深圳大学学报理工版

自治布尔网络作为可调控的非线性系统,易于产生混沌信号. 利用二输入异或门的非线性特性实现一种可产生高熵值混沌的18节点自治布尔网络电路. 通过引入滤波系数,建立该电路的改进数学模型. 通过数值仿真和电路对比实验研究滤波系数和时延参数对网络动态特性的影响. 数值仿真结果与电路实验现象基本一致. 当节点之间传输延迟不相等时,滤波系数对混沌的产生具有调控作用, 表明引入滤波系数后的数学模型可以更客观描述电路中的物理现象. 借助分岔图、李雅普诺夫指数及排序熵进一步分析自治布尔网络电路的非线性特性和随机性,表明该电路输出的混沌序列具有高带宽和高熵值的特点. 将该电路用于产生高速物理随机序列,并通过了美国国家标准与技术研究院NIST SP 800-22随机性检测标准.

As a controllable nonlinear system, autonomous Boolean network which is easy to generate chaotic signals has become a hot research topic. We realize an 18-node autonomous Boolean network circuit which can generate high entropy chaos by using the nonlinear characteristics of two-input XOR gate, and establish an improved mathematical model for the circuit by introducing the filter coefficient. Through numerical simulation and circuit comparison experiment, we study the influence of filter coefficient and delay parameters on network dynamic characteristics of this model. The numerical simulation results are basically consistent with those of the experimental phenomena. When the transmission delay between nodes is not equal, the filter coefficient has a modulation effect on the generation of chaos, which well indicates that the introduction of the filter coefficient makes the improved mathematical model more objective to describe the physical phenomena in the circuit. In addition, using bifurcation diagram, Lyapunov exponent and permutation entropy, we further analyze the nonlinear characteristics and randomness of the autonomous Boolean network. The output chaotic sequence of the network has the characteristics of high bandwidth, high entropy and strong robustness, which is used to generate high speed physical random sequences and has passed the NIST SP 800-22 randomness tests of National Institute of Standards and Technology of America.

引言
1 自治布尔网络
2 ABN数值仿真
3 ABN电路实验
4 基于ABN的物理随机数发生器
5 结语

图1 布尔网络示意图<br/>Fig.1 Autonomous Boolean network structure

图1 布尔网络示意图
Fig.1 Autonomous Boolean network structure

图2 自治布尔网络输出时序和相图<br/>Fig.2 (Color online)Autonomous Boolean network output time series and phase diagrams

图2 自治布尔网络输出时序和相图
Fig.2 (Color online)Autonomous Boolean network output time series and phase diagrams

图3 布尔网络电路实物图<br/>Fig.3 (Color online)Prototype board of Boolean circuit

图3 布尔网络电路实物图
Fig.3 (Color online)Prototype board of Boolean circuit

图4 不同供电电压时的布尔电路输出信号时序、功率谱及相图<br/>Fig.4 (Color online)Time series, power spectra and phase diagrams of the output signals of Boolean circuit with different supply voltages

图4 不同供电电压时的布尔电路输出信号时序、功率谱及相图
Fig.4 (Color online)Time series, power spectra and phase diagrams of the output signals of Boolean circuit with different supply voltages

图5 布尔电路输出信号随供电电压增加的变化趋势<br/>Fig.5 Output signals of the Boolean circuit as function of the supply voltage

图5 布尔电路输出信号随供电电压增加的变化趋势
Fig.5 Output signals of the Boolean circuit as function of the supply voltage

图6 物理随机数发生器<br/>Fig.6 Physical random number generator

图6 物理随机数发生器
Fig.6 Physical random number generator

图7 NIST测试结果<br/>Fig.7 Typical results of NIST statistical test

图7 NIST测试结果
Fig.7 Typical results of NIST statistical test

表1 本研究physical-RNG与其他文献中随机数发生器的性能比较<br/>Table 1 Comparison of the proposed physical-RNG with other integrated RNGs in the literature

表1 本研究physical-RNG与其他文献中随机数发生器的性能比较
Table 1 Comparison of the proposed physical-RNG with other integrated RNGs in the literature

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备注

引言

1 自治布尔网络

2 ABN数值仿真

3 ABN电路实验

4 基于ABN的物理随机数发生器

5 结语

期刊信息

备注