Abstract
Recently, a chaos-based symmetric image encryption scheme using a bit-level permutation was proposed. In this paper, we analyze the potential flaws in Zhu’s algorithm in detail and develop a chosen-plaintext attack and chosen-ciphertext attack on Zhu’s algorithm. The proposed attack indicates that the Arnold cat map applied directly in image encryptions is not suitable for cryptography. We also propose the corresponding improved scheme. The improved scheme preserves the merits of the original one.
Similar content being viewed by others
References
Dachselt, F., Schwarz, W.: Chaos and cryptography. IEEE Trans. Circuits Syst. l 48, 1498–1509 (2001)
Fraser, B., Yu, P., Lookman, T.: Steps towards improving the security of chaotic encryption. Phys. Rev. E 66, 017202–017204 (2002)
Liu, J.L., Lou, D.C., Tso, H.K.: A copyright protection scheme for digital image using chaos and fractal compression. Int. J. Nonlin. Sci. Num. Simul. 7(2), 197–202 (2006)
Deng, S.J., Wang, F.X., Pu, Z.L., Zhang, D.G.: A robust triple digital watermarking algorithm based on image blocking. Int. J. Nonlin. Sci. Num. Simul. 10(6), 727–733 (2009)
Cruz-Hernandez, C., Lopez-Gutierrez, R.M., Aguilar-Bustos, A.Y., Posadas-Castillo, C.: Communicating encrypted information based on synchronized hyperchaotic maps. Int. J. Nonlin. Sci. Num. Simul. 11(5), 337–349 (2010)
Chen, Y., Liao, X.F., Wong, K.W.: Chosen plaintext attack on a cryptosystem with discretized skew tent map. IEEE Trans. Circuits Syst. II 53, 527–529 (2006)
Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic map. Int. J. Bifurcation Chaos 8(6), 1256–1343 (1998)
Lian, S.G., Sun, J., Wang, Z.: A block cipher based on a suitable use of the chaotic standard map. Chaos Solitons Fract. 26(1), 117–129 (2005)
Guan, Z., Huang, F., Guan, W.: Chaos-based image encryption algorithm. Phys. Lett. A 346, 153–160 (2005)
Lian, S.G.: Efficient image or video encryption based on spatiotemporal chaos system. Chaos Solitions Fract. 40, 2509–2519 (2009)
Pisarchik, A., Flores-Carmona, N., Carpio-Valadez, M.: Encryption and decryption of images with chaotic map lattices. Chaos 16, 033118–6 (2006)
Arroyo, D., Rhouma, R., Alvarez, G., Li, S.J., Fernandez, V.: On the security of a new image encryption scheme based on chaotic map lattices. Chaos 18, 033112–7 (2008)
Xiao, D., Liao, X.F., Wei, P.C.: Analysis and improvement of a chaos-based image encryption algorithm. Chaos Solitions Fract. 40, 2191–2199 (2009)
Ge, X., Liu, F.L., Lu, B., Wang, W.: Cryptanalysis of a spatiotemporal chaotic image/video cryptosystem and its improved version. Phys. Lett. A 375(5), 908–913 (2011)
Xiang, T., Wong, K.W., Liao, X.F.: Selective image encryption using a spatiotemporal chaotic system. Chaos 17, 023115–12 (2007)
Zhu, Z.L., Zhang, W., Wong, K.W., Yu, H.: A chaos-based symmetric image encryption scheme using a bit-level permutation. Info. Sci. 181, 1171–1186 (2011)
Liu, H.J., Wang, X.Y.: Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt. Commun. 284, 3895–3903 (2011)
Ercan, S., Cahit, C.: Algebraic break of image ciphers based on discretized chaotic map lattices. Info. Sci. 181, 227–233 (2011)
Chen, H.C., Guo, J.I., Huang, L.C., Yen, J.C.: Design and realization of a new signal security system for multimedia data transmission. EURASIP J. Adv. Signal Process. 13, 1291–1305 (2003)
Liu, H.J., Wang, X.Y., Abdurahman, K.: Image encryption using DNA complementary rule and chaotic maps. Appl. Soft. Comput. 12, 1457–1466 (2012)
Rhouma, R., Safya, B.: Cryptanalysis of a spatiotemporal chaotic cryptosystem. Chaos Solitons Fract. 41, 1718–1722 (2009)
Sahar, M., Amir, M.E.: Color image encryption based on coupled nonlinear chaotic map. Chaos Solitions Fract. 42, 1745–1754 (2009)
Wang, X.Y., Zhang, N., Ren, X.L., Zhang, Y.L.: Synchronization of spatiotemporal chaotic systems and application to secure communication of digital image. Chin. Phys. B 20(2), 020507 (2011)
Masuda, N., Aihara, K.: Cryptosystems with discretized chaotic maps. IEEE Trans. Circuits Syst. I 49, 28–40 (2002)
Mirzaei, O., Yaghoobi, M., Irani, H.: A new image encryption method: parallel sub-image encryption with hyper chaos. Nonlin. Dyn. 67, 557–566 (2012)
Zhu, C.: A novel image encryption scheme based on improved hyperchaotic sequences. Opt. Commun. 258, 29–37 (2012)
Wang, X.Y., Liu, L.T.: Cryptanalysis of a parallel sub-image encryption method with high-dimensional chaos. Nonlin. Dyn. 73, 795–800 (2013)
Li, C.Q., Liu, Y.S., Xie, T., Chen, M.Z.Q.: Breaking a novel image encryption scheme based on improved hyperchaotic sequences. Nonlin. Dyn. 73, 2083–2089 (2013)
Dascalescu, A.C., Boriga, R.E.: A novel fast chaos-based algorithm for generating random permutations with high shift factor suitable for image scrambling. Nonlin. Dyn. 74, 307–318 (2013)
Zhang, Y.S., Xiao, D.: Double optical image encryption using discrete Chirikov standard map and chaos-based fractional random transform. Opt. Lasers Eng. 51, 472–480 (2013)
Zhang, Y.S., Xiao, D., Shu, Y.L., Li, J.: A novel image encryption scheme based on a linear hyperbolic chaotic system of partial differential equations. Signal Process: Image Commun. 28, 292–300 (2013)
Zhang, Y.S., Xiao, D.: Cryptanalysis of S-box-only chaotic image ciphers against chosen plaintext attack. Nonlin. Dyn. 72, 751–756 (2013)
Zhang, Y.S., Xiao, D.: An image encryption scheme based on rotation matrix bit-level permutation and block diffusion. Commun. Nonlin. Sci. Num. Simul. 19, 74–82 (2014)
Stinson, D.R.: Cryptography: Theory and Practice. CRC Press, Boca Raton (1995)
Acknowledgments
This research is supported by the National Natural Science Foundation of China (Nos: 61370145, 61173183, and 60973152), the Doctoral Program Foundation of Institute of Higher Education of China (No: 20070141014), Program for Liaoning Excellent Talents in University (No: LR2012003), the National Natural Science Foundation of Liaoning province (No: 20082165), and the Fundamental Research Funds for the Central University (No: DUT12JB06).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, YQ., Wang, XY. Analysis and improvement of a chaos-based symmetric image encryption scheme using a bit-level permutation. Nonlinear Dyn 77, 687–698 (2014). https://doi.org/10.1007/s11071-014-1331-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-014-1331-3