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Cited by 156Chaos-based Image/Signal EncryptionComputer Science and EngineeringCryptographic Implementations and Security

Image Encryption Using Josephus Problem and Filtering Diffusion

Open access
Hua, Zhongyun, Xu, Binxuan, Jin, Fan, Huang, Hejiao·2019·IEEE Access
DOI 10.1109/access.2018.2890116
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Abstract

Image encryption is an efficient visual technology to protect private images. This paper develops an image encryption algorithm utilizing the principles of the Josephus problem and the filtering technology. The encryption algorithm follows the classical diffusion and confusion structure. The principle of Josephus problem is used to shuffle the image pixels to different positions to achieve the confusion property. Using a randomly generated filter, the filtering technology can spread slight changes of the original image to all pixels of the cipher image to obtain diffusion property. The simulation results show that the developed image encryption algorithm is able to encrypt different kinds of images into cipher images with uniform distribution. The security analysis demonstrates that it has an extremely sensitive secret key, can resist various security attacks, and has a better performance than several advanced image encryption algorithms.

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Research works printed but not linked: 43

  1. L. Halbeisen and N. Hungerbühler, ''The Josephus problem,'' J. Théorie Nuombres Bordeaux, vol. 9, no. 2, pp. 303-318, 1997.
  2. C. Li, D. Lin, J. Lü, and F. Hao, ''Cryptanalyzing an image encryption algo- rithm based on autoblocking and electrocardiography,'' IEEE Multimedia, to be published, doi: 10.1109/MMUL.2018.2873472. · DOI · Paper page
  3. C. Li, D. Lin, and J. Lü, ''Cryptanalyzing an image-scrambling encryption algorithm of pixel bits,'' IEEE Multimedia, vol. 24, no. 3, pp. 64-71, Aug. 2017.
  4. S. Yi, Y. Zhou, and Z. Hua, ''Reversible data hiding in encrypted images using adaptive block-level prediction-error expansion,'' Signal Process., Image Commun., vol. 64, pp. 78-88, May 2018.
  5. F. Y. Shih, Digital Watermarking and Steganography: Fundamentals and Techniques. Boca Raton, FL, USA: CRC Press, 2017.
  6. Z. Hua and Y. Zhou, ''Design of image cipher using block-based scram- bling and image filtering,'' Inf. Sci., vol. 396, pp. 97-113, Aug. 2017.
  7. A. A. A. El-Latif, B. Abd-El-Atty, and M. Talha, ''Robust encryption of quantum medical images,'' IEEE Access, vol. 6, pp. 1073-1081, 2018.
  8. Z. Hua, S. Yi, and Y. Zhou, ''Medical image encryption using high- speed scrambling and pixel adaptive diffusion,'' Signal Process., vol. 144, pp. 134-144, Mar. 2018.
  9. M. H. Annaby, M. A. Rushdi, and E. A. Nehary, ''Image encryption via discrete fractional Fourier-type transforms generated by random matrices,'' Signal Process., Image Commun., vol. 49, pp. 25-46, Nov. 2016.
  10. Y.-Q. Zhang and X.-Y. Wang, ''A new image encryption algorithm based on non-adjacent coupled map lattices,'' Appl. Soft. Comput., vol. 26, pp. 10-20, Jan. 2015.
  11. X. Li, Y. Wang, Q.-H. Wang, Y. Liu, and X. Zhou, ''Modified integral imaging reconstruction and encryption using an improved sr reconstruction algorithm,'' Opt. Lasers Eng., vol. 112, pp. 162-169, Sep. 2019.
  12. Z. Hua, B. Zhou, and Y. Zhou, ''Sine chaotification model for enhancing chaos and its hardware implementation,'' IEEE Trans. Ind. Electron., vol. 66, no. 2, pp. 1273-1284, Feb. 2019.
  13. X. Huang and G. Ye, ''An image encryption algorithm based on hyper- chaos and DNA sequence,'' Multimedia Tools Appl., vol. 72, no. 1, pp. 57-70, 2014.
  14. Y.-Q. Zhang and X.-Y. Wang, ''A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice,'' Inf. Sci., vol. 273, pp. 329-351, Jul. 2014.
  15. Z. Hua, F. Jin, B. Xu, and H. Huang, ''2D logistic-sine-coupling map for image encryption,'' Signal Process., vol. 149, pp. 148-161, Aug. 2018.
  16. D. Jiang, Y. Chen, X. Gu, L. Xie, and L. Chen, ''Efficient and universal quantum key distribution based on chaos and middleware,'' Int. J. Mod. Phys. B, vol. 31, no. 2, p. 1650264, 2017.
  17. N. Zhou, Y. Hu, L. Gong, and G. Li, ''Quantum image encryption scheme with iterative generalized Arnold transforms and quantum image cycle shift operations,'' Quantum Inf. Process., vol. 16, no. 6, p. 164, 2017.
  18. N. Zhou, S. Pan, S. Cheng, and Z. Zhou, ''Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing,'' Opt. Laser Technol., vol. 82, pp. 121-133, Aug. 2016.
  19. X. Chai, Z. Gan, Y. Chen, and Y. Zhang, ''A visually secure image encryp- tion scheme based on compressive sensing,'' Signal Process., vol. 134, pp. 35-51, May 2017.
  20. R. Enayatifar, H. J. Sadaei, A. H. Abdullah, M. Lee, and I. F. Isnin, ''A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata,'' Opt. Lasers Eng., vol. 71, pp. 33-41, Aug. 2015.
  21. X. Chai, Y. Chen, and L. Broyde, ''A novel chaos-based image encryption algorithm using dna sequence operations,'' Opt. Lasers Eng., vol. 88, pp. 197-213, Jan. 2017.
  22. C. Li, G. Luo, K. Qin, and C. Li, ''An image encryption scheme based on chaotic tent map,'' Nonlinear Dyn., vol. 87, no. 1, pp. 127-133, 2017.
  23. W. Liu, K. Sun, and C. Zhu, ''A fast image encryption algorithm based on chaotic map,'' Opt. Lasers Eng., vol. 84, pp. 26-36, Sep. 2016.
  24. P. Ping, F. Xu, Y. Mao, and Z. Wang, ''Designing permutation-substitution image encryption networks with Henon map,'' Neurocomputing, vol. 283, pp. 53-63, Mar. 2017.
  25. Y. Zhou, L. Bao, and C. L. P. Chen, ''Image encryption using a new parametric switching chaotic system,'' Signal Process., vol. 93, no. 11, pp. 3039-3052, 2013.
  26. C. Li, S. Li, M. Asim, J. Nunez, G. Alvarez, and G. Chen, ''On the security defects of an image encryption scheme,'' Image Vis. Comput., vol. 27, no. 9, pp. 1371-1381, 2009.
  27. D. Arroyo, R. Rhouma, G. Alvarez, S. Li, and V. Fernandez, ''On the security of a new image encryption scheme based on chaotic map lattices,'' Chaos, Interdiscipl. J. Nonlinear Sci., vol. 18, no. 3, p. 033112, 2008.
  28. X. Wu, B. Zhu, Y. Hu, and Y. Ran, ''A novel color image encryption scheme using rectangular transform-enhanced chaotic tent maps,'' IEEE Access, vol. 5, pp. 6429-6436, 2017.
  29. C. Li, Y. Liu, T. Xie, and M. Z. Q. Chen, ''Breaking a novel image encryp- tion scheme based on improved hyperchaotic sequences,'' Nonlinear Dyn., vol. 73, no. 3, pp. 2083-2089, 2013.
  30. E. Y. Xie, C. Li, S. Yu, and J. Lü, ''On the cryptanalysis of Fridrich's chaotic image encryption scheme,'' Signal Process., vol. 132, pp. 150-154, Mar. 2017.
  31. C. Zhu and K. Sun, ''Cryptanalyzing and improving a novel color image encryption algorithm using RT-enhanced chaotic tent maps,'' IEEE Access, vol. 6, pp. 18759-18770, 2018.
  32. Y. Wu, Y. Zhou, J. P. Noonan, and S. Agaian, ''Design of image cipher using latin squares,'' Inf. Sci., vol. 264, pp. 317-339, Apr. 2014.
  33. R. Enayatifar, A. H. Abdullah, I. F. Isnin, A. Altameem, and M. Lee, ''Image encryption using a synchronous permutation-diffusion technique,'' Opt. Lasers Eng., vol. 90, pp. 146-154, Mar. 2017.
  34. X. Wang, Q. Wang, and Y. Zhang, ''A fast image algorithm based on rows and columns switch,'' Nonlinear Dyn, vol. 79, no. 2, pp. 1141-1149, 2015.
  35. C. Cao, K. Sun, and W. Liu, ''A novel bit-level image encryption algo- rithm based on 2D-LICM hyperchaotic map,'' Signal Process., vol. 143, pp. 122-133, Feb. 2018.
  36. L. Xu, Z. Li, J. Li, and W. Hua, ''A novel bit-level image encryption algorithm based on chaotic maps,'' Opt. Lasers Eng., vol. 78, pp. 17-25, Mar. 2016.
  37. Y. Guo, L.-P. Shao, and L. Yang, ''Bit-level image encryption algorithm based on Josephus and henon chaotic map,'' Appl. Res. Comput., vol. 32, no. 4, pp. 1131-1137, 2015.
  38. X. Wang, X. Zhu, and Y. Zhang, ''An image encryption algorithm based on Josephus traversing and mixed chaotic map,'' IEEE Access, vol. 6, pp. 23733-23746, 2018.
  39. G. Yang, H. Jin, and N. Bai, ''Image encryption using the chaotic Josephus matrix,'' Math. Problems Eng., vol. 2014, Mar. 2014, Art. no. 632060.
  40. J. Wu and L. Tu, ''An image encryption algorithm based on Josephus traversing and position disordering,'' in Proc. Int. Conf. Cybern. Inform. New York, NY, USA: Springer, 2014, pp. 1941-1946.
  41. G. Alvarez and S. Li, ''Some basic cryptographic requirements for chaos-based cryptosystems,'' Int. J. Bifurcation Chaos, vol. 16, no. 8, pp. 2129-2151, 2006.
  42. Y. Wu, J. P. Noonan, and S. Agaian, ''NPCR and UACI randomness tests for image encryption,'' Cyber J., Multidisciplinary J. Sci. Technol., J. Sel. Areas Telecommun., vol. 1, no. 2, pp. 31-38, 2011.
  43. I. F. Elashry, O. S. Faragallah, A. M. Abbas, S. El-Rabaie, and F. E. Abd El-Samie, ''A new method for encrypting images with few details using Rijndael and RC6 block ciphers in the electronic code book mode,'' Inf. Secur. J., Global Perspective, vol. 21, no. 4, pp. 193-205, 2012.

Cited by

Sorted by citations

Authors
Hua, Z., Xu, B., Jin, F., & Huang, H.
Affiliations
Harbin Institute of Technology (CN)
ORCID
Venue
IEEE Access
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2019
Volume
7
Pages
8660-8674
ISSN
2169-3536 (ISSN-L)
DOI
10.1109/access.2018.2890116
OpenAlex
W2907856008
Cited by
156
References
5
Citations by year
2026: 3 · 2025: 10 · 2024: 18 · 2023: 25 · 2022: 18 · 2021: 25 · 2020: 43 · 2019: 14
FWCI
11.19
Type
journal article
Language
en
Open access
Licence
ieeexplore.ieee.org/Xplorehelp/downloads/license-information/OAPA.html (vor)
Locations
  • IEEE Access (publishedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
  • National Key Research and Development Program of China (2016YFB0800804, 2017YFB0803002)
  • National Natural Science Foundation of China (61701137)
  • Shenzhen Science and Technology Plan (JCYJ20170307150704051, JCYJ20170811160212033)
Topics
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
  • Physical Sciences › Computer Science › Artificial Intelligence › Computer Science and Engineering
  • Physical Sciences › Computer Science › Artificial Intelligence › Cryptographic Implementations and Security
Keywords
image encryption, Josephus problem, confusion and diffusion, pixel shuffling, key sensitivity, security analysis

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