DNA编码、块元胞自动机与忆阻超混沌协同的医学图像加密算法

罗敏; 王世涛; 李子涵; 邱达; 刘嵩

doi:10.11999/JEIT260558

DNA编码、块元胞自动机与忆阻超混沌协同的医学图像加密算法

doi: 10.11999/JEIT260558 cstr: 32379.14.JEIT260558

湖北民族大学智能科学与工程学院恩施 445000

基金项目: 湖北省自然科学联合基金(2026AFC0242)，中国高校产学研创新基金(2024IT155)

详细信息

作者简介:
罗敏：女，副教授，研究方向为忆阻神经网络，图像加密，光电信号处理

王世涛：男，研究方向为忆阻器，图像加密，物联网

李子涵：男，硕士生，研究方向为忆阻神经网络

邱达：男，工程师，研究方向为智能检测与控制，光纤光栅传感，滑模切换系统，忆阻混沌系统

刘嵩：男，教授，研究方向为忆阻神经网络，信息安全，智能控制

通讯作者:
刘嵩　liusong@hbmzu.edu.cn

中图分类号: TN918.91; TP309.7
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出版历程
- 收稿日期: 2026-05-06
- 修回日期: 2026-08-26
- 录用日期: 2026-08-26
- 网络出版日期: 2026-10-20

A Collaborative Medical Image Encryption Scheme of DNA Coding, Block Cellular Automata, and Memristive Hyperchaos

College of Intelligent Systems Science and Engineering, Hubei Minzu University, Enshi 445000, China

Funds: Hubei Natural Science Joint Fund (2026AFC0242), The Fund of China University Research Innovation (No.2024IT155).

摘要

摘要: 针对医学图像在传输与存储过程中的安全防护需求，设计了一种DNA编码、块元胞自动机与忆阻超混沌协同的加密算法。该算法构建了“置乱-扩散-置乱-扩散”的安全架构：首先，利用五维忆阻超混沌系统及三组独立密钥产生序列；其次，采用全局置乱联合分块猫映射完成首次置乱；再次，通过DNA编码运算协同块元胞自动机实现首次扩散；最后，通过分块仿射变换与有限域扩散分别完成二次置乱及二次扩散。与采用全局元胞自动机演化的算法不同，该算法的分块机制使局部数据损坏仅局限于对应子块，显著提升抗噪声和裁剪能力；同时，基于五维忆超混沌系统与三组独立密钥的结构设计，有效扩大了密钥空间。仿真实验进一步证实了该算法的性能：其密钥空间大，密钥敏感性与抗差分攻击能力较强；面对噪声干扰与数据裁剪时，该算法亦表现出良好的鲁棒性与容错能力。因而该算法可为医学影像数据的机密性提供可靠保护。
- 忆阻超混沌系统 /
- 块元胞自动机 /
- DNA运算 /
- 医学图像加密
Abstract: Objective To address the privacy leakage risks of medical images during transmission and storage, and to overcome the shortcomings of existing encryption methods (such as insufficient cropping resistance of cellular automata and limited key space of low-dimensional chaotic systems), this study constructs a medical image encryption scheme based on a five-dimensional hyperchaotic system. The proposed scheme adopts a "scrambling-diffusion-scrambling-diffusion" encryption framework and performs block processing on cellular automata to enhance the security and robustness of the encryption algorithm, thereby providing technical support for data protection in smart healthcare scenarios. Methods First, a magnetron memristor is introduced into the classical Chen chaotic system to construct a five-dimensional dual-memristive hidden hyperchaotic system, and its dynamical behavior is verified through Lyapunov exponent spectra, bifurcation diagrams, and phase space trajectory analysis. Second, based on this system, a "scrambling-diffusion-scrambling-diffusion" encryption framework is designed: the SHA-256 hash algorithm combined with preset key parameters is used to generate the initial values of the chaotic system; global scrambling and block cat mapping are employed to achieve the first round of pixel position scrambling; DNA encoding, operation, and decoding, together with a block cellular automata diffusion mechanism, are used to perform the first round of pixel value transformation; then, block affine transformation is applied for the second round of pixel position scrambling, and diffusion based on the finite field GF(257) is used for the second round of pixel value transformation. Finally, the security performance of the algorithm is evaluated through multiple metrics, including information entropy, chi-square test, correlation analysis, key sensitivity analysis, differential attack resistance testing, as well as cropping and noise attack tests. Results and Discussions Analysis shows that the proposed five-dimensional dual-memristive system exhibits two positive Lyapunov exponents, demonstrating typical hyperchaotic behavior. The encryption algorithm designed based on this system achieves a key space of 2¹⁴⁹⁵ and is highly sensitive to tiny key perturbations (NPCR of 99.612% and UACI of 33.475% under a 10^–15 perturbation), enabling it to effectively resist brute-force. Meanwhile, the average information entropy (7.99933), average chi-square value (246.2866), and adjacent pixel correlation coefficients (close to 0) of the ciphertext images indicate that the statistical features have been concealed, allowing resistance against statistical attacks. Furthermore, the algorithm possesses outstanding differential attack resistance (average NPCR: 99.6096%, average UACI: 33.479%) along with good robustness against cropping and noise. Conclusions Based on a five-dimensional hyperchaotic system, we construct a medical image encryption scheme that integrates DNA coding and block cellular automata under a dual scrambling-diffusion architecture, and verify its security performance against statistical attacks, differential attacks, cropping, and noise. This study provides a reference for the application of high-dimensional hyperchaos in medical image encryption, and provides practical cases for enhancing the resistance of cellular automata against cropping and noise attacks.
- Memristive hyperchaotic system /
- Block cellular automata /
- DNA computing /
- Medical image encryption

HTML全文

图 1 系统(1)的相图

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图 2 随系统参数$ {k}_{1} $变化的动力学行为

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图 3 随系统初值w(0)变化的动力学行为

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图 4 吸引子生长

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图 5 敏感性分析：(a)-(c) 初值敏感性；(d)-(f) 参数敏感性

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图 6 加、解密流程图

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图 7 DNA操作

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图 8 2t×4t的二进制矩阵形成

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图 9 填充和正向更新

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图 10 反向更新

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图 11 加解密测试

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图 12 直方图测试

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图 13 密钥敏感性测试

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图 14 相关性测试

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图 15 抗裁剪和抗噪声测试

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表 1 卡方值

图像	R通道	G通道	B通道	平均值	标准/$ {\chi }^{2}=0.05 $
Lena	268.0547	233.5293	246.1094	249.2311	√
Lung	219.4941	237.0625	269.3672	241.9746	√
Kidney	261.1504	241.6172	247.8633	250.2103	√
Brain	250.1973	261.5781	252.8652	254.8802	√
Peppers	260.7891	226.4180	218.1934	235.1335	√

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表 2 信息熵

通道	Lena	Lung	Kidney	Brain	Peppers
R通道	7.9993	7.9994	7.9993	7.9993	7.9993
G通道	7.9994	7.9993	7.9993	7.9993	7.9994
B通道	7.9993	7.9993	7.9993	7.9993	7.9994

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表 3 抗差分攻击测试

图片	NPCR(%)	UACI(%)
Lena	99.603	33.474
Lung	99.611	33.500
Kidney	99.618	33.490
Brain	99.609	33.481
Peppers	99.607	33.468

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表 4 密钥敏感性测试

扰动	10^-15	10^-14	10^–9	10^–6	10^–3	0.1	[4]:10^–15	[24]:10^–14
NPCR(%)	99.612	99.605	99.608	99.615	99.617	99.623	99.606	99.6067
UACI(%)	33.475	33.416	33.484	33.487	33.417	33.500	33.466	NA

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表 5 平均相关性系数

图像集	水平方向	垂直方向	对角线方向
医学	0.0049	0.0027	0.0040
通用	0.0048	0.0052	0.0024

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表 6 抗噪声和裁剪测试

算法	抗噪声测试(PSNR)				抗裁剪测试(PSNR)
算法	0.0001%	0.0003%	0.0005%	0.0007%	8×8	16×16	32×32
本文(Kidney)	51.1183	49.8473	43.8562	42.2341	40.5762	36.8018	32.0749
本文(Lena)	53.1029	52.9894	48.3084	45.4511	39.7814	36.0242	31.2345
全局元胞自动机(Lena)^[25]	35.9325	34.1874	33.7120	28.6679	18.2841	14.0574	11.7849

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表 7 消融研究

实验	相关性系数			卡方值	信息熵	抗差分攻击
实验	水平方向	垂直方向	对角方向	卡方值	信息熵	NPCR	UACI
情形1：去除算法中的分块仿射变换	0.0059	0.0071	0.0053	256.4290	7.99927	99.6076	33.4828
情形2：保留算法中的分块仿射变换	0.0049	0.0037	0.0034	246.2859	7.99932	99.6096	33.4826

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表 9 测试数据平均值对比

方法	卡方值	相关性系数			信息熵	抗差分攻击		密钥空间	时间复杂度
方法	卡方值	水平方向	垂直方向	对角方向	信息熵	NPCR	UACI	密钥空间	时间复杂度
本文	246.2859	0.0049	0.0037	0.0034	7.99932	99.6096	33.4826	$ {2}^{1495} $	>O(15×M×N)
比特替换-DNA编码算法^[26]	259.5318	0.0053	0.0093	0.0119	7.99930	99.6125	33.6460	$ {2}^{747} $	O(7×M×N)
二维SCML-格密码算法^[27]	256.9033	0.0108	0.0071	0.0085	7.99930	99.6065	33.4722	$ {2}^{478} $	NA
超混沌映射-DNA立方体算法^[28]	249.3060	0.0030	0.0053	0.0052	7.9988	99.6074	33.4463	$ {2}^{256} $	NA

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表 8 NIST测试

测试项目	P-value	通过比例	通过率 (%)	结果
频率测试	0.904708	198/200	99.00%	通过
块内频率测试	0.021262	199/200	99.50%	通过
游程测试	0.296834	197/200	99.50%	通过
最长游程测试	0.289667	199/200	99.50%	通过
二元矩阵秩测试	0.554420	198/200	99.00%	通过
离散傅里叶变换测试	0.719747	194/200	97.00%	通过
非重叠模板匹配测试(最小)	0.978072	194/200	100.00%	通过
重叠模板匹配测试	0.924076	197/200	98.50%	通过
通用统计测试	0.319084	198/200	99.00%	通过
近似熵测试	0.137282	197/200	98.50%	通过
随机游走测试(最小)	0.059665	117/118	99.25%	通过
随机游走变体测试(最小)	0.462821	114/118	96.60%	通过
序列测试	0.437274	197/200	99.50%	通过
线性复杂度测试	0.093720	196/200	98.00%	通过
累积和测试(前向)	0.350485	198/200	99.00%	通过
累积和测试(后向)	0.296834	199/200	99.50%	通过

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