper 2021/504},
      year = {2021},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.