A novel method for reconstructing period with single input in NFSR

作者：Gao, Bo^*; Liu, Xuan; Lan, Zhongzhou; Fu, Rongrong

来源：Chaos Solitons & Fractals, 2018, 109: 36-40.

DOI：10.1016/j.chaos.2018.01.012

• Non-Linear Feedback Shift Registers (NFSR)
• Single input
• Semi-tensor product (STP)
• Period
• Reconstruction
• Boolean network (BN)

Non-Linear Feedback Shift Registers (NFSRs) are a generalization of Liner Feedback Shift Registers (LFSRs). The study of NFSR sequence helps to analyze the cryptographical security of NFSR-based stream cipher. Due to lack of efficient algebraic tools, the period of NFSR still remains an open crucial theoretical problem. In this paper, we view the NFSR as a Boolean network (BN), so that the study about the period of NFSR can be viewed as the study about period of BN. Furthermore, based on the mathematical tool of semi-tensor product (STP), a Boolean network can be mapped into an algebraic form. For these, we put forward a method for reconstructing the period of NFSR with single input. Especially, we propose a procedure to choose the controlled states and steer the controlled states from initial state to desirable one. At last, the general derivation is exemplified by numerical simulations for a land of NFSR.

• 出版日期2018-4
• 单位内蒙古大学