Analysis Of Grain-like Cascade Feedback Shift Registers

With the development of time,the application of the network in life and various aspects is becoming more and more important.Therefore,information security issues are also getting more and more attention,such as information attack and defense.Scholars' research on cryptography is also evolving.Shift registers occupy an important position in cryptography.Shift registers can not only register data,but can also be used to implement serial-parallel conversion of data,numerical operations,and data.According to the nature of its feedback function,shift registers can be divided into linear feedback shift registers(LFSRs)and nonlinear feedback shift registers(NLFSRs).This paper mainly studies Grain-like cascade feedback shift registers(Grain-like cascade FSRs),its dynamic equations are expressed as Boolean functions,and the semi-tensor product method is used to study some of its monotonicity and stability properties.Chapter 1 describes the research background of this paper.The development of the shift register and the related knowledge of the semi-tensor product of the matrix are introduced first,and then the Grain-like cascade FSRs system and its algebraic expressions are introduced.Chapter 2 studies the monotonicity of Grain-like cascade FSRs.First,according to the existing definition of monotonicity,the monotonicity concept of Grain-like cascade FSRs is defined.Based on the definition of the monotonicity of the feedback function structure matrix,the necessary conditions for the monotonicity of Grain-like cascade FSRs are obtained.Chapter 3 studies the local stability of Grain-like cascade FSRs.First,the semitensor product of the matrix is used to convert Grain-like cascade FSRs into an algebraic form of Boolean network.According to the definition of the local stability of the shift register,some stability property theorems of Grain-like cascade FSRs at the state 0 are mainly discussed.