Abstract
In this paper, two efficient cryptosystem schemes in the form of permutation–substitution based on chaotic systems are proposed. Firstly, a simple and efficient S-box method is introduced in order to use this S-box designed scheme in secure color image encryption technique. The major advantage of the proposed strategy is the dynamic aspect of keys used by chaotic map to generate strong S-boxes. Secondly, an efficient color encryption scheme based on chaotic maps and S-boxes in the form of permutation–substitution network is developed. Experimental results show the effectiveness of the proposed schemes. The suggested cryptosystems have superior performance and great potential for prominent prevalence in cryptographic applications compared to previous schemes.
Similar content being viewed by others
References
Jakimoski, G., Kocarev, L.: Chaos and cryptography: block encryption ciphers. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48(2), 163–169 (2001)
Baptista, M.S.: Cryptography with chaos. Phys. Lett. A 240(1–2), 50–54 (1998)
Schmitz, R.: Use of chaotic dynamical systems in cryptography. J. Frankl. Inst. 338(4), 429–441 (2001)
Chen, G., Mao, Y., Chui, C.K.: A symmetric image encryption scheme based on 3D chaotic standard maps. Chaos Solitons Fractals 21(3), 749–761 (2004)
Li, X., Wang, L., Yan, Y., Liu, P.: An improvement color image encryption algorithm based on DNA operations and real and complex chaotic systems. Opt. Int. J. Light Electron Opt. 127(5), 2558–2565 (2016)
Zhou, G., Zhang, D., Liu, Y., Yuan, Y., Liu, Q.: A novel image encryption algorithm based on chaos and Line map. Neurocomputing 169, 150–157 (2015)
Özkaynak, F., Yavuz, S.: Analysis and improvement of a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Nonlinear Dyn. 78(2), 1311–1320 (2014)
Diaconu, A.V.: Circular inter-intra pixels bit-level permutation and chaos-based image encryption. Inf. Sci. 355–365, 314–327 (2016)
Xu, L., Li, Z., Li, J., Hua, W.: A novel bit-level image encryption algorithm based on chaotic maps. Opt. Lasers Eng. 78, 17–25 (2016)
Hussain, I., Shah, T., Gondal, M.A.: A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm. Nonlinear Dyn. 70(3), 1791–1794 (2012)
Li, C., Zhang, L.Y., Ou, R., Wong, K.-W., Shu, S.: Breaking a novel colour image encryption algorithm based on chaos. Nonlinear Dyn. 70(4), 2383–2388 (2012)
Wang, X., Teng, L., Qin, X.: A novel colour image encryption algorithm based on chaos. Signal Process. 92(4), 1101–1108 (2012)
Liu, H., Wang, X.: Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt. Commun. 284(16–17), 3895–3903 (2011)
Khan, M., Shah, T.: A novel image encryption technique based on Hénon chaotic map and S8 symmetric group. Neural Comput. Appl. 25(7), 1717–1722 (2014)
Zhang, Y., Xiao, D.: Self-adaptive permutation and combined global diffusion or chaotic color image encryption. Int. J. Electron. Commun. 68(4), 361–368 (2014)
Liu, H., Kadir, A., Gong, P.: A fast color image encryption scheme using one-time S-Boxes based on complex chaotic system and random noise. Opt. Commun. 338, 340–347 (2015)
Zhang, W., Yu, H., Zhao, Y., Zhu, Z.: Image encryption based on three-dimensional bit matrix permutation. Signal Process. 118, 36–50 (2016)
Dawson, M., Tavares, S.: An expanded set of S-box design criteria based on information theory and its relation to differential-like attacks. In: Advances in Cryptology: Proceedings of EURO-CRYPT’91. Lecture Notes in Computer Science, pp. 352–367 (1991)
Zhang, Y., Li, C., Li, Q., Zhang, D., Shu, S.: Breaking a chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn. 69(3), 1091–1096 (2012)
Wang, Y., Xie, Q., Wu, Y., Du, B.: A software for S-box performance analysis and test. In: 2009 International Conference on Electronic Commerce and Business Intelligence (ECBI), pp. 125–128. IEEE (2009)
Wang, X.Y., Yang, L., Liu, R., Kadir, A.: A chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn. 62(3), 615–621 (2010)
Matsui, M.: Linear cryptanalysis method of DES cipher: advances in cryptology. In: Proceedings of the Eurocrypt’93, Lecture Notes in Computer Science, vol. 765, pp. 386–397 (1994)
Tang, G., Liao, X., Chen, Y.: A novel method for designing S-boxes based on chaotic maps. Chaos Solitons Fractals 23(2), 413–419 (2005)
Chen, G., Chen, Y., Liao, X.: An extended method for obtaining S-boxes based on 3-dimensional chaotic baker maps. Chaos Solitons Fractals 31(3), 571–579 (2007)
Özkaynak, F., Özer, A.B.: A method for designing strong S-boxes based on chaotic Lorenz system. Phys. Lett. A 374(36), 3733–3738 (2010)
Khan, M., Shah, T., Mahmood, H., Gondal, M.A., Hussain, I.: A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems. Nonlinear Dyn. 70(3), 2303–2311 (2012)
Hussain, I., Shah, T., Gondal, M.A., Mahmood, H.: A projective general linear group based algorithm for the construction of substitution box for block ciphers. Neural Comput. Appl. 22(6), 1085–1093 (2013)
Khan, M., Shah, T., Mahmood, H., Gondal, M.A.: An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn. 71(3), 489–492 (2013)
Abd El-Latif, A.A., Li, L., Wang, N., Han, Q., Niu, X.: A new approach to chaotic image encryption based on quantum chaotic systems, exploiting color spaces. Signal Process. 93(11), 2986–3000 (2013)
Bao, J., Yang, Q.: Period of the discrete arnold cat map and general cat map. Nonlinear Dyn. 70(2), 1365–1375 (2012)
Khan, M., Shah, T., Batool, S.I.: Construction of S-box based on chaotic Boolean functions and its application in image encryption. Neural Comput. Appl. 27(3), 677–685 (2016)
Liu, Y., Wang, J., Fan, J., Gong, L.: Image encryption algorithm based on chaotic system and dynamic S-boxes composed of DNA sequences. Multimed. Tools Appl. 75(8), 4363–4382 (2016)
Liu, G., Yang, W., Liu, W., Dai, Y.: Designing S-boxes based on 3-D four-wing autonomous chaotic system. Nonlinear Dyn. 82(4), 1867–1877 (2015)
Belazi, A., Rhouma, R., Belghith, S.: A novel approach to construct S-box based on Rossler system. In : 2015 International Conference on Wireless Communications and Mobile Computing (IWCMC), pp. 611–615. IEEE (2015)
Wang, Y., Lei, P., Wong, K.-W.: A method for constructing bijective S-Box with high nonlinearity based on chaos and optimization. Int. J. Bifurc. Chaos 25(10), 1–15 (2015)
Liu, Y., Tong, X., Ma, J.: Image encryption algorithm based on hyper-chaotic system and dynamic S-box. Multimed. Tools Appl. 75(13), 7739–7759 (2016)
Zhou, Y., Bao, L., Philip Chen, C.L.: A new 1D chaotic system for image encryption. Signal Process. 97, 172–182 (2014)
Webster, A.F., Tavares, S.: On the design of S-boxes. In: Advances in Cryptology: Proceedings of CRYPTO’85. Lecture Notes in Computer Science, pp. 523–534 (1986)
Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 4(1), 3–72 (1991)
Hua, Z., Zhou, Y., Pun, C.-M., Philip Chen, C.L.: 2D Sine Logistic modulation map for image encryption. Inf. Sci. 297, 80–94 (2015)
Wang, X., Liu, L., Zhang, Y.: A novel chaotic block image encryption algorithm based on dynamic random growth technique. Opt. Lasers Eng. 66, 10–18 (2015)
Zhang, Y.-Q., Wang, X.-Y.: A new image encryption algorithm based on non-adjacent coupled map lattices. Appl. Soft Comput. 26, 10–20 (2015)
Pareschi, F., Rovatti, R., Setti, G.: On statistical tests for randomness included in the NIST SP800-22 test suite and based on the binomial distribution. IEEE Trans. Inf. Forensics Secur. 7(2), 491–505 (2012)
Norouzi, B., Mirzakuchaki, S., Seyedzadeh, S.M., Mosavi, M.R.: A simple, sensitive and secure image encryption algorithm based on hyper-chaotic system with only one round diffusion. Multimed. Tools Appl. 71(3), 1469–1497 (2014)
Zhang, Y., Xiao, D., Wen, W., Li, M.: Breaking an image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Nonlinear Dyn. 76(3), 1645–1650 (2014)
SaberiKamarposhti, M., Mohammad, D., Rahim, M., Yaghobi, M.: Using 3-cell chaotic map for image encryption based on biological operations. Nonlinear Dyn. 75(3), 407–416 (2014)
Zhang, Y., Li, Y., Wen, W., Wu, Y., Che, J-x: Deciphering an image cipher based on 3-cell chaotic map and biological operations. Nonlinear Dyn. 82(4), 1831–1837 (2015)
Liu, Y., Zhang, L.Y., Wang, J., Zhang, Y., Wong, K.-W.: Chosen-plaintext attack of an image encryption scheme based on modified permutation-diffusion structure. Nonlinear Dyn. 84(4), 2241–2250 (2016)
Zhu, H., Zhao, C., Zhang, X., Yang, L.: An image encryption scheme using generalized Arnold map and affine cipher. Opt. Int. J. Light Electron Opt. 125(22), 6672–6677 (2014)
Wang, Y., Liao, X., Xiang, T., Wong, K.-W., Yang, D.: Cryptanalysis and improvement on a block cryptosystem based on iteration a chaotic map. Phys. Lett. A 363(4), 277–281 (2007)
Wei, J., Liao, X., Wong, K.-W., Zhou, T.: Cryptanalysis of a cryptosystem using multiple one-dimensional chaotic maps. Commun. Nonlinear Sci. Numer. Simul. 12(5), 814–822 (2007)
Wang, K., Pei, W., Zou, L., Song, A., He, Z.: On the security of 3D cat map based symmetric image encryption scheme. Phys. Lett. A 343(6), 432–439 (2005)
Zhang, Y., Xiao, D.: Cryptanalysis of S-box-only chaotic image ciphers against chosen plaintext attack. Nonlinear Dyn. 72(4), 751–756 (2013)
Acknowledgments
The authors would like to thank Mrs. Najet Yahia for her help in the proofreading of this work. This work is supported by Ministry of Higher Education and Scientific Research (Egypt-Tunisia Cooperation Program: 4-13 A1).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Belazi, A., Khan, M., El-Latif, A.A.A. et al. Efficient cryptosystem approaches: S-boxes and permutation–substitution-based encryption. Nonlinear Dyn 87, 337–361 (2017). https://doi.org/10.1007/s11071-016-3046-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-016-3046-0