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Random number generator (RNG) plays an important role in many areas including image encryption, secure communication, 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 surroundings, 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.#br#In this paper, a novel digital-analog hybrid chaotic system with only one analog device is constructed for the production of RN. The chosen analog device is a generalized memristor consisting of a diode bridge and a parallel RC filter.#br#Memristor is the fourth fundamental electronic component which has provoked extensive researches since the successful realization by Stan Williams's group at HP Labs in 2008.#br#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.#br#The hybrid system has the following advantages: firstly, the introduction of the analog memristor is able to overcome 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.#br#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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Keywords:
- random number generator /
- limited word length /
- digital-analog hybrid /
- memristor
[1] Sivakumar T, Venkatesan R 2015 KSII Trans. Internet Inf. Syst. 9 6
[2] van Wiggeren G D, Roy R 1998 Phys. Rev. Lett. 81 3547
[3] Yao J, Chen G R, Yue C, Zhao Y 2002 ICCA the 2002 International Conference on Control and Automation Xiamen, June 19-19, 2014 p152
[4] Gini F, Maio A D, Patton L 2012 Waveform Design and Diversity for Advanced Radar Systems (UK: The Institution of Engineering and Technology) pp31-32
[5] Li W, Reidler I, Aviad Y, Huang Y Y, Song H L, Zhang Y H, Rosenbluh M, Kanter I 2013 Phys. Rev. Lett. 111 044102
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[12] Bao B C 2013 An Introduction to Chaotic Circuits (Vol. 1) (Beijing: Science Press) pp87-89
[13] Shao S Y, Min F H, Wu X H, Zhang X G 2014 Acta Phys. Sin. 63 060501 (in Chinese) [邵书义, 闵富红, 吴薛红, 张新国 2014 63 060501]
[14] Wang G Y, Bao X L, Wang Z L 2008 Chin. Phys. B 17 3596
[15] Deng Y S, Hu H P, Xiong N X, Xiong W, Liu L F 2015 Inform. Sci. 305 146
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[17] Gler , Ergn S 2010 ICECS 17th IEEE International Conference Athens, December 12-15, 2010 p1037
[18] Ergn S 2014 Circuits and Systems (APCCAS), 2014 IEEE Asia Pacific Conference Ishigaki, November 17-20, 2014 p217
[19] Hu H P, Deng Y S, Liu L F 2014 Commu. Nonlinear Sci. 19 1970
[20] Yeniçeri R, Yalçın M E 2013 Electron. Lett. 49 543
[21] Chua L O 1971 IEEE Trans. Circ. Theor. 18 507
[22] Chua L O, Kang S M 1976 Proc. IEEE 64 209
[23] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[24] Bao B C, Ma Z H, Xu J P, Liu Z, Xu Q 2011 Int. J. Bifurc. Chaos 21 2629
[25] Wang L D, Drakakis E, Duan S K, He P F, Liao X F 2012 Int. J. Bifurc. Chaos 22 1250205
[26] Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502
[27] Muthuswamy B 2010 Int. J. Bifurc. Chaos 20 1335
[28] Kim H, Sah M P, Yang C J, Cho S, Chua L O 2012 IEEE Trans. Circ. Syst. I 59 2422
[29] Yu D S, Liang Y, Chen H, Iu H H C 2013 IEEE Trans. Circ. Syst. II 60 207
[30] Corinto F, Ascoli A 2012 Electron. Lett. 48 824
[31] Bao B C, Yu J J, Hu F W 2014 Int. J. Bifurc. Chaos 24 1450143
[32] Chua L O 2012 Proc. IEEE 100 1920
[33] Tong Q Y, Zeng Y C 2003 Acta Phys. Sin. 52 285 (in Chinese) [童勤业, 曾以成 2003 52 285]
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[1] Sivakumar T, Venkatesan R 2015 KSII Trans. Internet Inf. Syst. 9 6
[2] van Wiggeren G D, Roy R 1998 Phys. Rev. Lett. 81 3547
[3] Yao J, Chen G R, Yue C, Zhao Y 2002 ICCA the 2002 International Conference on Control and Automation Xiamen, June 19-19, 2014 p152
[4] Gini F, Maio A D, Patton L 2012 Waveform Design and Diversity for Advanced Radar Systems (UK: The Institution of Engineering and Technology) pp31-32
[5] Li W, Reidler I, Aviad Y, Huang Y Y, Song H L, Zhang Y H, Rosenbluh M, Kanter I 2013 Phys. Rev. Lett. 111 044102
[6] Naruse M, Kim S J, Aono M, Hori H, Ohtsu M 2014 Sci. Rep. 4 6039
[7] Petrie C S, Connelly J A 2000 IEEE Trans. Circ. I 47 5
[8] Bao B C, Hu W, Xu J P, Liu Z, Zou L 2011 Acta Phys. Sin. 60 120502 (in Chinese) [包伯成, 胡文, 许建平, 刘中, 邹凌 2011 60 120502]
[9] Li C B, Sprott J C 2014 Int. J. Bifurc. Chaos 24 1450131
[10] Li C B, Sprott J C, Thio W 2014 J. Exp. Theor. Phys. 118 494
[11] Li C B, Sprott J C 2014 Phys. Lett. A 378 178
[12] Bao B C 2013 An Introduction to Chaotic Circuits (Vol. 1) (Beijing: Science Press) pp87-89
[13] Shao S Y, Min F H, Wu X H, Zhang X G 2014 Acta Phys. Sin. 63 060501 (in Chinese) [邵书义, 闵富红, 吴薛红, 张新国 2014 63 060501]
[14] Wang G Y, Bao X L, Wang Z L 2008 Chin. Phys. B 17 3596
[15] Deng Y S, Hu H P, Xiong N X, Xiong W, Liu L F 2015 Inform. Sci. 305 146
[16] Ergun S, Özoğuz S 2010 Int. J. Circ. Theor. Appl. 38 1
[17] Gler , Ergn S 2010 ICECS 17th IEEE International Conference Athens, December 12-15, 2010 p1037
[18] Ergn S 2014 Circuits and Systems (APCCAS), 2014 IEEE Asia Pacific Conference Ishigaki, November 17-20, 2014 p217
[19] Hu H P, Deng Y S, Liu L F 2014 Commu. Nonlinear Sci. 19 1970
[20] Yeniçeri R, Yalçın M E 2013 Electron. Lett. 49 543
[21] Chua L O 1971 IEEE Trans. Circ. Theor. 18 507
[22] Chua L O, Kang S M 1976 Proc. IEEE 64 209
[23] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[24] Bao B C, Ma Z H, Xu J P, Liu Z, Xu Q 2011 Int. J. Bifurc. Chaos 21 2629
[25] Wang L D, Drakakis E, Duan S K, He P F, Liao X F 2012 Int. J. Bifurc. Chaos 22 1250205
[26] Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502
[27] Muthuswamy B 2010 Int. J. Bifurc. Chaos 20 1335
[28] Kim H, Sah M P, Yang C J, Cho S, Chua L O 2012 IEEE Trans. Circ. Syst. I 59 2422
[29] Yu D S, Liang Y, Chen H, Iu H H C 2013 IEEE Trans. Circ. Syst. II 60 207
[30] Corinto F, Ascoli A 2012 Electron. Lett. 48 824
[31] Bao B C, Yu J J, Hu F W 2014 Int. J. Bifurc. Chaos 24 1450143
[32] Chua L O 2012 Proc. IEEE 100 1920
[33] Tong Q Y, Zeng Y C 2003 Acta Phys. Sin. 52 285 (in Chinese) [童勤业, 曾以成 2003 52 285]
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