基于分区初等元胞自动机的二维伪随机耦合映像格系统及其动态特性

doi:10.11959/j.issn.1000-436x.2022001

Abstract

Abstract:

To solve the weak chaos in the spatiotemporal chaotic system based on coupled map lattices under some control parameters and the un-uniformity of sequences generated by the coupled map lattices, a two-dimensional pseudo-random coupled map lattices (2D-PRCML) system was proposed.Firstly, the two-dimensional partitioned elementary cellular automata (2D-PECA) was designed to establish pseudo-random coupling.Secondly, iterative results of 2D-PECA were utilized to perturb the 2D-PRCML system.The chaotic behaviors of the proposed system, such as the bifurcation diagram, Kolmogorov-Sinai entropy, were investigated.Moreover, the uniformity of sequences generated by the 2D-PRCML system was discussed, and the correlation coefficients between any two sequences generated by different lattices were acquired.The analyses and tests indicate that the 2D-PRCML system exhibits stronger chaotic behavior.Furthermore, the sequence generated by the proposed system possesses better uniformity, randomness, and unpredictability.The outstanding properties of the 2D-PRCML system prove that it is more suitable for applying in cryptography and chaotic secure communication.

Key words: spatiotemporal chaotic system, coupled map lattices, partitioned elementary cellular automata, bifurcation diagram, uniformity

CLC Number:

TN918

Youheng DONG, Geng ZHAO, Yingjie MA. Two-dimensional pseudo-random coupled map lattices system based on partitioned elementary cellular automata and its dynamic properties[J]. Journal on Communications, 2022, 43(1): 71-82.

Figures/Tables 12

References 51

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迭代结果	二进制数
S_t(i-1)	1	1	1	1	0	0	0	0
S_t(i)	1	1	0	0	1	1	0	0
S_t(i+1)	1	0	1	0	1	0	1	0
S_t+1(i)	1	0	0	1	0	1	1	0

种类	规则编号
	18(183), 22(151), 30(86, 135, 149), 45(75, 89, 101),
全局混沌	60(102, 153, 195), 90(165), 105, 106(120, 169, 225),
	129(126), 137(110, 124, 193), 146(182), 150, 161(122)

Two-dimensional pseudo-random coupled map lattices system based on partitioned elementary cellular automata and its dynamic properties

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Figures/Tables 12

References 51

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测试项目	Bit1st	Bit2nd	Bit3rd	Bit4th	Bit5th	Bit6th	Bit7th	Bit8th	Bit9th	Bit10th	Bit11th	Bit12th	Bit13th	Bit14th	Bit15th	Bit16th
Frequency	99	98	98	99	98	100	99	98	98	97	98	100	100	99	100	100
Block frequency	100	100	100	99	100	98	99	99	99	97	99	99	99	99	98	100
Cumulative Sums(Forward)	99	98	100	98	98	100	99	99	98	97	98	100	100	100	100	98
Cumulative Sums(Reverse)	99	98	99	100	100	100	98	100	96	98	98	100	100	100	100	100
Runs	97	100	99	100	97	99	99	100	100	99	99	99	100	97	100	99
Longest runs	96	99	98	99	100	100	98	99	96	99	100	100	99	100	98	99
Rank	99	100	100	97	99	100	99	97	98	100	100	97	99	99	100	100
FFT	100	99	100	100	99	99	96	98	99	99	99	100	100	98	98	99
Non-overlapping template^*	98	99	99	100	99	99	100	100	100	100	100	100	99	99	100	100
Overlapping template	98	100	100	99	100	100	100	99	98	98	100	100	100	98	100	98
Universal	98	99	99	99	98	100	100	100	98	99	100	99	100	98	99	98
Approximate Entropy	100	97	99	98	100	98	100	97	100	99	99	99	99	99	99	100
Random Excursions^*	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass
Random Excursions Variant^*	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass	pass
Serial 1	100	100	100	98	100	100	99	100	99	99	99	100	99	99	98	100
Serial 2	100	99	100	99	98	99	98	99	99	99	98	100	99	98	100	99
Linear Complexity	100	99	99	98	98	99	98	99	99	100	100	100	99	99	98	97
注：带“*”的测试下还包含多个子测试，利用子测试中的最低通过率来判断是否通过该测试，通过则用“pass”来表示