A novel synthesis method for reliable feedback shift registers via Boolean networks

A random fault or a malicious attack can compromise the security of decryption systems. Using a stable and monotonous feedback shift register (FSR) as the main building block in a convolutional decoder can limit some error propagation. This work foucus on the synthesis of reliable (i.e., globally stable and monotonous) FSRs using the Boolean networks (BNs) method. First, we obtain an algebraic expression of the FSRs, based on which one necessary and sufficient condition for the monotonicity of the FSRs is given. Then, we obtain the upper bound of the number of cyclic attractors for monotonous FSRs. Furthermore, we propose one method of constructing n-stage reliable FSRs, and figure out that the number of reliable

[1]  Dongdai Lin,et al.  Stability of nonlinear feedback shift registers , 2014, 2014 IEEE International Conference on Information and Automation (ICIA).

[2]  Guodong Zhao,et al.  A survey on applications of semi-tensor product method in engineering , 2017, Science China Information Sciences.

[3]  Wen-Feng Qi,et al.  Further Results on the Decomposition of an NFSR Into the Cascade Connection of an NFSR Into an LFSR , 2015, IEEE Trans. Inf. Theory.

[4]  Yuqian Guo,et al.  Observability of Boolean control networks , 2017, 2017 36th Chinese Control Conference (CCC).

[5]  Shuang Liang,et al.  Structural controllability of Boolean control networks with an unknown function structure , 2020, Science China Information Sciences.

[6]  Dongdai Lin,et al.  On Minimum Period of Nonlinear Feedback Shift Registers in Grain-Like Structure , 2018, IEEE Transactions on Information Theory.

[7]  Jinde Cao,et al.  Synchronization of Arbitrarily Switched Boolean Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Jinde Cao,et al.  Observability of Boolean control networks , 2018, Science China Information Sciences.

[9]  Yang Liu,et al.  Observability of Boolean networks via STP and graph methods , 2019, IET Control Theory & Applications.

[10]  Hu Chuan-Gan,et al.  On The Shift Register Sequences , 2004 .

[11]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[12]  Jinde Cao,et al.  Robust Event-Triggered Control Invariance of Probabilistic Boolean Control Networks , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Xiang Li,et al.  Structural Controllability of Temporally Switching Networks , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Yuzhen Wang,et al.  Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method , 2012, Autom..

[15]  Frederic J. Mowle,et al.  An Algorithm for Generating Stable Feedback Shift Registers of Order n , 1967, JACM.

[16]  Jinde Cao,et al.  Stabilization of logical control networks: an event-triggered control approach , 2019, Science China Information Sciences.

[17]  Daizhan Cheng,et al.  Nonsingularity of feedback shift registers , 2015, Autom..

[18]  Yang Liu,et al.  Nonlinear second-order multi-agent systems subject to antagonistic interactions without velocity constraints , 2020, Appl. Math. Comput..

[19]  Wen-Feng Qi,et al.  Further Results on the Decomposition of an NFSR Into the Cascade Connection of an NFSR Into an LFSR , 2013, IEEE Transactions on Information Theory.

[20]  Jinde Cao,et al.  Synchronization criteria for multiple memristor-based neural networks with time delay and inertial term , 2018 .

[21]  Jinde Cao,et al.  The transformation between the Galois NLFSRs and the Fibonacci NLFSRs via semi-tensor product of matrices , 2018, Autom..

[22]  Then,et al.  Ieee Transactions on Information Theory July Application of Lyapunov's Direct Method to the Error- Propagation Effect in Convolutional Codes , .

[23]  Guang Gong,et al.  Periods on Two Kinds of nonlinear Feedback Shift Registers with Time Varying Feedback Functions , 2011, Int. J. Found. Comput. Sci..

[24]  Zheng-Guang Wu,et al.  Set Stabilization of Probabilistic Boolean Control Networks: A Sampled-Data Control Approach , 2020, IEEE Transactions on Cybernetics.

[25]  Jianquan Lu,et al.  Boolean-network-based approach for construction of filter generators , 2020, Science China Information Sciences.

[26]  Zengqiang Chen,et al.  Modeling and analysis of colored petri net based on the semi-tensor product of matrices , 2017, Science China Information Sciences.

[27]  James L. Massey,et al.  Application of Lyapunov's direct method to the error-propagation effect in convolutional codes (Corresp.) , 1964, IEEE Trans. Inf. Theory.

[28]  Elena Dubrova,et al.  Finding Matching Initial States for Equivalent NLFSRs in the Fibonacci and the Galois Configurations , 2009, IEEE Transactions on Information Theory.

[29]  Daizhan Cheng,et al.  Controllability and observability of Boolean control networks , 2009, Autom..

[30]  D. Cheng,et al.  Analysis and control of Boolean networks: A semi-tensor product approach , 2010, 2009 7th Asian Control Conference.

[31]  Haitao Li,et al.  On feedback invariant subspace of Boolean control networks , 2020, Science China Information Sciences.

[32]  Yang Liu,et al.  Nonsingularity of Grain-like cascade FSRs via semi-tensor product , 2017, Science China Information Sciences.

[33]  Yang Liu,et al.  Output feedback stabilizer design of Boolean networks based on network structure , 2019, Frontiers of Information Technology & Electronic Engineering.