基于约瑟夫遍历和超混沌Lorenz系统的医学图像加密

doi:10.1007/s12204-022-2555-x

摘要/Abstract

摘要： 本研究提供了一种基于约瑟夫遍历和超混沌Lorenz系统的医学图像加密方案。首先，利用超混沌系统生成超混沌序列，超混沌序列被用于算法的置乱阶段和扩散阶段；其次，在置乱阶段，利用约瑟夫置乱对图像进行初始置乱，然后利用猫映射对图像进行再次置乱。最后，利用生成的超混沌序列和异或操作对图像进行正向扩散和逆向扩散，以此改变图像的像素值，从而进一步隐藏图像中的有效信息。另外，明文图像的信息被用于生成算法中的密钥，这增加了抵抗明文攻击的能力。实验结果和安全性分析表明，该方案能够根据医学图像的特征有效地隐藏明文图像信息，并能够抵抗常见类型的攻击。此外，该方案在鲁棒性实验中表现良好，能够解决远程医疗中的图像信息丢失问题。这对今后的研究具有积极意义。

关键词: 医学图像，图像加密，约瑟夫遍历，超混沌Lorenz系统

Abstract: This study proposes a new medical image encryption scheme based on Josephus traversing and hyperchaotic Lorenz system. First, a chaotic sequence is generated through hyperchaotic system. This hyperchaotic sequence is used in the scrambling and diffusion stages of the algorithm. Second, in the scrambling process, the image is initially confused by Josephus scrambling, and then the image is further confused by Arnold map. Finally, generated hyperchaos sequence and exclusive OR operation is used for the image to carry on the positive and reverse diffusion to change the pixel value of the image and further hide the effective information of the image. In addition, the information of the plaintext image is used to generate keys used in the algorithm, which increases the ability of resisting plaintext attack. Experimental results and security analysis show that the scheme can effectively hide plaintext image information according to the characteristics of medical images, and is resistant to common types of attacks. In addition, this scheme performs well in the experiments of robustness, which shows that the scheme can solve the problem of image damage in telemedicine. It has a positive significance for the future research.

Key words: medical image, image encryption, Josephus traversing, hyperchaotic Lorenz system

中图分类号:

TP309.7
R319

杨娜，张淑霞，白牡丹，李珊珊. 基于约瑟夫遍历和超混沌Lorenz系统的医学图像加密[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(1): 91-108.

YANG Na (杨娜), ZHANG Shuxia (张淑霞), BAI Mudan (白牡丹), LI Shanshan^∗ (李珊珊). Medical Image Encryption Based on Josephus Traversing and Hyperchaotic Lorenz System[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(1): 91-108.

参考文献

[1] EL-SHAFAI W, KHALLAF F, EL-RABAIE E S M, et al. Robust medical image encryption based on DNAchaos cryptosystem for secure telemedicine and healthcare applications [J]. Journal of Ambient Intelligence and Humanized Computing, 2021, 12(10): 9007-9035.
[2] WAHEZI S E, KOHAN L R, SPEKTOR B, et al. Telemedicine and current clinical practice trends in the COVID-19 pandemic [J]. Best Practice & Research Clinical Anaesthesiology, 2021, 35(3): 307-319.
[3] RAJ V, JANAKIRAMAN S, AMIRTHARAJAN R. Optimal concurrency on FPGA for lightweight medical image encryption [J]. Journal of Intelligent & Fuzzy Systems, 2021, 40(6): 10385-10400.
[4] LIU S, LIU L, PANG M. Encryption method and security analysis of medical images based on stream cipher enhanced logical mapping [J]. Technology and Health Care, 2021, 29(S1): 185-193.
[5] CHAI X L, ZHI X C, GAN Z H, et al. Combining improved genetic algorithm and matrix semi-tensor product (STP) in color image encryption [J]. Signal Processing, 2021, 183: 108041.
[6] CHAI X L, FU J Y, GAN Z H, et al. An image encryption scheme based on multi-objective optimization and block compressed sensing [J]. Nonlinear Dynamics, 2022, 108(3): 2671-2704.
[7] CHAI X L, ZHANG J T, GAN Z H, et al. Medical image encryption algorithm based on Latin Square and memristive chaotic system [J]. Multimedia Tools and Applications, 2019, 78(24): 35419-35453.
[8] RAVICHANDRAN D, PRAVEENKUMAR P, BALAGURU RAYAPPAN J B, et al. Chaos based crossover and mutation for securing DICOM image [J]. Computers in Biology and Medicine, 2016, 72: 170-184.
[9] WANG M X, WANG X Y, ZHANG Y Q, et al. A novel chaotic system and its application in a color image cryptosystem [J]. Optics and Lasers in Engineering, 2019, 121: 479-494.
[10] ABUHAIBA IS I, ALSALLUT A Y, HEJAZI H H, et al. Cryptography using multiple two-dimensional chaotic maps [J]. International Journal of Computer Network and Information Security, 2012, 4(8): 1-7.
[11] ZAREBNIA M, PARVAZ R. Image encryption algorithm by fractional based chaotic system and framelet transform [J]. Chaos, Solitons & Fractals, 2021, 152: 111402.
[12] BELAZI A, TALHA M, KHARBECH S, et al. Novel medical image encryption scheme based on chaos and DNA encoding [J]. IEEE Access, 2019, 7: 36667-36681.
[13] HAO J, MOU J, XIONG L, et al. A novel color image encryption algorithm based on the fractional order laser chaotic system and the DNA mutation principle [J]. Multimedia Tools and Applications, 2022, 81(1): 559-587.
[14] KUMAR D, JOSHI A B, MISHRA V N. Optical and digital double color-image encryption algorithm using 3D chaotic map and 2D-multiple parameter fractional discrete cosine transform [J]. Results in Optics, 2020, 1: 100031.
[15] HOSNY K M, KAMAL S T, DARWISH M M. A color image encryption technique using block scrambling and chaos [J]. Multimedia Tools and Applications, 2022, 81(1): 505-525.
[16] ZHOU W J, WANG X Y, WANG M X, et al. A new combination chaotic system and its application in a new Bit-level image encryption scheme [J]. Optics and Lasers in Engineering, 2022, 149: 106782.
[17] LI S S, ZHAO L, YANG N. Medical image encryption based on 2D zigzag confusion and dynamic diffusion [J]. Security and Communication Networks, 2021, 2021: 6624809.
[18] WANG X Y, REN Q, JIANG D H. An adjustable visual image cryptosystem based on 6D hyperchaotic system and compressive sensing [J]. Nonlinear Dynamics, 2021, 104(4): 4543-4567.
[19] BENKOUIDER K, BOUDEN T, YALC? IN M, et al. A new family of 5D, 6D, 7D and 8D hyperchaotic systems from the 4D hyperchaotic Vaidyanathan system, the dynamic analysis of the 8D hyperchaotic system with six positive Lyapunov exponents and an application to secure communication design [J]. International Journal of Modelling, Identification and Control, 2020, 35(3): 241-257.
[20] YANG Q G, BAI M L. A new 5D hyperchaotic system based on modified generalized Lorenz system [J]. Nonlinear Dynamics, 2017, 88(1): 189-221.
[21] JAVAN A A K, JAFARI M, SHOEIBI A, et al. Medical images encryption based on adaptive-robust multimode synchronization of Chen hyper-chaotic systems [J]. Sensors, 2021, 21(11): 3925.
[22] RAN Q W, WANG L, MA J, et al. A quantum color image encryption scheme based on coupled hyperchaotic Lorenz system with three impulse injections [J]. Quantum Information Processing, 2018, 17(8): 1-30.
[23] NAIM M, PACHA A A, SERIEF C. A novel satellite image encryption algorithm based on hyperchaotic systems and Josephus problem [J]. Advances in Space Research, 2021, 67(7): 2077-2103.
[24] WANG X Y, SUN H H. A chaotic image encryption algorithm based on improved Joseph traversal and cyclic shift function [J]. Optics & Laser Technology, 2020, 122: 105854.
[25] SINGH J P, ROY B K. Hidden attractors in a new complex generalised Lorenz hyperchaotic system, its synchronisation using adaptive contraction theory, circuit validation and application [J]. Nonlinear Dynamics, 2018, 92(2): 373-394.
[26] SHEVCHENKO I I. Lyapunov exponents in resonance multiplets [J]. Physics Letters A, 2014, 378(1/2): 34-42.
[27] HUA Z Y, ZHOU Y C. Image encryption using 2D Logistic-adjusted-Sine map [J]. Information Sciences, 2016, 339: 237-253.
[28] KOVALNOGOV V N, FEDOROV R V, CHUKALIN A V, et al. Evolutionary derivation of runge–kutta pairs of orders 5(4) specially tuned for problems with periodic solutions [J]. Mathematics, 2021, 9(18): 2306.
[29] MANSOURI A, WANG X Y. Image encryption using shuffled Arnold map and multiple values manipulations [J]. The Visual Computer, 2021, 37(1): 189-200.
[30] YASSER I, KHALIFA F, MOHAMED M A, et al. A new image encryption scheme based on hybrid chaotic maps [J]. Complexity, 2020, 2020: 9597619.
[31] ZHOU S H, HE P Y, KASABOV N. A dynamic DNA color image encryption method based on SHA-512 [J]. Entropy, 2020, 22(10): 1091.
[32] SARAVANAN S, SIVABALAKRISHNAN M, . A framework for digital image encryption using chaotic baker map with SHA algorithm [J]. International Journal of Innovative Technology and Exploring Engineering, 2019, 2(9): 4093-4097.
[33] WANG X Y, SI R Y. A new chaotic image encryption scheme based on dynamic L-shaped scrambling and combined map diffusion [J]. Optik, 2021, 245: 167658.
[34] SANG Y P, SANG J, ALAM M S. Image encryption based on logistic chaotic systems and deep autoencoder [J]. Pattern Recognition Letters, 2022, 153: 59-66.
[35] HUANG X L, YE G D. An image encryption algorithm based on hyper-chaos and DNA sequence [J]. Multimedia Tools and Applications, 2014, 72(1): 57-70.
[36] LIU H, XIAO D, LIU Y B, et al. Securely compressive sensing using double random phase encoding [J]. Optik, 2015, 126(20): 2663-2670.
[37] DIVYA M, KAMALESH M. Recovery of watermarked image from geometrics attacks using effective histogram shape based index [J]. Indian Journal of Science and Technology, 2016, 9(44): 1-6.
[38] XU Z, JI X, WANG M, et al. Edge detection algorithm of medical image based on Canny operator [J]. Journal of Physics: Conference Series, 2021, 1955: 012080.
[39] CHAI X L, WU H Y, GAN Z H, et al. An efficient approach for encrypting double color images into a visually meaningful cipher image using 2D compressive sensing [J]. Information Sciences, 2021, 556: 305-340.
[40] BENTAHAR T. Number of pixel change rate and unified average changing intensity for sensitivity analysis of encrypted inSAR interferogram [J]. Ingenierie Des Systemes D Information, 2020, 25(5): 601-607.
[41] GUPTA M, TANEJA H, CHAND L, et al. Enhancement and analysis in MRI image denoising for different filtering techniques [J]. Journal of Statistics and Management Systems, 2018, 21(4): 561-568.
[42] GUPTA R, MEHROTRA D, TYAGI R K. Computational complexity of fractal image compression algorithm [J]. IET Image Processing, 2020, 14(17): 4425-4434.
[43] AHMED F, ANEES A, ABBAS V U, et al. A noisy channel tolerant image encryption scheme [J]. Wireless Personal Communications, 2014, 77(4): 2771-2791.
[44] MASOOD F, DRISS M, BOULILA W, et al. A lightweight chaos-based medical image encryption scheme using random shuffling and XOR operations [J]. Wireless Personal Communications, 2021. https://doi.org/10.1007/s11277-021-08584-z.
[45] CHAI X L, GAN Z H, YUAN K, et al. A novel image encryption scheme based on DNA sequence operations and chaotic systems [J]. Neural Computing and Applications, 2019, 31(1): 219-237.
[46] PRAVEENKUMAR P, AMIRTHARAJAN R, THENMOZHI K, et al. Fusion of confusion and diffusion: A novel image encryption approach [J]. Telecommunication Systems, 2017, 65(1): 65-78.
[47] KUMAR S, PANNA B, JHA R K. Medical image encryption using fractional discrete cosine transform with chaotic function [J]. Medical & Biological Engineering & Computing, 2019, 57(11): 2517-2533.
[48] GUPTA A, SINGH D, KAUR M. An efficient image encryption using non-dominated sorting genetic algorithm-III based 4-D chaotic maps [J]. Journal of Ambient Intelligence and Humanized Computing, 2020, 11(3): 1309-1324.
[49] LIU H, ZHAO B, HUANG L Q. A novel quantum image encryption algorithm based on crossover operation and mutation operation [J]. Multimedia Tools and Applications, 2019, 78(14): 20465-20483.