布尔混沌系统的物理随机性分析

doi:10.11959/j.issn.1000-436x.2019048

通信学报 ›› 2019, Vol. 40 ›› Issue (3): 190-195.doi: 10.11959/j.issn.1000-436x.2019048

布尔混沌系统的物理随机性分析

龚利爽^1,²,侯二林^1,²,刘海芳^1,²,李凯凯^1,²,王云才^1,²()

¹ 太原理工大学物理与光电工程学院，山西太原 030024
² 新型传感器与智能控制教育部和山西省重点实验室，山西太原 030024

修回日期:2018-08-01 出版日期:2019-03-01 发布日期:2019-04-04
作者简介:龚利爽（1991- ），女，河南漯河人，太原理工大学博士生，主要研究方向为混沌理论与混沌密码。|侯二林（1992- ），男，河南漯河人，太原理工大学硕士生，主要研究方向为物理随机数发生器技术。|刘海芳（1989- ），女，山西晋中人，太原理工大学博士生，主要研究方向为混沌理论与混沌密码。|李凯凯（1994- ），男，山西晋城人，太原理工大学硕士生，主要研究方向为物理随机数发生器技术。|王云才（1965- ），男，山西运城人，博士，太原理工大学教授、博士生导师，主要研究方向为混沌信号的产生与应用。
基金资助:
国家自然科学基金资助项目(61731014)

Physical random analysis of Boolean chaos

Lishuang GONG^1,²,Erlin HOU^1,²,Haifang LIU^1,²,Kaikai LI^1,²,Yuncai WANG^1,²()

¹ College of Physics and Optoelectronics,Taiyuan University of Technology,Taiyuan 030024,China
² Key Laboratory of Advanced Transducers and Intelligent Control System,Ministry of Education,Taiyuan 030024,China

Revised:2018-08-01 Online:2019-03-01 Published:2019-04-04
Supported by:
The National Natural Science Foundation of China(61731014)

摘要/Abstract

摘要：

为了分析布尔混沌系统的物理随机性，构建了基于自治布尔网络的电路混沌模型，建立了包含相位噪声特性的数学方程，研究了相位噪声对布尔混沌熵增长时间（记忆时间）的影响。研究结果表明，在相位噪声的影响下，布尔混沌输出将在有限的记忆时间（数十纳秒）后达到无法预测，且相位噪声越强，布尔混沌平均记忆时间越短。这证明了相位噪声是布尔混沌物理随机性的来源，且布尔混沌可以作为性能良好的真随机数物理熵源。

关键词: 自治布尔网络, 布尔混沌, 相位噪声, 物理随机性

Abstract:

To analyze the physical randomness of Boolean chaos,the model for chaotic circuit system based on autonomous Boolean network was established.In addition,the equations of the Boolean network with phase noise were deduced.By considering the phase noise,the time for the growth of entropy for an ensemble of trajectories,called the memory time,was analyzed.It was demonstrated that Boolean chaos would be unpredictable after tens of nanoseconds,and less average memory time was required as the phase noise strength increased.It is shown that Boolean chaos has physical randomness because of phase noise and it also lays the theoretical foundation for the entropy source of true random number generator based on chaotic Boolean network.

Key words: autonomous Boolean network, Boolean chaos, phase noise, physical random

中图分类号:

TN91

龚利爽,侯二林,刘海芳,李凯凯,王云才. 布尔混沌系统的物理随机性分析[J]. 通信学报, 2019, 40(3): 190-195.

Lishuang GONG,Erlin HOU,Haifang LIU,Kaikai LI,Yuncai WANG. Physical random analysis of Boolean chaos[J]. Journal on Communications, 2019, 40(3): 190-195.

图/表 9

图1

表1

图2

图3

图4

图5

图6

图7

图8

参考文献 19

[1]	WIECZOREK P Z , GOLOFIT K . Dual-metastability time- competitive true random number generator[J]. IEEE Transactions on Circuits and Systems I-Regular Papers, 2014,61(1): 134-145.
[2]	CHEN X , WANG L , LI B ,et al. Modeling random telegraph noise as a randomness source and its application in true random number generation[J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2016,35(9): 1435-1448.
[3]	GABRIEL C , WITTMANN C , SYCH D ,et al. A generator for unique quantum random numbers based on vacuum states[J]. Nature Photonics, 2010,4(10): 711-715.
[4]	ROBSON S , LEUNG B , GONG G . Truly random number generator based on a ring oscillator utilizing last passage time[J]. IEEE Transactions on Circuits and Systems Ⅱ-Express Briefs, 2014,61(12): 937-941.
[5]	MATHEW S K , JOHNSTON D , SATPATHY S ,et al. RNG:a 300-950 mV,323 Gbps/W all-digital full-entropy true random number generator in 14 nm FinFET CMOS[J]. IEEE Journal of Solid-State Circuits, 2016,51(7): 1695-1704.
[6]	LUBICZ D , BOCHARD N . Towards an oscillator based TRNG with a certified entropy rate[J]. IEEE Transactions on Computers, 2015,64(4): 1191-1200.
[7]	LIU D , LIU Z , LI L ,et al. A low-cost low-power ring oscillator-based truly random number generator for encryption on smart cards[J]. IEEE Transactions on Circuits and Systems Ⅱ-Express Briefs, 2016,63(6): 608-612.
[8]	ERGUN S , GULER U , ASADA K . A high speed ic truly random number generator based on chaotic sampling of regular waveform[J]. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2011,E94A(1): 180-190.
[9]	PARESCHI F , SETTI G , ROVATTI R . A fast chaos-based true random number generator for cryptographic applications[C]// The Solid-State Circuits Conference. 2006: 130-133.
[10]	PARESCHI F , SETTI G , ROVATTI R . Implementation and testing of high-speed CMOS true random number generators based on chaotic systems[J]. IEEE Transactions on Circuits and Systems I-Regular Papers, 2010,57(12): 3124-3137.
[11]	ROSIN D P , RONTANI D , GAUTHIER D J . Ultrafast physical generation of random numbers using hybrid Boolean networks[J]. Physical Review E, 2013,87(4):040902.
[12]	PARK M , RODGERS J C , LATHROP D P . True random number generation using CMOS Boolean chaotic oscillator[J]. Microelectronics Journal, 2015,46(12): 1364-1370.
[13]	CICEK I , PUSANE A E , DUNDAR G . A novel design method for discrete time chaos based true random number generators[J]. Integration-the VLSI Journal, 2014,47(1): 38-47.
[14]	GHIL M , MULLHAUPT A . Boolean delay equations.II.Periodic and aperiodic solutions[J]. Journal of Statistical Physics, 1985,41(1-2): 125-173.
[15]	BOCKMAN S F , . Lyapunov exponents for systems described by differential equations with discontinuous right-hand sides[C]// The American Control Conference. 1991: 1673-1678.
[16]	ZHANG R , CAVALCANTE H L D D S , GAO Z ,et al. Boolean chaos[J]. Physical Review E, 2009,80(4):045202(R).
[17]	HAJIMIRI A , LIMOTYRAKIS S , LEE T H . Jitter and phase noise in ring oscillators[J]. IEEE Journal of Solid-State Circuits, 2002,34(6): 790-804.
[18]	DEMIR A , SANGIOVANNIVINCENTELLI A . Analysis and simulation of noise in nonlinear electronic circuits and systems[M]. Germany: Springer-VerlagPress, 1998.
[19]	SUNADA S , HARAYAMA T , DAVIS P ,et al. Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation[J]. Chaos, 2012,22(4):047513.

布尔混沌系统的物理随机性分析

Physical random analysis of Boolean chaos

在线阅读

PDF下载

可视化

摘要/Abstract

引用本文

使用本文

图/表 9

参考文献 19

相关文章 3

Metrics

推荐阅读 0

[1]	张琪琪,张建国,李璞,郭龑强,王云才. 基于布尔混沌的物理随机数发生器[J]. 通信学报, 2019, 40(1): 201-206.
[2]	牟宁,高万荣,吕望晗. 基于光子射频振荡器的高灵敏度光学探测方法[J]. 通信学报, 2018, 39(12): 69-74.
[3]	柯熙政,王晨昊,陈丹. Malaga大气湍流信道下副载波调制系统相位噪声分析[J]. 通信学报, 2018, 39(11): 80-86.

输入	XOR输出	XNOR输出
00	0	1
01	1	0
10	1	0
11	0	1