数字方法实现的混沌随机数发生器存在有限字长效应，无法保证随机数良好的统计特性。本文构建了一类包含最少模拟器件的新数模混合系统，分析了混合系统的非线性动力学行为。利用现场可编程逻辑门阵列和一阶广义忆阻器实现了复杂混沌映射，克服了有限字长效应，构造了稳定的高速混沌随机数发生器，可以产生100 Gbit/s以上速率的随机数。研究表明，数模混合系统的混沌性对元件参数变化不敏感。混合系统易于集成在图像加密、保密通信和雷达波形设计等应用系统中。%Random number generator (RNG) plays an important role in many areas including image encryption, secure com-munication, radar waveform generation, etc. However, existing analog methods for random number (RN) cannot satisfy the demand of bit rate. In the even worse case, system parameters from analog devices are easily distorted by surround-ings, leading to a weak system robustness. As a result, researchers start to turn to digital implementation which is stabler and more efficient than analog counterpart to produce RN. However, digital methods suffer dynamical degradation due to the limited word length effect. Though some remedies, such as increasing computing precision, cascading multiple chaotic systems, pseudo-randomly perturbing the chaotic system, switching multiple chaotic systems, and error compensation method, are proposed, the limitations are even inevitable. Recently, some continuous-time chaotic oscillators combined with digital devices were used to realize RNG, and a novel approach was proposed to solve the dynamical degradation of digital chaotic system by coupling the given digital chaotic map with an analog chaotic system, where the analog chaotic system is used to anti-control the given digital chaotic map. But this method requires a whole continuous-time system realized with analog devices which restrict the performance of the integral system. In this paper, a novel digital-analog hybrid chaotic system with only one analog device is constructed for the pro-duction of RN. The chosen analog device is a generalized memristor consisting of a diode bridge and a parallel RC filter. Memristor is the fourth fundamental electronic component which has provoked extensive researches since the suc-cessful realization by Stan Williams’s group at HP Labs in 2008. The paper is arranged as follows. Firstly, a generalized memristor realized by a memristive circuit is introduced and its basic properties are given. Then the block diagram of the digital-analog hybrid system based on a single memristor feedback is depicted, and the mathematical model of the system is derived from the block diagram. Thirdly, the simple Logistic map is applied to the hybrid model and its dynamic behaviors are simulated and compared with those from the ideal Logistic before a more complex two-way coupled saw tooth map is applied to the same simulation, verifying the effectiveness of the proposed hybrid system. Finally, the complex coupled map is applied to the practical circuit producing RN which passes the NIST test suite smoothly. The hybrid system has the following advantages: firstly, the introduction of the analog memristor is able to over-come the dynamical degradation in a digital system, avoiding the limited word length effect essentially. Secondly, the least analog device alleviates the sensibility to parameters and the restriction on bit rate in analog systems, ensuring that the hybrid system is robust. Thirdly, the system structure can be easily integrated into a relevant system. By designing the circuits of the system, the field programmable logic gate array of digital part can be used to realize chaotic map while the single memristor acts as a feedback to the digital part. The experimental results show that the novel hybrid system is insensitive to the variations of circuit parameters and the produced RN is of great randomness, satisfying the practical applications.
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