【作者】 黄春光；

【导师】 丁群；

【作者基本信息】 黑龙江大学 ， 微电子学与固体电子学， 2020， 博士

【摘要】 混沌是非线性科学的一个重要分支,既具有局部发散性又具有整体的收敛性,表现为初值的极端敏感性以及混沌系统的有界性,混沌系统由于具有这些良好非线性特性而被广泛应用。混沌系统需要根据具体应用的需求进行设置,才能充分利用混沌系统的特性。本文围绕基于混沌的有限域上的LFSR与PUF应用进行了研究,具体研究内容如下:1、提出有限域GF(p)上的线性反馈移位寄存器PLFSR。PLFSR每个寄存器的宽度大于1比特,根据不可约多项式构建的PLFSR结构,对特定的寄存器在有限域内采取模加运算,将结果作为PLFSR的输入,并给出该移位寄存器精确的最大周期计算方法。由于系统周期验证时间随着移位寄存器数量的增加成指数增长,为了缩短验证时间,设计了在有限域上快速矩阵计算方法,使得验证时间随寄存器数量线性增长,提高周期的验证速度,并验证周期的正确性。该结构提高了序列生成速度,便于CPU及嵌入式设备应用。2、提出基于PLFSR的混沌序列发生器。利用有限域上的线性反馈移位寄存器,结合Logistic混沌系统,提出基于PLFSR的混沌序列发生器。由于有限域GF(p)上的LFSR线性复杂度低,容易受到攻击,产生的序列随机性差。本文利用Logistic映射的初值敏感性和不可预测性的非线性特点,在不改变寄存器特征的前提下,对有限域GF(p)上的反馈移位寄存器数值进行非线性变换,同时利用S-box模块和异或模块,提高系统的随机性。3、提出基于物理不可克隆函数(PUF)的混沌序列发生器。PUF是利用生产过程中制作工艺的随机性差异所形成的硬件唯一标识,针对基于仲裁器的PUF和基于环形的PUF资源利用率低的缺点,本文提出基于混合型PUF的Logistic混沌序列发生器,利用Xilinx FPGA中的6＿2查找表双输出结构,既保证信号传输路径的对称性,又提高FPGA的资源利用率。利用约束文件保证PUF电路的布局布线的一致性,利用Logistic映射作为非线性模块,产生随机序列,并对生成的随机序列特性进行分析。4、提出基于PUF的Lorenz混沌系统设计。仲裁型PUF是一种强PUF,虽然具有物理唯一性,但是其工作模式依赖于硬件激励响应对,容易受到机器学习的攻击。本文通过对有限精度3维Lorenz映射特性进行分析,给出步长的有效区间以及与系统Lyapunov指数之间的关系,保证Lorenz映射的收敛。然后提出基于Lorenz映射的仲裁型PUF结构,该结构利用Lorenz映射的三维分量作用于仲裁型PUF,通过XOR Gate得到激励对应的响应,能够抵抗机器学习的攻击。更多还原

【Abstract】 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.更多还原