Nonlinear Dynamics

, Volume 92, Issue 2, pp 575–593 | Cite as

SPRING: a novel parallel chaos-based image encryption scheme

  • Wai-Kong Lee
  • Raphael C.-W. Phan
  • Wun-She Yap
  • Bok-Min Goi
Original Paper


Due to the increasing demand on secure image transmission, image encryption has emerged as an active research field in recent years. Many of the proposed image encryption schemes are designed based on chaotic maps with permutation–diffusion architecture. While most of these schemes reported good statistical properties, they are slow in execution speed due to inherent data dependency of the proposed schemes. Some of these schemes are designed based on complex chaotic systems that require significant computational resources to obtain the keystream for encryption. In this paper, we propose SPRING, a novel image encryption scheme designed based on lightweight chaotic maps and simple logical and arithmetic operations, which is also highly optimized for massively parallel architecture (e.g. GPU). The extensive experimental results show that SPRING is not only secure but also able to achieve high encryption speed in single-core CPU, multi-core CPU and many-core GPU. Encrypting a 512 \(\times \) 512 grayscale image in serial takes 0.9126 ms which is 220% faster than state-of-the-art ARX-based image encryption scheme proposed by Choi et al. SPRING can be implemented in parallel to encrypt the same image in 0.0862 ms by exploiting many-core GPU, which is 10\(\times \) faster than the serial version implemented using CPU.


Logistic map Block cipher Cryptography Chaos theory Image encryption 



This work was supported partially by Universiti Tunku Abdul Rahman Research Fund (UTARRF) under Grant Numbers IPSR/RMC/UTARRF/2016-C2/L04 and IPSR/RMC/UTARRF/2016-C1/G1. Wun-She Yap would like to acknowledge the financial support by the Malaysian MOSTI Science Fund Number 01-02-11-SF0189.


  1. 1.
    Furht, B., Kirovski, D.: Chaos-based encryption for digital images and videos. Multimedia security handbook (2004)Google Scholar
  2. 2.
    Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurc. Chaos 8, 1259–84 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Pareek, N., Patidar, V., Sud, K.: Discrete chaotic cryptography using external key. Phys. Lett. A 309, 75–82 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Mao, Y., Chen, M., Lian, S.: A novel fast image encryption scheme based on 3D chaotic baker maps. Int. J. Bifurc. Chaos 14, 3613–3624 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Mirzaei, O., Yaghoobi, M., Irani, H.: A new image encryption method: parallel sub-image encryption with hyper chaos. Nonlinear Dyn. 67, 557–66 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Wong, K., Kwok, B., Law, W.: A fast image encryption scheme based on chaotic standard map. Phys. Lett. A 372, 2645–2652 (2008)CrossRefzbMATHGoogle Scholar
  7. 7.
    Huang, C., Nien, H.: Multi chaotic systems based pixel shuffle for image encryption. Optik Commun. 282, 2123–2327 (2009)CrossRefGoogle Scholar
  8. 8.
    Zhu, Z., Zhang, W., Wong, K., Yu, H.: A chaos-based symmetric image encryption scheme using a bit-level permutation. Inf. Sci. 181, 1171–1786 (2011)CrossRefGoogle Scholar
  9. 9.
    Zhang, W., Wong, K., Yu, H., Zhu, Z.: A symmetric color image encryption algorithm using the intrinsic features of bit distributions. Commun. Nonlinear Sci. Numer. Simul. 18, 584–600 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Zhang, Y., Xiao, D.: An image encryption scheme based on rotation matrix bit-level permutation and block diffusion. Commun. Nonlinear Sci. Numer. Simul. 19, 74–82 (2014)CrossRefzbMATHGoogle Scholar
  11. 11.
    Zhang, W., Yu, H., Zhao, Y., Zhu, Z.: Image encryption based on three-dimensional bit matrix permutation. J. Signal Process. 118, 36–50 (2015)CrossRefGoogle Scholar
  12. 12.
    Zhang, L., Hu, X., Liu, Y., Wong, K., Gan, J.: A chaotic image encryption scheme owning temp-value feedback. Commun. Nonlinear Sci. Numer. Simul. 19, 3653–3659 (2014)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Fu, C., Chen, J., Zou, H., Meng, W., Zhan, Y., Yu, Y.: A chaos-based digital image encryption scheme with an improved diffusion strategy. Opt. Express 20, 2363–78 (2012)CrossRefGoogle Scholar
  14. 14.
    Chen, J., Zhu, Z., Fu, C., Yu, H.: An improved permutation diffusion type image cipher with a chaotic orbit perturbing mechanism. Opt. Express 21, 27873–90 (2013)CrossRefGoogle Scholar
  15. 15.
    Zhang, Y., Xiao, D., Shu, Y., Li, J.: A novel image encryption scheme based on a linear hyperbolic chaotic system of partial differential equations. Signal Process. Image 28, 292–300 (2013)CrossRefGoogle Scholar
  16. 16.
    Zhu, C.: A novel image encryption scheme based on improved hyperchaotic sequences. Opt. Commun. 285, 29–37 (2012)CrossRefGoogle Scholar
  17. 17.
    Wu, X., Li, Y., Kurths, J.: A new color image encryption scheme using CML and a fractional-order chaotic system. PLoS One 10(3), e0119660 (2015).
  18. 18.
    Fu, C., Zhang, G.Y., Bian, O., Lei, W.M., Ma, H.F.: A novel medical image protection scheme using a 3-dimensional chaotic system. PLoS One 9(12), e115773 (2014).
  19. 19.
    Lima, J.B., Madeiro, F., Sales, F.J.R.: Encryption of medical images based on cosine number transform. Signal Process. Image 35, 1–8 (2015)CrossRefGoogle Scholar
  20. 20.
    Zhang, Y., Xiao, D., Wen, W., Nan, H., Su, M.: Secure binary arithmetic coding based on digitalized modified logistic map and linear feedback shift register. Commun. Nonlinear Sci. Numer. Simul. 27, 22–29 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Yang, Y., Pan, Q., Sun, S., Xu, P.: Novel image encryption based on quantum walks. Sci. Rep. 5, 77–84 (2015)Google Scholar
  22. 22.
    Li, Y., Ge, G., Xia, Y.: Chaotic hash function based on the dynamic S-Box with variable parameters. Nonlinear Dyn. 84, 2387–2402 (2016)CrossRefzbMATHGoogle Scholar
  23. 23.
    Wang, X., Liu, L.: Cryptanalysis of a parallel sub-image encryption method with high-dimensional chaos. Nonlinear Dyn. 73, 795–800 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Yap, W.-S., Phan, R.C.-W., Yau, W.-C., Heng, S.-H.: Cryptanalysis of a new image alternate encryption algorithm based on chaotic map. Nonlinear Dyn. 80, 1483–1491 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Yuen, C., Wong, K.: Cryptanalysis on secure fractal image coding based on fractal parameter encryption. Fractals 20, 41–51 (2012)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Li, Q., Lo, K.: Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process. 4, 949–954 (2011)CrossRefzbMATHGoogle Scholar
  27. 27.
    Li, C., Zhang, L., Ou, R., Wong, K., Shu, S.: Breaking a novel colour image encryption algorithm based on chaos. Nonlinear Dyn. 70, 2383–2388 (2012)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Yap, W.-S., Phan, R.C.-W., Goi, B.-M., Heng, S.-H.: On the effective subkey space of some image encryption algorithms using external key. J. Vis. Commun. Image Represent. 40, 51–57 (2016)CrossRefGoogle Scholar
  29. 29.
    Yap, W.-S., Phan, R.C.-W.: Commentary on “A block chaotic image encryption scheme based on self-adaptive modelling”. Appl. Soft Comput. 52, 501–504 (2017)CrossRefGoogle Scholar
  30. 30.
    Zhang, Y., Li, Y., Wen, W., Wu, Y., Chen, J.: Deciphering an image cipher based on 3-cell chaotic map and biological operations. Nonlinear Dyn. 82, 1831–1837 (2016)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Zhou, Q., Wong, K., Liao, X., Xiang, T., Hu, Y.: Parallel image encryption algorithm based on discretized chaotic map. Chaos Solitons Fractals 38, 1081–92 (2008)CrossRefGoogle Scholar
  32. 32.
    Wang, J., Jiang, G.: A self-adaptive parallel encryption algorithm based on discrete 2D-logistic map. Int. J. Mod. Nonlinear Theory Appl. 2, 89–96 (2013)CrossRefGoogle Scholar
  33. 33.
    Vihari, P.L.V., Mishra, M.: Chaotic image encryption on GPU. In: Proceedings of the CUBE International Information Technology Conference, pp. 753–758 (2012)Google Scholar
  34. 34.
    Burak, D.: Parallelization of an encryption algorithm based on a spatiotemporal chaotic system and a chaotic neural network. Proc. Comput. Sci. 51, 2888–92 (2015)CrossRefGoogle Scholar
  35. 35.
    Yuan, H., Liu, Y., Lin, T., Hu, T., Gong, L.-H.: A new parallel image cryptosystem based on 5D hyper-chaotic system. Signal Process. Image Commun. 52, 87–96 (2017)CrossRefGoogle Scholar
  36. 36.
    Choi, J., Seok, S., Seo, H., Kim, H.: A fast ARX model-based image encryption scheme. Multimed. Tools Appl. 75, 14685–14706 (2016)CrossRefGoogle Scholar
  37. 37.
    Gao, J.Q., Liang, R.H., Wang, J.: Research on the conjugate gradient algorithm with a modified incomplete Cholesky preconditioner on GPU. J. Parallel Distrib. Comput. 74, 2088–2098 (2014)CrossRefGoogle Scholar
  38. 38.
    Kim, J.W., Kim, S.G., Nam, B.S.: Parallel multi-dimensional range query processing with R-trees on GPU. J. Parallel Distrib. Comput. 73, 1195–1207 (2013)CrossRefGoogle Scholar
  39. 39.
    Zanella, R., Zanghirati, G., Cavicchioli, R., Zanni, L., Boccacci, P., Bertero, M., Vicidomini, G.: Towards real-time image deconvolution: application to ocal and STED microscopy. Sci. Rep. 3, 2523 (2013)CrossRefGoogle Scholar
  40. 40.
    Shibuta, Y., Oguchi, K., Takaki, O., Ohno, M.: Homogeneous nucleation and microstructure evolution in million-atom molecular dynamics simulation. Sci. Rep. 5, 13534 (2015)CrossRefGoogle Scholar
  41. 41.
    Dworkin, M.: Recommendation for Block Cipher Mode of Operations. NIST (2001)Google Scholar
  42. 42.
    Wadi, S.M., Zainal, N.: High definition image encryption algorithm based on AES modification. Wirel. Pers. Commun. 79, 811–829 (2014)CrossRefGoogle Scholar
  43. 43.
    Yap, W.-S., Phan, R.C.-W., Goi, B.-M.: Cryptanalysis of a high-definition image encryption based on AES modification. Wirel. Pers. Commun. 88(3), 685–699 (2016)CrossRefGoogle Scholar
  44. 44.
    May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)CrossRefzbMATHGoogle Scholar
  45. 45.
    Jakimoski, G., Kocarev, L.: Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans. Circuits Syst. I: Fund. Theory Appl. 48, 163–169 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Eckmann, J.P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57, 617–657 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Shen, C., Yu, S., Lu, L., Chen, G.: Designing hyperchaotic systems with any desired number of positive Lyapunov exponents via a simple model. IEEE Trans. Circuits Syst. I Regul. Pap. 61, 2380–2389 (2014)CrossRefGoogle Scholar
  48. 48.
    Sam, I.S., Devaraj, P., Bhuvaneswaran, R.S.: An intertwining chaotic maps based image encryption scheme. Nonlinear Dyn. 79, 2449–2456 (2015)CrossRefGoogle Scholar
  49. 49.
    Li, S., Chen, S., Mou, X.: On the dynamical degradation of digital piecewise linear chaotic maps. Int. J. Bifurc. Chaos 15(10), 3119–3151 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos 16(08), 2129–2151 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Öztürk, I., Kiliç, R.: Cycle lengths and correlation properties of finite precision chaotic maps. Int. J. Bifurc. Chaos 24(09), 1450107 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Li, S., Mou, X., Cai, Y.: Improving security of a chaotic encryption approach. Phys. Lett. A 290, 127133 (2001)MathSciNetCrossRefGoogle Scholar
  53. 53.
    IEEE Computer Society: IEEE Standard for Floating-Point Arithmetic. IEEE Std 754TM-2008, pp. 1–70 (2008)Google Scholar
  54. 54.
    Dworkin, M.: NIST: Statistical test suite (sts 2.1). NIST (2010)Google Scholar
  55. 55.
    Yap, W.-S., Yeo, S., Henricksen, M., Heng, S.-H.: Security analysis of GCM for communication. Secur Commun. Netw. 7(5), 854–864 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Information and Communication TechnologyUniversiti Tunku Abdul RahmanKamparMalaysia
  2. 2.Faculty of EngineeringMultimedia UniversityCyberjayaMalaysia
  3. 3.Lee Kong Chian Faculty of Engineering and ScienceUniversiti Tunku Abdul RahmanSungai LongMalaysia

Personalised recommendations