Cryptology ePrint Archive: Report 2021/504

A Generic Method for Investigating Nonsingular Galois NFSRs

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

Abstract: 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.

Category / Keywords: foundations / Stream ciphers; nonlinear feedback shift registers; Galois configuration; periodic sequences

Date: received 18 Apr 2021

Contact author: tiantian_d at 126 com, Xiaojuan_Wang0 at 163 com, wenfeng qi at 263 net

Available format(s): PDF | BibTeX Citation

Version: 20210419:061350 (All versions of this report)

Short URL: ia.cr/2021/504


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