Abstract
Recently, there has been explosive growth in the sharing of images on social media networks. This has occurred primarily because people are using smart phones with high quality imaging facilities and a mobile Internet connection. Accordingly, digital image security has formed a particular focus of recent research. Image encryption is the most common method used to keep images safe during their transmission over the Internet. There are two main phases in image encryption: permutation and diffusion. In this paper, a hybrid model is proposed, which is a combination of a novel permutation technique in conjunction with a new diffusion method. In the permutation phase of the suggested model, pixels are relocated based on their indices. The resulting permuted image has a high difference (more than 99.3%) in the gray level of pixels compared to the corresponding pixels in a plain image. The proposed diffusion method is based on a combination of an Imperialist Competitive Algorithm (ICA) and adjacent lattices as a chaotic function. To date, the ICA, as an evolutionary algorithm, in combination with adjacent lattices, has never been exploited for image encryption. The result analysis demonstrates that the proposed method has excellent resistance against brute force and statistical attacks, in addition to obtaining a 7.9993 entropy score for the encrypted image.
Similar content being viewed by others
References
Abdullah AH, Enayatifar R, Lee M (2012) A hybrid genetic algorithm and chaotic function model for image encryption. AEU-Int J Electron C 66:806–816. https://doi.org/10.1016/j.aeue.2012.01.015
Annaby MH, Rushdi MA, Nehary EA (2016) Image encryption via discrete fractional Fourier-type transforms generated by random matrices. Sig Process Image Commun 49:25–46. https://doi.org/10.1016/j.image.2016.09.006
Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition. 2007 IEEE Congress on Evolutionary Computation, 4661–4667. https://doi.org/10.1109/CEC.2007.4425083
Cao C, Sun K, Liu W (2018) A novel bit-level image encryption algorithm based on 2D-LICM hyperchaotic map. Sig Process 143:122–133. https://doi.org/10.1016/j.sigpro.2017.08.020
de Oliveira FB, Enayatifar R, Sadaei HJ, Guimarães FG, Potvin J-Y (2016) A cooperative coevolutionary algorithm for the Multi-Depot Vehicle Routing Problem. Expert Syst Appl 43:117–130. https://doi.org/10.1016/j.eswa.2015.08.030
Enayatifar R, Abdullah AH, Lee M (2013) A weighted discrete imperialist competitive algorithm (WDICA) combined with chaotic map for image encryption. Opt Lasers Eng 51:1066–1077. https://doi.org/10.1016/j.optlaseng.2013.03.010
Enayatifar R, Abdullah AH, Isnin IF (2014) Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence. Opt Lasers Eng 56:83–93. https://doi.org/10.1016/j.optlaseng.2013.12.003
Enayatifar R, Abdullah AH, Isnin IF, Altameem A, Lee M (2017) Image encryption using a synchronous permutation-diffusion technique. Opt Lasers Eng 90:146–154. https://doi.org/10.1016/j.optlaseng.2016.10.006
Fakhrzad MB, Goodarzian F (2019) A fuzzy multi-objective programming approach to develop a green closed-loop supply chain network design problem under uncertainty: modifications of imperialist competitive algorithm. RAIRO: Recherche Opérationnelle, 53. https://doi.org/10.1051/ro/2019018
Hosseini S, Al Khaled A (2014) A survey on the imperialist competitive algorithm metaheuristic: implementation in engineering domain and directions for future research. Appl Soft Comput 24:1078–1094. https://doi.org/10.1016/j.asoc.2014.08.024
Kanso A, Ghebleh M (2015) An efficient and robust image encryption scheme for medical applications. Commun Nonlinear Sci Numer Simul 24:98–116. https://doi.org/10.1016/j.cnsns.2014.12.005
Laiphrakpam DS, Khumanthem MS (2017) Medical image encryption based on improved ElGamal encryption technique. Optik 147:88–102. https://doi.org/10.1016/j.ijleo.2017.08.028
Lima JB, Madeiro F, Sales FJR (2015) Encryption of medical images based on the cosine number transform. Sig Process Image Commun 35:1–8. https://doi.org/10.1016/j.image.2015.03.005
Mahmud M, Lee M, Choi JY (2020) Evolutionary-based image encryption using RNA codons truth table. Opt Laser Technol 121:105818. https://doi.org/10.1016/j.optlastec.2019.105818
Mirzaei Talarposhti K, Khaki Jamei M (2016) A secure image encryption method based on dynamic harmony search (DHS) combined with chaotic map. Opt Lasers Eng 81:21–34. https://doi.org/10.1016/j.optlaseng.2016.01.006
Mirzaei Talarposhti F, Javedani Sadaei H, Enayatifar R, Gadelha Guimarães F, Mahmud M, Eslami T (2016) Stock market forecasting by using a hybrid model of exponential fuzzy time series. Int J Approx Reason 70:79–98. https://doi.org/10.1016/j.ijar.2015.12.011
Qin C, He Z, Luo X, Dong J (2018) Reversible data hiding in encrypted image with separable capability and high embedding capacity. Inf Sci 465:285–304. https://doi.org/10.1016/j.ins.2018.07.021
Sadaei HJ, Enayatifar R, Lee MH, Mahmud M (2016) A hybrid model based on differential fuzzy logic relationships and imperialist competitive algorithm for stock market forecasting. Appl Soft Comput 40:132–149. https://doi.org/10.1016/j.asoc.2015.11.026
Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Stallings W, Brown L, Bauer MD, Bhattacharjee AK (2012) Computer security: principles and practice. Pearson Education, Upper Saddle River, NJ, USA
Tao R, Meng X, Wang Y (2010) Image encryption with multiorders of fractional fourier transforms. IEEE Trans Inf Forensics Secur 5:734–738. https://doi.org/10.1109/TIFS.2010.2068289
Teng L, Wang X (2012) A bit-level image encryption algorithm based on spatiotemporal chaotic system and self-adaptive. Opt Commun 285:4048–4054. https://doi.org/10.1016/j.optcom.2012.06.004
Vaish A, Kumar M (2017) Color image encryption using MSVD, DWT and Arnold transform in fractional Fourier domain. Optik 145:273–283. https://doi.org/10.1016/j.ijleo.2017.07.041
Wang X, Liu L, Zhang Y (2015) A novel chaotic block image encryption algorithm based on dynamic random growth technique. Opt Lasers Eng 66:10–18. https://doi.org/10.1016/j.optlaseng.2014.08.005
Wang H, Qin Y, Huang Y, Wang Z, Zhang Y (2017) Multiple-image encryption and authentication in interference-based scheme by aid of space multiplexing. Opt Laser Technol 95:63–71. https://doi.org/10.1016/j.optlastec.2017.04.019
Wu Y, Noonan JP, Agaian S (2011) NPCR and UACI randomness tests for image encryption. Cyber journals: multidisciplinary journals in science and technology. J Sel Areas Telecommunications (JSAT) 1(2):31–38
Wu J, Liao X, Yang B (2018) Cryptanalysis and enhancements of image encryption based on three-dimensional bit matrix permutation. Sig Process 142:292–300. https://doi.org/10.1016/j.sigpro.2017.06.014
Xiang T, Wong K, Liao X (2007) Selective image encryption using a spatiotemporal chaotic system, Chaos: An Interdisciplinary. J Nonlinear Sci 17:023115. https://doi.org/10.1063/1.2728112
Xu L, Li Z, Li J, Hua W (2016) A novel bit-level image encryption algorithm based on chaotic maps. Opt Lasers Eng 78:17–25. https://doi.org/10.1016/j.optlaseng.2015.09.007
Yao L, Yuan C, Qiang J, Feng S, Nie S (2017) An asymmetric color image encryption method by using deduced gyrator transform. Opt Lasers Eng 89:72–79. https://doi.org/10.1016/j.optlaseng.2016.06.006
Yavuz E, Yazıcı R, Kasapbaşı MC, Yamaç E (2016) A chaos-based image encryption algorithm with simple logical functions. Comput Electr Eng 54:471–483. https://doi.org/10.1016/j.compeleceng.2015.11.008
Yousefi M, Enayatifar R, Darus AN, Abdullah AH (2012) A robust learning based evolutionary approach for thermal-economic optimization of compact heat exchangers. Int Commun Heat Mass Transfer 39:1605–1615. https://doi.org/10.1016/j.icheatmasstransfer.2012.10.002
Zhang Y-Q, Wang X-Y (2015) A new image encryption algorithm based on non-adjacent coupled map lattices. Appl Soft Comput 26:10–20. https://doi.org/10.1016/j.asoc.2014.09.039
Zhu Z-l, Zhang W, Wong K-w, Yu H (2011) A chaos-based symmetric image encryption scheme using a bit-level permutation. Inf Sci 181:1171–1186. https://doi.org/10.1016/j.ins.2010.11.009
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author declare that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Golalipour, K. A novel permutation-diffusion technique for image encryption based on the Imperialist Competitive Algorithm. Multimed Tools Appl 82, 725–746 (2023). https://doi.org/10.1007/s11042-022-12883-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-022-12883-3