Image encryption based on a novel memristive chaotic system, Grain-128a algorithm and dynamic pixel masking

doi:10.23919/JSEE.2022.000053

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (3): 534-550.doi: 10.23919/JSEE.2022.000053

收稿日期:2021-03-09 出版日期:2022-06-18 发布日期:2022-06-24

Image encryption based on a novel memristive chaotic system, Grain-128a algorithm and dynamic pixel masking

Lilian HUANG^1,²(), Yi SUN^1,²(), Jianhong XIANG^1,^2,*(), Linyu WANG^1,²()

¹ College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
² Key Laboratory of Advanced Marine Communication and Information Technology-Ministry of Industry and Information Technology, Harbin Engineering University, Harbin 150001, China

Received:2021-03-09 Online:2022-06-18 Published:2022-06-24
Contact: Jianhong XIANG E-mail:lilian_huang@163.com;sun_yi@hrbeu.edu.cn;xiangjianhong@hrbeu.edu.cn;wanglinyu@hrbeu.edu.cn
About author:|HUANG Lilian was born in 1972. She received her M.E. and Ph.D. degrees in navigation, guidance and control from Harbin Institute of Technology, Harbin, China, in 2002 and 2005, respectively. She is a a professor in Harbin Engineering University. Her research interests are in the study and application of nonlinear chaotic systems. E-mail: lilian_huang@163.com||SUN Yi was born in 1994. She is currently pursuing her M.S. degree in Harbin Engineering University. Her research interests are the study of nonlinear chaotic systems and their applications in image encryption. E-mail: sun_yi@hrbeu.edu.cn||XIANG Jianhong was born in 1977. He received his M.E. and Ph.D. degrees in communication and information system from Harbin Engineering University, Harbin, China, in 2006 and 2009, respectively. He is a professor in Harbin Engineering University. His research interests are communication and signal processing, deep learning and artificial intelligence. E-mail: xiangjianhong@hrbeu.edu.cn||WANG Linyu was born in 1977. She received her M.E. and Ph.D. degrees in communication and information system from Harbin Engineering University, Harbin, China, in 2003 and 2006, respectively. She is a professor in Harbin Engineering University. Her research interests are communications and information processing. E-mail: wanglinyu@hrbeu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (61203004), the Natural Science Foundation of Heilongjiang Province (F201220), and the Heilongjiang Provincial Natural Science Foundation of Joint Guidance Project (LH2020F022).

摘要/Abstract

Abstract:

In this paper, we first propose a memristive chaotic system and implement it by circuit simulation. The chaotic dynamics and various attractors are analysed by using phase portrait, bifurcation diagram, and Lyapunov exponents. In particular, the system has robust chaos in a wide parameter range and the initial value space, which is favourable to the security communication application. Consequently, we further explore its application in image encryption and present a new scheme. Before image processing, the external key is protected by the Grain-128a algorithm and the initial values of the memristive system are updated with the plain image. We not only perform random pixel extraction and masking with the chaotic cipher, but also use them as control parameters for Brownian motion to obtain the permutation matrix. In addition, multiplication on the finite field GF(2⁸) is added to further enhance the cryptography. Finally, the simulation results verify that the proposed image encryption scheme has better performance and higher security, which can effectively resist various attacks.

Key words: memristive chaotic system, super-wide parameter range, image encryption, Grain-128a algorithm, dynamic pixel masking

. [J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 534-550.

Lilian HUANG, Yi SUN, Jianhong XIANG, Linyu WANG. Image encryption based on a novel memristive chaotic system, Grain-128a algorithm and dynamic pixel masking[J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 534-550.

图/表 23

参考文献 25

1	MATTHEWS R On the derivation of a “Chaotic” encryption algorithm. Cryptologia, 1989, 13 (1): 29- 42. doi: 10.1080/0161-118991863745
2	FRIDRICH J Symmetric ciphers based on two-dimensional chaotic maps. International Journal of Bifurcation and Chaos, 1998, 8 (6): 1259- 1284. doi: 10.1142/S021812749800098X
3	SU Y G, TANG C, LI B Y, et al Single-lens Fourier-transform-based optical color image encryption using dual two-dimensional chaotic maps and the Fresnel transform. Applied Optics, 2017, 56 (3): 498- 505. doi: 10.1364/AO.56.000498
4	KHAN M A, AHMAD J, JAVAID Q, et al An efficient and secure partial image encryption for wireless multimedia sensor networks using discrete wavelet transform, chaotic maps and substitution box. Journal of Modern Optics, 2017, 64 (5): 531- 540. doi: 10.1080/09500340.2016.1246680
5	WANG X Y, XU D H A novel image encryption scheme based on Brownian motion and PWLCM chaotic system. Nonlinear Dynamics, 2014, 75, 345- 353. doi: 10.1007/s11071-013-1070-x
6	HUSSAIN I, SHAH T, GONDAL M A, et al A novel image encryption algorithm based on chaotic maps and GF(2⁸) exponent transformation . Nonlinear Dynamics, 2013, 72, 399- 406. doi: 10.1007/s11071-012-0723-5
7	ZHANG L M, SUN K H, LIU W H, et al A novel color image encryption scheme using fractional-order hyperchaotic system and DNA sequence operations. Chinese Physics B, 2017, 26 (10): 100504. doi: 10.1088/1674-1056/26/10/100504
8	NASKAR P K, BHATTACHARYYA S, NANDY D, et al A robust image encryption scheme using chaotic tent map and cellular automata. Nonlinear Dynamics, 2020, 100 (3): 2877- 2898. doi: 10.1007/s11071-020-05625-3
9	NJITACKE Z T, ISAAC S D, NESTOR T, et al. Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption. Neural Computing and Applications, 2021, 33: 6733–6752.
10	GONG L H, HE X T, CHENG S, et al Quantum image encryption algorithm based on quantum image XOR operations. International Journal of Theoretical Physics, 2016, 55, 3234- 3250. doi: 10.1007/s10773-016-2954-6
11	NATIQ H, AL-SAIDI N M G, SAID M R M, et al A new hyperchaotic map and its application for image encryption. European Physical Journal Plus, 2018, 133 (1): 6. doi: 10.1140/epjp/i2018-11834-2
12	WANG X Y, WANG Y, WANG S W, et al A novel pseudo-random coupled LP spatiotemporal chaos and its application in imageencryption. Chinese Physics B, 2018, 27 (11): 110502. doi: 10.1088/1674-1056/27/11/110502
13	LIU H J, ZHANG Y Q, KADIR A, et al. Image encryption using complex hyper chaotic system by injecting impulse into parameters. Applied Mathematics and Computation, 2019, 360(1): 83−93.
14	STRUKOV D B, SNIDER G S, STEWART D R, et al The missing memristor found. Nature, 2008, 453 (7191): 80- 83. doi: 10.1038/nature06932
15	PENG G Y, MIN F H Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit. Nonlinear Dynamics, 2017, 90 (3): 1607- 1625. doi: 10.1007/s11071-017-3752-2
16	LI C L, LI Z Y, FENG W, et al Dynamical behavior and image encryption application of a memristor-based circuit system. International Journal of Electronics and Communications, 2019, 110, 152861.
17	CHUA L O, KANG S M Memristive devices and systems. Proccedings of the IEEE, 1976, 64 (2): 209- 223. doi: 10.1109/PROC.1976.10092
18	BAO B C, XU J P, ZHOU G H, et al. Chaotic memristive circuit: equivalent circuit realization and dynamical analysis. Chinese Physics B, 2011, 20(12): 120502.
19	AGREN M, HELL M, JOHANSSON T. Grain-128a: a new version of Grain-128 with optional authentication. International Journal of Wireless and Mobile Computing, 2011, 5(1): 48–59.
20	HELL M, JOHANSSON T, MEIER W. Grain– a stream cipher for constrained environments. International Journal of Wireless and Mobile Computing, 2006, 2(1): 86–93.
21	HELL M, JOHANSSON T, MAXIMOV A, et al A stream cipher proposal: Grain-128. Proc. of the IEEE International Symposium on Information Theory, 2006, 1614- 1618.
22	CHAI X L, GAN Z H, LU Y, et al A novel color image encryption algorithm based on genetic recombination and the four-dimensional memristive hyperchaotic system. Chinese Physics B, 2016, 25 (10): 100503. doi: 10.1088/1674-1056/25/10/100503
23	HASANZADEH E, YAGHOOBI M A novel color image encryption algorithm based on substitution box and hyper-chaotic system with fractal keys. Multimedia Tools and Applications, 2020, 79, 7279- 7297. doi: 10.1007/s11042-019-08342-1
24	LIU H J, KADIR A, XU C B Color image encryption with cipher feedback and coupling chaotic map. International Journal of Bifurcation and Chaos, 2020, 30 (12): 2050173. doi: 10.1142/S0218127420501734
25	ZHOU J, ZHOU N R, GONG L H Fast color image encryption scheme based on 3D orthogonal Latin squares and matching matrix. Optics & Laser Technology, 2020, 131, 106437.

Attractor	Parameter				Initial value
Attractor	a	b	c	d	(x₀,y₀,z₀,w₀)
Fig. 1(a)?Fig. 1(c)	16	9	5	8	(1,0,0,1)
Fig. 1(d)?Fig. 1(f)	16	9	30	8	(1,0,0,1)
Fig. 1(g)?Fig. 1(i)	16	9	5	8	(1,0,0,40)

Image	Information entropy
Image	R	G	B
Girl	6.4200	6.4457	6.3807
Cipher of Girl	7.9974	7.9975	7.9973
Baboon	7.7067	7.4744	7.7522
Cipher of Baboon	7.9994	7.9994	7.9992
Peppers	7.3388	7.4963	7.0583
Cipher of Peppers	7.9994	7.9994	7.9993
Lena	7.2531	7.5940	6.9684
Cipher of Lena	7.9993	7.9993	7.9994
Lena in [22]	7.9993	7.9993	7.9993
Lena in [23]	7.9994	7.9994	7.9993
Lena in [24]	7.9896	7.9885	7.9899
Lena in [25]	7.9972	7.9972	7.9975

Method	Space
Proposed method	2²⁵⁶×10¹¹²
Method in [5]	10⁶⁴
Method in [16]	2²⁶⁷
Method in [22]	2¹²⁸
Method in [23]	2¹⁴⁴×10¹²⁶

Secret key	Value
Key₁	$\{ {k_1} + 1,{k_2}, \cdots ,{k_{32}},x_0^{(1)},y_0^{(1)},z_0^{(1)},w_0^{(1)},x_0^{(2)},y_0^{(2)},z_0^{(2)},w_0^{(2)}\} $
Key₂	$\{ {k_{32}},x_0^{(1)} + {10^{ - 14}},y_0^{(1)},z_0^{(1)},w_0^{(1)},x_0^{(2)},y_0^{(2)},z_0^{(2)},w_0^{(2)}\} $
Key₃	$\{ {k_{32}},x_0^{(1)},y_0^{(1)},z_0^{(1)},w_0^{(1)},x_0^{(2)} + {10^{ - 14}},y_0^{(2)},z_0^{(2)},w_0^{(2)}\} $

Image		Correlation coefficient
Image		H	V	D	A
Baboon	R	0.8670	0.9203	0.8609	0.8600
	G	0.7651	0.8739	0.7406	0.7362
	B	0.8795	0.9084	0.8430	0.8458
Cipher of Baboon	R	?0.0009	?0.0015	?0.0019	0.0023
	G	0.0019	0.0040	?0.0001	0.0039
	B	?0.0004	0.0027	?0.0079	?0.0017
Peppers	R	0.9693	0.9625	0.9620	0.9598
	G	0.9829	0.9743	0.9685	0.9689
	B	0.9610	0.9670	0.9483	0.9452
Cipher of Peppers	R	?0.0003	?0.0028	?0.0058	0.0066
	G	?0.0025	0.0044	?0.0053	?0.0037
	B	0.0053	?0.0027	?0.0017	?0.0028
Lena	R	0.9892	0.9817	0.9707	0.9780
	G	0.9834	0.9703	0.9580	0.9621
	B	0.9600	0.9306	0.9147	0.9116
Cipher of Lena	R	?0.0005	?0.0072	?0.0049	0.0077
	G	?0.0025	?0.0055	0.0007	0.0046
	B	0.0030	?0.0019	?0.0004	0.0068
Lena in [22]	R	0.0128	?0.0031	?0.0033	?
	G	?0.0170	0.0160	?0.0093	?
	B	0.0001	?0.0190	?0.0130	?
Lena in [23]	R	0.0001	?0.0064	?0.0214	?
	G	0.0010	?0.0314	?0.0662	?
	B	0.0603	0.0005	?0.0019	?
Lena in [25]	R	0.0083	?0.0049	?0.0095	?
	G	?0.0054	0.0100	?0.0017	?
	B	?0.0010	0.0124	?0.0042	?

Image encryption based on a novel memristive chaotic system, Grain-128a algorithm and dynamic pixel masking

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图/表 23

参考文献 25

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Image	NPCR
Image	R	G	B
Baboon	99.6088	99.6077	99.6070
Peppers	99.6008	99.6152	99.6093
Girl	99.6111	99.6016	99.6022
Lena	99.6110	99.6041	99.6084
Lena in [22]	99.6000	99.6000	99.6000
Lena in [23]	99.6065	99.6147	99.6235
Lena in [24]	99.6399	99.5987	99.6307
Lena in [25]	99.6078	99.667	99.6078

Image	UACI
Image	R	G	B
Baboon	33.4644	33.4690	33.4543
Peppers	33.4560	33.4633	33.4781
Girl	33.4955	33.4847	33.4735
Lena	33.4592	33.4626	33.4548
Lena in [22]	33.2500	33.2800	33.3100
Lena in [23]	33.4108	33.4653	33.4901
Lena in [24]	33.6190	33.5406	33.5727
Lena in [25]	33.5644	33.4458	33.5055

Image	PSNR
Image	Gaussian noise (3×10^?6)	Salt&Pepper noise (0.1)	Speckle noise (5×10^?6)
Baboon	12.4589	16.1340	14.5581
Peppers	11.6110	15.2191	13.7482
Girl	10.7942	14.4801	12.9366
Lena	12.1042	15.8221	14.2614

Image	PSNR
Image	12.5% attacked	25% attacked	50% attacked
Baboon	17.9758	14.8644	11.9696
Peppers	17.1096	14.0529	11.0862
Girl	16.1824	13.1821	10.2404
Lena	17.6411	14.5278	11.5540
Image in [25]	17.1595	14.3720	11.3589