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SPRING: a novel parallel chaos-based image encryption scheme

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Abstract

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.

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References

  1. Furht, B., Kirovski, D.: Chaos-based encryption for digital images and videos. Multimedia security handbook (2004)

  2. Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurc. Chaos 8, 1259–84 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Pareek, N., Patidar, V., Sud, K.: Discrete chaotic cryptography using external key. Phys. Lett. A 309, 75–82 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  6. Wong, K., Kwok, B., Law, W.: A fast image encryption scheme based on chaotic standard map. Phys. Lett. A 372, 2645–2652 (2008)

    Article  MATH  Google Scholar 

  7. Huang, C., Nien, H.: Multi chaotic systems based pixel shuffle for image encryption. Optik Commun. 282, 2123–2327 (2009)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  16. Zhu, C.: A novel image encryption scheme based on improved hyperchaotic sequences. Opt. Commun. 285, 29–37 (2012)

    Article  Google Scholar 

  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). https://doi.org/10.1371/journal.pone.0119660

  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). https://doi.org/10.1371/journal.pone.0115773

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. Li, Y., Ge, G., Xia, Y.: Chaotic hash function based on the dynamic S-Box with variable parameters. Nonlinear Dyn. 84, 2387–2402 (2016)

    Article  MATH  Google Scholar 

  23. Wang, X., Liu, L.: Cryptanalysis of a parallel sub-image encryption method with high-dimensional chaos. Nonlinear Dyn. 73, 795–800 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yuen, C., Wong, K.: Cryptanalysis on secure fractal image coding based on fractal parameter encryption. Fractals 20, 41–51 (2012)

    Article  MathSciNet  Google Scholar 

  26. Li, Q., Lo, K.: Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process. 4, 949–954 (2011)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  36. Choi, J., Seok, S., Seo, H., Kim, H.: A fast ARX model-based image encryption scheme. Multimed. Tools Appl. 75, 14685–14706 (2016)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  41. Dworkin, M.: Recommendation for Block Cipher Mode of Operations. NIST (2001)

  42. Wadi, S.M., Zainal, N.: High definition image encryption algorithm based on AES modification. Wirel. Pers. Commun. 79, 811–829 (2014)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  44. May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  46. Eckmann, J.P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57, 617–657 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  48. Sam, I.S., Devaraj, P., Bhuvaneswaran, R.S.: An intertwining chaotic maps based image encryption scheme. Nonlinear Dyn. 79, 2449–2456 (2015)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  50. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos 16(08), 2129–2151 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  51. Öztürk, I., Kiliç, R.: Cycle lengths and correlation properties of finite precision chaotic maps. Int. J. Bifurc. Chaos 24(09), 1450107 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  52. Li, S., Mou, X., Cai, Y.: Improving security of a chaotic encryption approach. Phys. Lett. A 290, 127133 (2001)

    Article  MathSciNet  Google Scholar 

  53. IEEE Computer Society: IEEE Standard for Floating-Point Arithmetic. IEEE Std 754TM-2008, pp. 1–70 (2008)

  54. Dworkin, M.: NIST: Statistical test suite (sts 2.1). NIST (2010)

  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)

    Article  Google Scholar 

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Acknowledgements

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.

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Correspondence to Wai-Kong Lee.

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Lee, WK., Phan, R.CW., Yap, WS. et al. SPRING: a novel parallel chaos-based image encryption scheme. Nonlinear Dyn 92, 575–593 (2018). https://doi.org/10.1007/s11071-018-4076-6

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