The Design Of LFSR Over Prime Field And The Application Research About PUF Based On Chaotic Systems

Chaos is an important branch of nonlinear science.It has both local divergence and overall convergence,manifested in the extreme sensitivity of initial values and the boundedness of chaotic system.Chaotic system is wildly used due to their good nonlinear characteristics.The chaotic system needs to be set according to the needs of the specific application in order to make full use of characteristics of the chaotic system.This paper focus on the design of LFSR over prime field and the application research about PUF based on chaotic system.The specific research content is shown as follows:1.This paper proposes a feedback shift register over prime field with register larger than 1 bit.A modular addition operation over prime field is used for specific architecture of irreducible polymomial and result is used as input of LFSR.The accurate maximum period of LFSR is given for LFSR in GF(p).The period verification time increases exponentially with the increase of number of registers.In order to shorten the verification time,a fast matrix calculation method over prime field is proposed,so that the verification time increases linearly with the number of the registers and improves the speed of verification.This kind of LFSR can improve the speed of generation and is suitable for some applications with CPU and embedded devices.2.This paper proposes a chaotic pseudorandom number generator base on PLFSR.The LFSR over prime field is linear and vulnerable to attacks.To improve the security of stream cipher,a nonlinear module is introduced.Chaotic systems have nonlinear characteristics such as initial value sensitivity and unpredictability.These characteristics are similar to replacement and scrambling functions in information security.This paper analyzes the chaotic degradation of discrete finite-precision Logistic chaotic system,and proposes a Logistic chaotic random number generator based LFSR over prime field GF(p).Nonlinear transformation of LFSR over prime field based on nonlinear characteristics of Logistic map.S-box and XOR modules are also used to generate a pseudo random number generator to improve the randomness of the system.3.This paper proposes a pseudorandom number generator based on PUF.The physical unclonable function(PUF)is a unique hardware identifier formed by the random difference in the production process in the production process.For the shortcomings of oscillation PUF and Arbiter PUF,a mixed PUF based on logistic chaotic system is proposed.Dual output of 6?2 look up table(LUT)of Xilinx FPGA is used to design a chaotic number generator based on PUF.The route and placement are well designed to meet the requirement of the PUF with XDC file.Logistic map is used as nonlinear module to generate the PRNG.The performance of the output is also evaluated by NIST test.4.This paper proposes Lorenz chaotic system based on PUF.Although PUF is physically unique,Challenge and response can be used for machine learning attack.According to the analysis of 3-demision Lorenz map,the relationship between effective interval of step and Lyapunov index is discussed to guarantee the convergence.In order to resist machine learning attack,arbiter PUF with a 3-demision Lorenz map is used with APUF.The response is generated though XOR gate to resist machine learning attacks.