Abstract
A new chaotic image encryption scheme based on permutation and substitution in the Fourier domain is presented. Fractional Fourier Transform (FRFT) is used before the encryption scheme to get a large degree of randomization. The permutation is achieved by Baker map and the substitution by a key-related-to-plain-image algorithm based on the modified Logistic map. Modification of the Logistic map is developed to increase the space of the encryption key, and hence increase the security. The key of the encryption algorithm dependents on the plain image, and thus, the cipher image is sensitive to both the initial key and the plain image to resist known-plaintext and chosen plaintext attacks. The key space is large and hence the algorithm can effectively resist brute-force attacks. The proposed scheme is examined using different performance evaluation metrics and the results prove that the proposed scheme is highly secure, and it can effectively resist different attacks.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
BURR W E. Data encryption standard [M]// NIST’s anthology. A Century of Excellence in Measurements Standards and Technology: A Chronicle of Selected NBS/NIST Publications, 2000.
FIPS PUB 197. Advanced Encryption Standard (AES) [S]. National Institute of Standards and Technology, U.S. Department of Commerce, 2001.
RIVEST R L, ROBSHAW M J B, SIDNEY R, YIN Y L. The RC6TM Block Cipher [M]. Cambridge, USA: MIT Laboratory for Computer Science, 1998.
PATIDAR V, PAREEK N K, SUD K K. A new substitution–diffusion based image cipher using chaotic standard and logistic maps[J]. Nonlinear Sci Numer Simulat, 2009, 14: 3056–3075.
ZHANG L H, LIAO X F, WANG X B. An image encryption approach based on chaotic maps [J]. Chaos, Solitons & Fractals, 2005, 24: 759–765.
SHANNON C E. A mathematical theory of communication [J]. Bell System Technical Journal, 1948, 27: 379–423.
YANG M, BOURBAKIS N, LI S. Data-image-video encryption [M]. IEEE, 2004.
MAO Y, CHEN G, LIAN S. A novel fast image encryption scheme based on 3D chaotic Baker maps [J]. International Journal of Bifurcation and Chaos, 2004, 14(10): 3613–3624.
SHEN J, JIN X, ZHOU C. A color image encryption algorithm based on magic cube transformation and modular arithmetic operation [J]. Advances in Multimedia Information Processing, Lecture Notes in Computer Science, 2005, 3768: 270–280.
HE X, ZHU Q, GU P. A new chaos-based encryption method for color image [J]. Rough Sets and Knowledge Technology, Lecture Notes in Computer Science, 2006, 4062: 671–678.
LI C, CHEN G. On the security of a class of image encryption schemes [C]// Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’ 08). Seattle, Wash, USA, 2008: 3290–3293.
CAO Guang-hui, HU Kai, ZHANG Yi-zhi, ZHOU Jun, ZHANG Xing. Chaotic image encryption based on running-key related to plaintext [J]. Hindawi Publishing Corporation the Scientific World Journal, 2014(6): 490179.
OZAKTAS H M, ZALEVSKY Z, KUTAY M A. The fractional Fourier transform [M]. Chichester: Wiley, 2001.
OZAKTAS H M. Fractional Fourier domains [J]. Signal Process, 1995, 46: 119–124.
FRIDRICH J. Symmetric ciphers based on two-dimensional chaotic maps [J]. Int J Bifurcation and Chaos, 1998, 8(6): 1259–1284.
BAKER G L, GOLLUB J P. Chaotic dynamics an Introduction [M]. First Ed. New York: Press Syndicate of the University of Cambridge, 1990.
EL-HOSENY H, AHMED H H, KAZEMIAN H, ABD EL-SAMIE F E, ABBAS A M. Digital image encryption in transform domains [D]. Faculty of Electronic Engineering, Menofia University, Menof, 2014.
FRIDRICH J. Symmetric ciphers based on two-dimensional chaotic maps [J]. Int J Bifurcation and Chaos, 1998, 8(6): 1259–1284.
ZHU Cong-xu, XU Si-yuan, HU Yu-ping. Breaking a novel image encryption scheme based on Brownian motion and PWLCM chaotic system [J]. Nonlinear Dynamics, 2015, 79(2): 1511–1518.
ZHU Cong-xu, LIAO Chun-long, DENG Xiao-heng. Breaking and improving an image encryption scheme based on total shuffling scheme [J]. Nonlinear Dynamics, 2013, 71(1, 2): 25–34.
MERKLE R C, HELLMAN M. On the security of multiple encryption [J]. Communications of the ACM, 1981, 24(7): 465–467.
http://in.mathworks.com/help/images/ref/corr2.html
CURRAN K, BAILEY K. An evaluation of image based steganography methods [J]. International Journal of Digital Evidence, 2003, 2(2): 55–88.
FU Chong, CHEN Jun-jie, ZOU Hao, MENG Wei-hong, ZHAN Yong-feng. A chaos based digital image encryption scheme with an improved diffusion strategy [J]. Optics Express, 2012, 20(3): 2363–2378.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ramadan, N., Ahmed, H.H., El-khamy, S.E. et al. Permutation-substitution image encryption scheme based on a modified chaotic map in transform domain. J. Cent. South Univ. 24, 2049–2057 (2017). https://doi.org/10.1007/s11771-017-3614-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-017-3614-6