Advertisement

Multimedia Tools and Applications

, Volume 78, Issue 24, pp 35419–35453 | Cite as

Medical image encryption algorithm based on Latin square and memristive chaotic system

  • Xiuli Chai
  • Jitong Zhang
  • Zhihua GanEmail author
  • Yushu Zhang
Article
  • 78 Downloads

Abstract

Medical image encryption may help protect medical privacy. In this paper, we propose a new medical image encryption scheme combined Latin square and chaotic system. The architecture of permutation and diffusion is adopted. Using Latin square and the plain image information, permutation based on plain image and Latin square (PPILS) is presented to shuffle the pixels of the plain image to different rows and columns, effectively weaken the strong correlations between adjacent pixels, and different images have different permutation effect. To improve the encryption effect, bi-directional adaptive diffusion is proposed to spread little change of plain images to the entire pixels of cipher images. Chaotic sequences employed in permutation and diffusion are generated from the four-dimensional memristive chaotic system, its initial values are computed by SHA 256 hash value of the plain image, and thus the proposed algorithm may withstand known-plaintext and chosen-plaintext attacks. Simulation results and performance analyses show that our image encryption scheme has good security and robustness, and it may be applied for medical image encryption applications.

Keywords

Image encryption Medical image Latin square Chaotic system 

Notes

Acknowledgments

All the authors are deeply grateful to the editors for smooth and fast handling of the manuscript. The authors would also like to thank the anonymous referees for their valuable suggestions to improve the quality of this paper. The authors also thank Dr. Daojun Han for his hard work in the revised manuscript. This work is supported by the National Natural Science Foundation of China (Grant No. 41571417, U1604145, 61802111, 61872125, 61871175), Science and Technology Foundation of Henan Province of China (Grant No. 182102210027, 182102410051), China Postdoctoral Science Foundation (Grant No. 2018 T110723, 2016 M602235), Key Scientific Research Projects for Colleges and Universities of Henan Province (Grant No. 19A413001), the Research Foundation of Henan University (Grant No. xxjc20140006), and Engineering Research Center of Mobile Communications, Ministry of Education (Grant No. cqupt-mct-201901).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Abdelkader M, Mohamed B, Hocine S (2015) New secure partial encryption method for medical images using graph coloring problem. Nonlinear Dyn 82:1475–1482MathSciNetzbMATHGoogle Scholar
  2. 2.
    Adb El-Latif Ahmed A, Bassem A-E-A, Muhammad T (2018) Robust encryption of quantum medical images. IEEE Access 6:1073–1081Google Scholar
  3. 3.
    Ahmad M, Ahmad F (2015) Cryptanalysis of image encryption based on permutation-substitution using chaotic map and Latin square image cipher. In: Proceeding of the 3rd international conference on Frontiers on intelligent computing: theory and applications (FICTA) 2014, 327: 481–488Google Scholar
  4. 4.
    Ahmad J, Hwang SO (2016) A secure image encryption scheme based on chaotic maps and affine transformation. Multimed Tools Appl 75(21):1–26Google Scholar
  5. 5.
    Ahmed F, Anees A (2014) A Noisy Channel Tolerant Image Encryption Scheme. Wirel Pers Commun 77(4):2771–2791Google Scholar
  6. 6.
    Alvarez G, Li SJ (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurcat Chaos 16:2129–2151MathSciNetzbMATHGoogle Scholar
  7. 7.
    Anees A, Ahmed F (2014) Chaotic substitution for highly auto correlated data in encryption algorithm. Commun Nonlinear Sci 19(9):3106–3118MathSciNetGoogle Scholar
  8. 8.
    Cao WJ, Zhou YC, Philip Chen CL, Xia LM (2017) Medical image encryption using edge maps. Signal Process 132:96–109Google Scholar
  9. 9.
    Chai XL, Chen YR, Lucie B (2017) A novel chaos-based image encryption algorithm using DNA sequence operations. Opt Lasers Eng 88:197–213Google Scholar
  10. 10.
    Chai XL, Fu XL, Gan ZH, Lu Y, Chen YR (2019) A color image cryptosystem based on dynamic DNA encryption and chaos. Signal Process 155:44–62Google Scholar
  11. 11.
    Chai XL, Gan ZH, Chen YR, Zhang YS (2017) A visually secure image encryption scheme based on compressive sensing. Signal Process 134:35–51Google Scholar
  12. 12.
    Chai XL, Gan ZH, Yuan K, Chen YR, Liu XX (2019) A novel image encryption scheme based on DNA sequence operations and chaotic systems. Neural Comput & Applic 31:219–237Google Scholar
  13. 13.
    Chai XL, Gan ZH, Yuan K, Yang L, Chen YR (2017) An image encryption scheme based on three-dimensional Brownian motion and chaotic system. Chin Phys B 26(2):99–113Google Scholar
  14. 14.
    Chen JX, Chen L, Yu ZL, Zhu ZL (2019) Medical image cipher using hierarchical diffusion and non-sequential encryption. Nonlinear Dyn 96:301–322Google Scholar
  15. 15.
    Chen X, Hu CJ (2017) Adaptive medical image encryption algorithm based on multiple chaotic mapping. Saudi J Biol Sci 24(8):1821–1827Google Scholar
  16. 16.
    Chen L, Wang SH (2015) Differential cryptanalysis of a medical image cryptosystem with multiple rounds. Comput Biol Med 65:69–75Google Scholar
  17. 17.
    Chen JX, Zhu ZL, Fu C, Zhang LB, Zhang YS (2015) An efficient image encryption scheme using lookup table-based confusion and diffusion. Nonlinear Dyn 81:1151–1166Google Scholar
  18. 18.
    Chua LO, Kang SM (1976) Memristive devices and systems. Proc. IEEE 375:209–223Google Scholar
  19. 19.
    Dai Y, Wang HZ, Wang YY (2016) Chaotic medical image encryption algorithm based on bit-plane decomposition. Int J Pattern Recogn 30:1657001Google Scholar
  20. 20.
    Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurcat Chaos 8:1259–1284MathSciNetzbMATHGoogle Scholar
  21. 21.
    Gan ZH, Chai XL, Zhang MH, Lu Y (2018) A double color image encryption scheme based on three-dimensional Brownian motion. Multimed Tools Appl 77:27919–27953Google Scholar
  22. 22.
    Hu GQ, Xiao D, Wang Y, Li XY (2017) Cryptanalysis of a chaotic image cipher using Latin square-based confusion and diffusion. Nonlinear Dyn 88:1305–1316zbMATHGoogle Scholar
  23. 23.
    Hu GQ, Xiao D, Wang Y, Xiang T (2017) An image coding scheme using parallel compressive sensing for simultaneous compression-encryption applications. J Vis Commun Image R 44:116–127Google Scholar
  24. 24.
    Hua ZY, Jin F, Xu BX, Huang HJ (2018) 2D logistic-sine-coupling map for image encryption. Signal Process 149:148–161Google Scholar
  25. 25.
    Hua ZY, Yi S, Zhou YC (2018) Medical image encryption using high-speed scrambling and pixel adaptive diffusion. Signal Process 144:134–144Google Scholar
  26. 26.
    Huang XL, Ye GD (2014) An efficient self-adaptive model for chaotic image encryption algorithm. Commun Nonlinear Sci 19:4094–4104Google Scholar
  27. 27.
    Huang XL, Ye GD (2014) An image encryption algorithm based on hyper-chaos and DNA sequence. Multimed Tools Appl 72:57–70Google Scholar
  28. 28.
    Jin X, Yin S, Liu NN, Li XD, Zhao G, Ge SM (2018) Color Image Encryption in Non-RGB Color Spaces. Multimed Tools Appl 77:15851–15873Google Scholar
  29. 29.
    Laiphrakpam DS, Khumanthem MS (2017) Medical image encryption based on improved EIGamal encryption technique. Optik 147:88–102Google Scholar
  30. 30.
    Li CQ, Lin DD, Feng BB, Lü JH (2018) Cryptanalysis of a chaotic image encryption algorithm based on information entropy. IEEE Access.  https://doi.org/10.1109/ACCESS.2018.2883690 Google Scholar
  31. 31.
    Li CQ, Lin DD, Lu JH (2017) Cryptanalyzing an image-scrambling encryption algorithm of pixel bits. IEEE Multimedia 24:64–71Google Scholar
  32. 32.
    Li CQ, Lin DD, Lu JH, Hao F (2018) Cryptanalyzing an image encryption algorithm based on autoblocking and electrocardiography. IEEE Multimedia.  https://doi.org/10.1109/MMUL.2018.2873472 Google Scholar
  33. 33.
    Li C, Pehlivan I, Sprott JC, Agkul A (2015) A novel four-wing strange attractor in bistability. IEICE Electron Express 12:2011116–20141116Google Scholar
  34. 34.
    Liu YS, Fan H, Xie EY, Cheng G, Li CQ (2015) Deciphering an image cipher based on mixed transformed logistic maps. Int J Bifurcat Chaos 25(13):1550188MathSciNetzbMATHGoogle Scholar
  35. 35.
    Liu HJ, Kadir A (2015) Asymmetric color image encryption scheme using 2D discrete-time map. Signal Process 113:104–112Google Scholar
  36. 36.
    Liu H, Kadir A, Gong P (2015) A fast color image encryption scheme using one-time S-Boxes based on complex chaotic system and random noise. Opt Commun 338:340–347Google Scholar
  37. 37.
    Liu G, Kadir A, Liu H (2016) Color pathological image encryption scheme with S-boxes generated by complex chaotic system and environmental noise. Neural Comput & Applic 27:687–697Google Scholar
  38. 38.
    Liu JZ, Ma YD, Li SL, Lian J, Zhang XG (2018) A new simple chaotic system and its application in medical image encryption. Multimed Tools Appl 77:22787–22808Google Scholar
  39. 39.
    Liu W, Sun K, Zhu C (2016) A fast image encryption algorithm based on chaotic map. Opt Lasers Eng 84:26–36Google Scholar
  40. 40.
    Liu JY, Yang DD, Zhou HB (2018) A digital image encryption algorithm based on bit-planes and an improved logistic map. Multimed Tools Appl 77(8):10217–10233Google Scholar
  41. 41.
    Liu DD, Zhang W, Yu H, Zhu ZL (2018) An image encryption scheme using self-adaptive selective permutation and inter-intra-block feedback diffusion. Signal Process 151:130–143Google Scholar
  42. 42.
    Luo YL, Zhou RL, Liu JX, Cao Y, Ding XM (2018) A parallel image encryption algorithm based on the piecewise linear chaotic map and hyper-chaotic map. Nonlinear Dyn 93:1165–1181Google Scholar
  43. 43.
    Machkour M, Saaidi A, Benmaati M (2015) A novel image encryption algorithm based on the two-dimensional logistic map and the Latin square image cipher. 3D Res 6:1–18Google Scholar
  44. 44.
    Mariusz D, Michal P, Roman R (2015) A new quaternion-based encryption method for DICOM images. IEEE T Image Process 24:4614–4622MathSciNetzbMATHGoogle Scholar
  45. 45.
    Mariusz D, Roman R (2019) Secure quaternion feistel cipher for DICOM images. IEEE T Image Process 28:371–380MathSciNetzbMATHGoogle Scholar
  46. 46.
    Natiq H, Saidi MRM, Kilicman A (2018) A new hyper chaotic map and its application for image encryption. Eur Phys J Plus 133(1):6Google Scholar
  47. 47.
    Nematzadeh H, Enayatifar R, Motameni H, Guimaraes FG, Coelho VN (2018) Medical image encryption using a hybrid model of modified genetic algorithm and coupled map lattices. Opt Lasers Eng 110:24–32Google Scholar
  48. 48.
    Norcen R, Podesser A, Pommer A, Schmidt HP, Uhl A (2003) Confidential storage and transmission of medical image data. Comput Biol Med 33:277–292Google Scholar
  49. 49.
    Pal SK, Kapoor S, Arora A, Chaudhary R, Khurana J (2010) Design of strong cryptographic schemes based on Latin squares. J Discret Math Sci Cryptogr 13:233–256MathSciNetzbMATHGoogle Scholar
  50. 50.
    Pal D, Geza H (2015) A novel cryptosystem based on abstract automata and latin cubes. Stud Sci Math Hung 52:221–232MathSciNetzbMATHGoogle Scholar
  51. 51.
    Panduranga HT, Naveen Kumar SK, Kiran (2014) Image encryption based on permutation-substitution using chaotic map and Latin Square Image Cipher. Eur Phys J Spec Top 223:1663–1677Google Scholar
  52. 52.
    Parah SA, Sheikh JA, Ahad F, Loan NA, Bhat GM (2017) Information hiding in medical images: a robust medical image watermarking system for E-healthcare. Multimed Tools Appl 76:10599–10633Google Scholar
  53. 53.
    Pareek NK, Patidar V (2016) Medical image protection using genetic algorithm operations. Soft Comput 20:763–772Google Scholar
  54. 54.
    Preishuber M, Huetter T, Katzenbeisser S, Uhl A (2018) Depreciating motivation and empirical security analysis of chaos-based image and video encryption. IEEE T Inf Foren Sec 13:2137–2150Google Scholar
  55. 55.
    Preishuber M, Hutter T, Katzenbeisser S, Uhl A (2018) Depreciating motivation and empirical security analysis of chaos-based image and video encryption. IEEE Transactions on Information Forensics and Security 13:2137–2150Google Scholar
  56. 56.
    Prousalis DA, Volos CK, Stouboulos IN, Kyprianidis IM (2017) Hyperchaotic memristive system with hidden attractors and its adaptive control scheme. Nonlinear Dyn 90:1681–1694MathSciNetGoogle Scholar
  57. 57.
    Wang XY, Liu LT, Zhang YQ (2015) A novel chaotic block image encryption algorithm based on dynamic random growth technique. Opt Lasers Eng 66:10–18Google Scholar
  58. 58.
    Wang XY, Wang Q (2014) A novel image encryption algorithm based on dynamic S-boxes constructed by chaos. Nonlinear Dyn 75(3):567–576Google Scholar
  59. 59.
    Wang MX, Wang XY, Zhang YQ, Gao ZG (2018) A novel chaotic encryption scheme based on image segmentation and multiple diffusion models. Opt Laser Technol 108:558–573Google Scholar
  60. 60.
    Wang XY, Xu DH (2015) A novel image encryption scheme using chaos and Langton's Ant cellular automaton. Nonlinear Dyn 79(4):2449–2456MathSciNetGoogle Scholar
  61. 61.
    Wen WY, Zhang YS, Fang YM, Fang ZJ (2016) Image salient regions encryption for generating visually meaningful ciphertext image. Neural Comput & Applic 6:1–11Google Scholar
  62. 62.
    Wolf A, Swift JB, Swinney HL, Vastano J (1985) Determining Lyapunov exponents from a time series. Physica D 16:285–317MathSciNetzbMATHGoogle Scholar
  63. 63.
    Wu XJ, Wang KS, Wang XY, Kan HB (2017) Lossless chaotic color image cryptosystem based on DNA encryption and entropy. Nonlinear Dyn 90:855–875MathSciNetzbMATHGoogle Scholar
  64. 64.
    Wu XJ, Wang KS, Wang XY, Kan HB, Kurths J (2018) Color image DNA encryption using NCA map-based CML and one-time keys. Signal Process 148:272–287Google Scholar
  65. 65.
    Wu Y, Zhou YC, George S, Sos A, Noonan Joseph P, Premkumar N (2013) Local Shannon entropy measure with statistical tests for image randomness. Inf Sci 222:323–342MathSciNetzbMATHGoogle Scholar
  66. 66.
    Wu Y, Zhou YC, Noonan JP, Agaian S (2014) Design of image cipher using latin squares. Inf Sci 264:317–339MathSciNetzbMATHGoogle Scholar
  67. 67.
    Xiuli C, Yang K, Zhihua G (2017) A new chaos-based image encryption algorithm with dynamic key selection mechanisms. Multimed Tools Appl 76:9907–9927Google Scholar
  68. 68.
    Xiuli C, Zhihua G, Yang K, Yiran C, Xianxing L (2017) An image encryption algorithm based on the memristive hyperchaotic system, cellular automata and DNA sequence operations. Signal Process: Image 52:6–19Google Scholar
  69. 69.
    Zhang LY, Liu YS, Wang C, Zhou JT, Zhang YS, Chen GR (2018) Improved known-plaintext attack to permutation-only multimedia ciphers. Inf Sci 430:228–239MathSciNetGoogle Scholar
  70. 70.
    Zhang YQ, Wang XY (2014) A symmetric image encryption algorithm based on mixed linear- nonlinear coupled map lattice. Inf Sci 273:329–351Google Scholar
  71. 71.
    Zhang YQ, Wang XY (2014) Analysis and improvement of a chaos-based symmetric image encryption scheme using a bit-level permutation. Nonlinear Dyn 77:687–698Google Scholar
  72. 72.
    Zhang YS, Xiao D, Shu YL (2013) A novel image encryption scheme based on a linear hyperbolic chaotic system of partial differential equations. Signal Process: Image 28:292–300Google Scholar
  73. 73.
    Zhang YS, Xiao D, Wen WY, Kwok-Wo W (2014) On the security of symmetric ciphers based on DNA coding. Inf Sci 289:254–261zbMATHGoogle Scholar
  74. 74.
    Zhang X, Zhao Z, Wang J (2014) Chaotic image encryption based on circular substitution box and key stream buffer. Signal Process: Image 29(8):902–913Google Scholar
  75. 75.
    Zhang LB, Zhu ZL, Yang BQ, Liu WY, Zhu HF, Zou MY (2015) Medical image encryption and compression scheme using compressive sensing and pixel swapping based permutation approach. Math Probl Eng 2015:940638Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer and Information Engineering, Henan Key Laboratory of Big Data Analysis and ProcessingHenan UniversityKaifengChina
  2. 2.School of SoftwareHenan UniversityKaifengChina
  3. 3.School of Communication and Information EngineeringChongqing University of Posts and TelecommunicationsChongqingChina
  4. 4.College of Computer Science and TechnologyNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations