A Novel Method for Image Encryption Using Modified Logistic Map
: Image Processing
Omid R.B. Speily
With the development of the internet and social networks, the interest on multimedia data, especially digital images, has been increased among scientists. Due to their advantages such as high speed as well as high security and complexity, chaotic functions have been extensively employed in images encryption. In this paper, a modified logistic map function was proposed, which resulted in higher scattering in obtained results. Confusion and diffusion functions, as the two main actions in cryptography, are not necessarily performed respectively, i.e. each of these two functions can be applied on the image in any order, provided that the sum of total functions does not exceed 10. In calculation of sum of functions, confusion has the coefficient of 1 and diffusion has the coefficient of 2. To simulate this method, a binary stack is used. Application of binary stack and pseudo-random numbers obtained from the modified chaotic function increased the complexity of the proposed encryption algorithm. The security key length, entropy value, NPCR and UICA values and correlation coefficient analysis results demonstrate the feasibility and validity of the proposed method. Analyzing the obtained results and comparing the algorithm to other investigated methods clearly verified high efficiency of proposed method.
 Kardan, O. R. B. Speily. Increasing Information Reposting Behavior in Online Learning Community. Educational Technology & Society, 21(4), 100–110. 2018.
 Speily, O. R. B.. De-lurking in Online Communities Using Repost Behavior Prediction Method. Information Systems & Telecommunication, 192. 2017.
 Tarokh, M. J., Arian, H. S., & Speily, O. R. B.. Discovering Influential Users in Social Media to Enhance Effective Advertisement. Advances in Computer Science: An International Journal, 4(5), 23–28. 2015.
 H. Natiq,M. Said, & A. Kilicman. “A new hyperchaotic map and its application for image”, https://doi.org/10.1140/epjp/i2018-11834-2' target='blank'>https://doi.org/10.1140/epjp/i2018-11834-2. 2018.
 Z. Hua, S. Yi & Y. Zhou, “Medical image encryption using high-speed scrambling and pixel adaptive diffusion”, Signal Processing. https://doi.org/10.1016/j.sigpro.2017.10.004, 2017.
 B. Gaurav, Q. M. Jonathan Wu & B. Raman. “Discrete fractional wavelet transforms and its application to multiple encryption.” Inf. Sci. 223-297-316, 2013.
 Z. Hua & Y. Zhou. “Design of image cipher using block-based scrambling and image filtering”. Information Sciences. https://doi.org/10.1016/j.ins.2017.02.036, 2017.
 L. D. Singh & K. M. Singh. ‘Image Encryption using Elliptic Curve Cryptography”, Procedia - Procedia Computer Science, 54, 472–481. https://doi.org/10.1016/j.procs.2015.06.054, 2015.
 X. Wang & D. Luan. “A novel image encryption algorithm using chaos and reversible cellular automata”. Communications in Nonlinear Science and Numerical Simulation, 18(11), 3075–3085. https://doi.org/10.1016/j.cnsns.2013.04.008, 2013.
 O. Lafe, “Data Compression and Encryption using Cellular Automata Transform”, Engineering Applications of Articial Intelligence, Vol. 10, No. 6, pp. 581–591, 1998.
 R. J. Chen and J. L. Lai, “Image Security System using Recursive Cellular Automata Substitution,” Pattern Recognition , Vol. 40, pp. 1621–1631, 2007.
 A. Jolfaei and A. Mirghadri, “Survey: Image Encryption Using Salsa20”, International Journal of Computer Science Issues, Vol. 7, Issue 5, pp. 213-220, September 2010.
 S. E. Borujeni and M. Eshghi, “Chaotic Image Encryption System using Phase-Magnitude Transformation and Pixel Substitution”, J. Telecommun. Syst. DOI:10.1007/s11235-011-9458-8. 2011.
 C. Zhu, “A Novel Image Encryption Scheme based on Improved Hyperchaotic Sequences,” Journal of Optics Communications, Vol. 285, pp 29–37, 2012.
 B. Norouzi, S. Mirzakuchaki, S. M. Seyedzadeh, and M. R. Mosavi, “A Simple,Sensitive and Secure Image Encryption Algorithm based on Hyper-Chaotic System with Only One Round Diffusion Process,” The Journal of Multimedia Tools and Applications, DOI 10.1007/s11042-012-1292-9, 2012.
 X. Wang and L. Teng, “An Image Blocks Encryption Algorithm based on Spatiotemporal Chaos”, J Nonlinear Dyn., Vol. 67, pp. 365–371, 2012.
 H. Natiq, M. R. M. Said & A. Kilicman. “A new hyperchaotic map and its application for image”. https://doi.org/10.1140/epjp/i2018-11834-2' target='blank'>https://doi.org/10.1140/epjp/i2018-11834-2, 2018.
 X. Huang, G. Ye, “An image encryption algorithm based on irregular wave representation”. https://doi.org/10.1007/s11042-017-4455-x. 2017.
 R. Enayatifar, A. H. Abdullah, I. F. Isnin, A. Altameem & M. Lee, “Image encryption using a synchronous permutation diffusion technique”. Optics and Lasers in Engineering, 90(June 2016), 146–154. https://doi.org/10.1016/j.optlaseng.2016.10.006. 2017.
 C. Li, G. Luo & K. Qin. “An image encryption scheme based on chaotic tent map”. Nonlinear Dynamics. https://doi.org/10.1007/s11071-016-3030-8.2016.
 K. Mishra, R. Saharan, & B. Rathor, “A new cryptographic method for image encryption”, 32, 2885–2892. https://doi.org/10.3233/JIFS-169231. 2017.
 M. H. Annaby, M. A. Rushdi, & E. A. Nehary. “Color image encryption using random transforms, phase retrieval, chaotic maps, and diffusion”. Optics and Lasers in Engineering, 103, 9–23. https://doi.org/10.1016/j.optlaseng.2017.11.005. 2018.
 S. M. Ismail, L. A. Said, A. G. Radwan, A. H. Madian & M. F. Abu-elyazeed. “Generalized double-humped logistic map-based medical image encryption”. Journal of Advanced Research, 10, 85–98. https://doi.org/10.1016/j.jare.2018.01.009. 2018.
 L. Zhang, X. Liao, X. Wang, “An image encryption approach based on chaotic maps”, Chaos Solitons & Fractals, Vol. 24, pp. 759-765, 2005.
 Barker, E., Roginsky, A., & Barker, E. (n.d.). “Transitioning the Use of Cryptographic Algorithms and Key Lengths”, NIST Special Publication 800-131A Transitioning the Use of Cryptographic Algorithms and Key Lengths. July 2018.
 A. Kulsoom, D. Xiao, A. Rehman, S. A. Abbas, “An efficient and noise resistive selective image encryption scheme for gray images based on chaotic maps and DNA complementary rules”, Multimed Tools Appl., DOI 10.1007/s11042-014-2221-x. 2014.
 Wu, Yue, Joseph P. Noonan, and Sos Agaian. "NPCR and UACI randomness tests for image encryption." Cyber journals: multidisciplinary journals in science and technology, Journal of Selected Areas in Telecommunications (JSAT) 1.2: 31-38, (2011).
 Y. Wang, K. Wong, X. Liao & G. Chen. “A new chaos-based fast image encryption algorithm”, 11, 514–522. https://doi.org/10.1016/j.asoc.2009.12.011. 2011.
 A. Hanan,R. Enayatifar & M. Lee., “A hybrid genetic algorithm and chaotic function model for image encryption. AEUE - International Journal of Electronics and Communications, 66(10), 806–816. https://doi.org/10.1016/j.aeue.2012.01.015. 2012.
 Z. Zhu, W. Zhang, K. Wong & H. Yu. “A chaos-based symmetric image encryption scheme using a bit-level permutation”. Information Sciences, 181(6), 1171–1186. https://doi.org/10.1016/j.ins.2010.11.009. 2011.
 G. Zhang & Q. Liu. “A novel image encryption method based on total shuffling scheme”. OPTICS, 284(12), 2775–2780. https://doi.org/10.1016/j.optcom.2011.02.039. 2011.
 A. Akhshani, A. Akhavan, S. C. Lim, Z. Hassan, “An image encryption scheme based on quantum logistic map”, Communications in Nonlinear Science and Numerical Simulation, Vol. 17, pp. 4653-4661, 2012.
 S. M. Seyedzadeh, S. Mirzakuchaki, “A fast color image encryption algorithm based on coupled two-dimensional piecewise chaotic map, “Signal Processing, Vol. 92, pp. 1202-1215, 2012.
 E. Vaferi, R. Sabbaghi-Nadooshan, “A New Encryption Algorithm for Color Images based on Total Chaotic Shuffling Scheme”, Optik - International Journal for Light and Electron Optics, Volume 126, Issue 20, Pages 2474–2480, October 2015.
 M. Mohammadizadeh, B. Pourabbas, K. Foroutani, M. Fallahian, “Conductive polythiophene nanoparticles deposition on transparent PET substrates: effect of modification with hybrid organic-inorganic coating”, International Journal of Engineering (IJE), TRANSACTIONS C: Aspects Vol. 28, No. 4, (April 2015) 567-572.