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

摘要/Abstract

摘要：

针对高级加密标准(advanced encryption standard, AES)用于图像加密安全性不高、密钥空间小等问题, 提出一种基于四维混沌系统的改进AES图像加密算法。密钥由四维混沌系统得到, 通过在Lorenz-Chen-Lu混沌中引入非线性项、反馈控制器等提升了混沌复杂度, 经过动力学特性、稳定性分析, 验证了其混沌特性。加密时, 使用混沌Cubic-S盒和动态交叉变换的方法对传统AES进行了改进。同时, 对密钥扩展函数进行了修改, 使得每一轮密钥与上两轮密钥有关, 并将混沌序列引入其中, 提升了密钥的安全性。该算法的密钥空间达2⁴⁷⁶, 密文图像信息熵为7.997 7 bits, 像素数变化率和统一平均变化强度分别为99.613%和33.473%, 像素间相关性接近于0, 加密速度为45.85 Mbits/s。仿真结果表明, 密钥具有良好的敏感性, 加密算法具有良好的安全性和鲁棒性, 能实现快速加密和有效抵抗各类攻击。

关键词: 图像加密, 混沌系统, 高级加密标准, 安全性分析

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

中图分类号:

TN911.73

唐辰, 涂喜梅, 陆晓刚, 张琦, 张小贝. 基于四维混沌系统的改进AES图像加密算法[J]. 系统工程与电子技术, 2023, 45(12): 4040-4051.

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.

图/表 22

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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