基于四维混沌系统的改进AES图像加密算法

doi:10.12305/j.issn.1001-506X.2023.12.35

Abstract

Abstract:

An improved advanced encryption standard (AES) image encryption algorithm based on four-dimensional chaotic system is proposed to solve problems of the insecurity of AES for image encryption and the insufficient key space. The key is obtained from a four-dimensional chaotic system and the complexity of the system is improved by introducing nonlinear terms and feedback controllers into the Lorenz-Chen-Lu chaotic system. The chaotic characteristics are verified by analyzing the dynamics and stability. During the process of encryption, the traditional AES is improved by using the chaotic Cubic-S box and dynamic cross transform method. At the same time, the key expansion function is modified, so that the key of each round is related to the keys of the previous two rounds. The chaotic sequence is introduced into the key expansion function to improve the security of the key. The key space of the proposed algorithm is 2⁴⁷⁶ and the ciphertext image information entropy is 7.997 7 bits. The number of pixels change rate and unified average changing intensity are 99.613% and 33.473% respectively. The correlation between pixels is close to 0 and the encryption speed is 45.85 Mbits/s. The simulation result show that based on the excellent sensitivity of the key and the good security and robustness of the encryption method, the proposed algorithm can realize fast encryption and effective resisting for various attacks.

Key words: image encryption, chaotic system, advanced encryption standard (AES), security analysis

CLC Number:

TN911.73

Chen TANG, Ximei TU, Xiaogang LU, Qi ZHANG, Xiaobei ZHANG. Improved AES image encryption algorithm based on four-dimensional chaotic system[J]. Systems Engineering and Electronics, 2023, 45(12): 4040-4051.

Figures/Tables 22

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References 32

1	Al-KHASAWNEH M A , UDDIN I , SHAH S A A , et al. An improved chaotic image encryption algorithm using hadoop-based mapreduce framework for massive remote sensed images in parallel IoT applications[J]. Cluster Computing, 2022, 25 (2): 999- 1013. doi: 10.1007/s10586-021-03466-2
2	KAUR M , KUMAR V . A comprehensive review on image encryption techniques[J]. Archives of Computational Methods in Engineering, 2020, 27 (1): 15- 43. doi: 10.1007/s11831-018-9298-8
3	SUN F Y , LU Z W . A secure image encryption based on spatial surface chaotic system and AES algorithm[J]. Multimedia Tools and Applications, 2022, 81 (3): 3959- 3979. doi: 10.1007/s11042-021-11690-6
4	ZHAO H Y , WANG S S , WANG X Y . Fast image encryption algorithm based on multi-parameter fractal matrix and MPMCML system[J]. Chaos, Solitons & Fractals, 2022, 164, 112742.
5	LUO Y Q , YU J , LAI W R , et al. A novel chaotic image encryption algorithm based on improved baker map and logistic map[J]. Multimedia Tools and Applications, 2019, 78 (15): 22023- 22043. doi: 10.1007/s11042-019-7453-3
6	YEN J C , GUO J I . Efficient hierarchical chaotic image encryption algorithm and its VLSI realization[J]. IEE Proceedings. Part K. Vision, Image and Signal Processing, 2000, 147 (2): 167- 175. doi: 10.1049/ip-vis:20000208
7	MAY R M . Simple mathematical models with very complicated dynamics[J]. Nature, 1976, 261 (5560): 459- 467. doi: 10.1038/261459a0
8	HUA Z Y , ZHOU Y C . Image encryption using 2D Logistic-adjust-ed-Sine map[J]. Information Sciences, 2016, 339, 237- 253. doi: 10.1016/j.ins.2016.01.017
9	LYU J H , CHEN G R , CHENG D Z , et al. Bridge the gap between the Lorenz system and the Chen system[J]. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2002, 12 (12): 2917- 2926.
10	LORENZ E N . Deterministic nonperiodic flow[J]. Journal of Atmospheric Sciences, 1963, 20 (2): 130- 141. doi: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
11	CHEN G R , UETA T . Yet another chaotic attractor[J]. International Journal of Bifurcation and Chaos, 1999, 9 (7): 1465- 1466. doi: 10.1142/S0218127499001024
12	LU J H , CHEN G R , ZHANG S C . The compound structure of a new chaotic attractor[J]. Chaos, Solitons and Fractals, 2002, 14 (5): 669- 672. doi: 10.1016/S0960-0779(02)00007-3
13	田嘉琪, 谢淑翠, 张建中. 基于混沌系统的彩色图像加密算法[J]. 计算机工程与设计, 2019, 40 (7): 1816- 1822.
	TIAN J Q , XIE S C , ZHANG J Z . Color image encryption algorithm based on chaotic system[J]. Computer Engineering & Design, 2019, 40 (7): 1816- 1822.
14	张雷, 陈川, 谭淇匀, 等. 结合S盒与混沌映射的图像加密算法[J]. 北京邮电大学学报, 2021, 44 (6): 40- 47.
	ZHANG L , CHEN C , TAN Q Y , et al. An image encryption algorithm combining S-Box and chaotic mapping[J]. Journal of Beijing University of Posts & Telecommunications, 2021, 44 (6): 40- 47.
15	WANG X Y , ZHANG M Z . An image encryption algorithm based on new chaos and diffusion values of a truth table[J]. Information Sciences, 2021, 579, 128- 149. doi: 10.1016/j.ins.2021.07.096
16	KUMAR C M , VIDHYA R , BRINDHA M . An efficient chaos based image encryption algorithm using enhanced thorp shuffle and chaotic convolution function[J]. Applied Intelligence, 2022, 52 (3): 2556- 2585. doi: 10.1007/s10489-021-02508-x
17	TENG L , WANG X Y , XIAN Y J . Image encryption algorithm based on a 2D-CLSS hyperchaotic map using simultaneous permutation and diffusion[J]. Information Sciences, 2022, 605, 71- 85. doi: 10.1016/j.ins.2022.05.032
18	MANSOURI A , WANG X Y . A novel one-dimensional sine powered chaotic map and its application in a new image encryption scheme[J]. Information Sciences, 2020, 520, 46- 62. doi: 10.1016/j.ins.2020.02.008
19	WANG X F , CHEN G R . Chaotification via arbitrarily small feedback controls: theory, method, and applications[J]. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2000, 10 (3): 549- 570.
20	刘思聪, 李春彪, 李泳新. 基于指数-余弦离散混沌映射的图像加密算法研究[J]. 电子与信息学报, 2021, 44 (5): 1754- 1762.
	LIU S C , LI C B , LI Y X . A novel image encryption algorithm based on exponent-cosine chaotic mapping[J]. Journal of Electronics & Information Technology, 2021, 44 (5): 1754- 1762.
21	彭再平, 王春华, 林愿, 等. 一种新型的四维多翼超混沌吸引子及其在图像加密中的研究[J]. 物理学报, 2014, 63 (24): 101- 110.
	PENG Z P , WANG C H , LIN Y , et al. A novel four-dimensional multi-wing hyper-chaotic attractor and its application in image encryption[J]. Acta Physica Sinica, 2014, 63 (24): 101- 110.
22	ZOU Y , DONNER R V , MARWAN N , et al. Complex network approaches to nonlinear time series analysis[J]. Physics Reports, 2019, 787, 1- 97.
23	BANERJEE T , BISWAS D , SARKAR B C . Design and analysis of a first order time-delayed chaotic system[J]. Nonlinear Dynamics, 2012, 70 (1): 721- 734.
24	HAFSA A , SGHAIER A , MALEK J , et al. Image encryption method based on improved ECC and modified AES algorithm[J]. Multimedia Tools and Applications, 2021, 80 (13): 19769- 19801.
25	YIN Q , WANG C H . A new chaotic image encryption scheme using breadth-first search and dynamic diffusion[J]. International Journal of Bifurcation and Chaos, 2018, 28 (4): 1850047.
26	WU X J , WANG K S , WANG X Y , et al. Color image DNA encryption using NCA map-based CML and one-time keys[J]. Signal Processing, 2018, 148, 272- 287.
27	YANG C H , CHIEN Y S . FPGA implementation and design of a hybrid Chaos-AES color image encryption algorithm[J]. Symmetry, 2020, 12 (2): 189.
28	牛莹, 张勋才. 基于填充曲线和相邻像素比特置乱的图像加密方法[J]. 电子与信息学报, 2022, 44 (3): 1137- 1146.
	NIU Y , ZHANG X C . An image encryption algorithm based on filling curve and adjacent pixel bit scrambling[J]. Journal of Electronics & Information Technology, 2022, 44 (3): 1137- 1146.
29	NOROUZI B , SEYEDZADEH S M , MIRZAKUCHAKI S , et al. A novel image encryption based on Hash function with only two-round diffusion process[J]. Multimedia Systems, 2014, 20 (1): 45- 64.
30	SAM S I , DEVARAJ P , BHUVANESWARAN R S . An intertwining chaotic maps based image encryption scheme[J]. Nonlinear Dynamics, 2012, 69 (4): 1995- 2007.
31	YE G D , PAN C , HUANG X L , et al. An efficient pixel-level chaotic image encryption algorithm[J]. Nonlinear Dynamics, 2018, 94 (1): 745- 756.
32	WU Y , NOONAN J P , AGAIAN S . NPCR and UACI randomness tests for image encryption[J]. Cyber Journals: Multidisciplinary Journals in Science Technology, 2011, 1 (2): 31- 38.

平衡点	特征值
平衡点	λ₁	λ₂	λ₃	λ₄
S₀	-27.71	19.71	-1.57	-0.30
S₁	-19.24	4.85+14.34i	4.85-14.34i	-0.32
S₂	-21.22	5.85+8.59i	5.85-8.59i	-0.35
S₃	-17.55	3.97+13.68i	3.97-13.68i	-0.26
S₄	-18.83	4.62+14.86i	4.62-14.86i	-0.28

算法	Lena	Camerman	Boat	Avg.
原图	7.428 5	7.022 2	7.158 2	7.203 0
本文算法	7.997 8	7.997 9	7.997 5	7.997 7
传统AES	7.995 8	7.992 4	7.993 7	7.994 0
文献[26]	7.989 9	7.989 7	7.989 1	7.989 5
文献[27]	7.993 2	7.992 8	7.993 1	7.993 0
文献[28]	7.997 5	7.997 1	7.997 4	7.997 3

算法	水平	垂直	对角
原图	0.971 2	0.978 2	0.954 7
本文算法	0.000 5	-0.001 0	-0.000 6
传统AES	-0.016 0	0.011 8	0.015 2
文献[26]	0.000 6	0.003 2	-0.001 7
文献[27]	-0.000 5	-0.001 0	-0.001 0
文献[28]	0.001 3	-0.002 9	-0.007 8

算法	参数	Cameraman	Lena	Boat
本文算法	NPCR	99.613	99.604	99.608
本文算法	UACI	33.459	33.460	33.473
传统AES	NPCR	99.588	99.544	99.646
传统AES	UACI	33.556	33.489	33.488
文献[26]	NPCR	99.604	99.615	99.611
文献[26]	UACI	33.566	33.455	33.499
文献[27]	NPCR	99.628	99.604	99.605
文献[27]	UACI	33.503	33.460	33.497
文献[28]	NPCR	99.626	99.675	99.578
文献[28]	UACI	33.215	33.458	33.264

算法	加密效率/(Mbit/s)
本文算法	45.85
传统AES	18.82
文献[26]	20.48
文献[27]	17.68
文献[28]	18.54

Improved AES image encryption algorithm based on four-dimensional chaotic system

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