Abstract
Communication networks, play a major role in keeping us connected and sharing the details of our lives with each other. The main driver of multimedia data transmission is to enhance security protection of this multimedia data (speech, image and video). In this paper we addresses the synchronization problem of the masterslave type via a static error feedback. Sufficient conditions expressed by means of linear matrix inequalities (LMI) for the synchronization of fractional-order hyperchaotic systems with a known time delay between them is presented. The delay-dependent criterion is given based upon a Lyapunov function. We take the fractional-order hyperchaotic Liu system as an illustrative example to demonstrate the effectiveness of the proposed synchronization scheme. Moreover, as an application an images cryptosystem is presented. We considered two scenarios corresponding to the transmission channel, under occlusion attack and under noisse addition respectively. Results for the studied scenarios are presented and compared. The extensive simulation results prove that proposed cryptosystem has clear advantage over other proposed in the litterature.
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References
Behnia S, Akhshani A, Mahmodi H, Akhavan A (2008) A novel algorithm for image encryption based on mixture of chaotic maps. Chaos Solitons Fractals 35:408–419
Biham E, Shamir A (1991) Differential cryptanalysis of DES-like cryptosystems. J Cryptol 4:36–72
Biham E, Shamir A (1993) Differential cryptanalysis of the full 16-round DES BT - advances in cryptology – CRYPTO.’ 92. In: Brickell EF (ed) 12th annual international cryptology conference santa barbara, California, USA August 16–20, 1992 Proceedings, Springer Berlin Heidelberg, Berlin, Heidelberg pp 487–496
Bowong S (2004) Stability analysis for the synchronization of chaotic systems with different order: application to secure communications. Phys Lett A 326:102–113
Chai X, Chen Y, Broyde L (2017) A novel chaos-based image encryption algorithm using DNA sequence operations. Opt Lasers Eng 88:197–213
Chapaneri S, Chapaneri R, Sarode T (2014) Evaluation of chaotic map lattice systems for image encryption. In: Proceedings of international conference on circuits, systems, communication and information technology applications (CSCITA) pp 59–62
Chen C, Feng G, Guan X (2004) Robust synchronization of chaotic Lur’e systems via delayed feedback control. Phys Lett A 321:344–354
Chen HF, Liu JM (2000) Open-loop chaotic synchronization of injection-locked semiconductor lasers with Gigahertz range modulation. IEEE J Quant Electron 36:27–34
Chen F, Zhang W (2007) LMI Criteria for robust chaos synchronization of a class of chaotic systems. Nonlinear Anal 67:3384–3393
Diaconu AV, Costea A, Costea MA (2014) Color image scrambling technique based on transposition of pixels between RGB channels using knight’s moving rules and digital chaotic map. Mathematical Problems in Engineering. https://doi.org/10.1155/2014/932875
Enayatifar R, Sadaei HJ, Abdullah AH, Lee M, Isnin IF (2015) A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata. Opt Lasers Eng 71:33–41
Feng D, An H, Zhu H, Zhao Y (2019) The synchronization method for fractional-order hyperchaotic systems. Phys Lett A 383:1427–1434
Firdous A, ur Rehman A, Saad Missen MM (2019) A highly efficient color image encryption based on linear transformation using chaos theory and SHA-2. Multimed Tools Appl 78:24809–248352
Gan Z, Chai X, Han D, Chen TY (2019) A chaotic image encryption algorithm based on 3-D bit-plane permutation. Neural Comput Applic 31:7111–7130
Gu K (2000) An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE conference on decision and control, Los Alamitos, CA pp 2805–2810
Han Q, Liu CX, Sun L, Zhu R (2013) A fractional order hyperchaotic system derived from a Liu system and its circuit realization. Chin Phys B 22:020502–02050
Hartley TT, Lorenzo CF, Qammer HK (1995) Chaos in a fractional order Chua’s system. IEEE Trans Circuits Syst I 42:485–490
Hegazi AS, Matouk AE (2011) Dynamical behaviors and synchronization in the fractional order hyperchaotic Chen system. Appl Math Lett 24:1938–1944
Hua Z, Jin F, Xu B, Huang H (2018) 2D logistic-sine-coupling map for image encryption. Signal Process 149:148–161
Huang X, Sun T, Li Y, Liang J (2014) A color image encryption algorithm based on a fractional-order hyperchaotic system. Entropy 17:28–38
Huang Y, Huang L, Wang Y, Peng Y, Yu F (2020) Shape Synchronization in Driver-Response of 4-D Chaotic System and Its Application in Image Encryption. IEEE Access 8:135308–135319
Kalpana J, Murali P (2015) An improved color image encryption based on multiple DNA sequence operations with DNA synthetic image and chaos. Opt - Int J Light Electron Opt 126:5703–5709
Khalil HK (1993) Nonlinear systems. Macmillan Publishing, Company NY
Kiani-B A, Fallahi K, Pariz N, Leung H (2009) A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter. Commun Nonlinear Sci 14:63–79
Kilbas A, Srivastava H, Trujillo J (2006) Theory and applications of fractional differential equations. NorthHolland mathematics studies 204
Kulsoom A, Xiao D, ur-Rehman A, Abbas SA (2016) An efficient and noise resistive selective image encryption scheme for gray images based on chaotic maps and DNA complementary rules. Multimed Tools Appl 75:1–23
Li Z, Xu D (2204) A secure communication scheme using projective chaos synchronization. Chaos Soliton Fract 22:77–81
Liang Y, Liu G, Zhou N, Wu J (2015) Color image encryption combining a reality-preserving fractional dct with chaotic mapping in hsi space. Multimed Tools Appl 75:6605–6620
Liao X, Chen G (2003) SChaos synchronization of general Lur’e systems via time-delay feedback control. Int J Bifurc Chaos 13:207–213
Liu Y, Zhang J, Han D, Wu P, Sun Y, MY S (2020) A multidimensional chaotic image encryption algorithm based on the region of interest. Multimed Tools Appl 79:17669–17705
Liu S, Zhou X, Li X, Jiang W (2016) Asymptotical stability of Riemann–Liouville fractional nonlinear systems. Nonlinear Dyn 86:65–71
Muthukumar P, Balasubramaniam P (2013) Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography. Nonlinear Dyn 74:1169–1181
Muthukumar P, Balasubramaniam P, Ratnavelu K (2017) A novel cascade encryption algorithm for digital images based on anti-synchronized fractional order dynamical systems. Multimed Tools Appl 76:23517–23538
Nana B, Woafo P, Domngang S (2009) Chaotic synchronization with experimental application to secure communications. Commun Nonlinear Sci 14:66–76
Odibat ZM (2010) Synchronization of chaotic fractional-order systems via linear control. Int J Bifurcat Chaos 20:81–97
Pak C, Huang L (2017) A new color image encryption using combination of the 1D chaotic map. Signal Process 138:129–137
Podlubny I (1999) Fractional differential equations. Academic Press, New York
Smaoui N, Karouma A, Zribi M (2011) Secure communications based on the synchronization of the hyperchaotic Chen and the unified chaotic systems. Commun Nonlinear Sci Numer Simul 16:79–93
ur Rehman A, Liao X (2019) A novel robust dual diffusion/confusion encryption technique for color image based on Chaos DNA and SHA-2. Multimed Tools Appl 78:2105–2133
ur Rehman A, Liao X, Ashraf R, Ullah S, Wang H (2018) A color image encryption technique using exclusive-OR with DNA complementary rules based on chaos theory and SHA-2. Int J Light Electron Opt 159:348–367
Vidhya R, Brindha M (2020) A novel dynamic chaotic image encryption using butterfly network topology based diffusion and decision based permutation. Multimed Tools Appl. https://doi.org/10.1007/s11042-020-09462-9
Wang X, Zhang H (2015) A color image encryption with heterogeneous bit-permutation and correlated chaos. Opt Commun 342:51–60
Wang X, Zhang H (2015) A color image encryption with heterogeneous bit-permutation and correlated chaos. Opt Commun 342:51–60
Wei X, Guo L, Zhang Q, Zhang J, Lian S (2012) A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system. J Syst Softw 85:290–299
Wu X, Kan H, Kurths J (2015) A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps. Appl Soft Comput J 37:24–39
Wu X, Li Y, Kurths J (2015) A new color image encryption scheme using cml and a fractional-order chaotic system. PloS one. https://doi.org/10.1371/journal.pone.0119660
Xu Y, Wang H, LI Y, Pei B (2014) Image encryption based on synchronization of fractional chaotic systems. Commun Nonlinear Sci Numer Simulat 19:3735–3744
Xu Y, Wang H, Li Y, Pei B (2014) Image encryption based on synchronization of fractional chaotic systems. Commun Nonlinear Sci Numer Simulat 19:3735–3744
Yalçin ME, Suykens JAK, Vandewalle J (2001) Master-slave synchronization of Lur’e systems with time-delay. Int J Bifurc Chaos 11:1707–1722
Zhang W, Cao J, Wu R, Alsaadi FE, Alsaedi A (2019b) Lag projective synchronization of Fractional-Order delayed chaotic systems. J Franklin Inst 356:1522–1534
Zhang Q, Guo L, Wei X (2010) Image encryption using DNA addition combining with chaotic maps. Math Comput Model 52:2028–2035
Zhang YQ, Hao JL, Wang XY (2020) An efficient image encryption scheme based on S-Boxes and fractional-order differential Logistic map. IEEE Access 8:54175–54188
Zhang LM, Sun KH, Liu WH, He SB (2017) A novel color image encryption scheme using fractional-order hyperchaotic system and DNA sequence operations. Chin Phys B 26:100504
Zhang YQ, Wang XY (2014) A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice. Inf Sci 273:329–351
Zhang H, Ye R, Liu S, Cao J, Alsaedi A, Li X (2018) LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays. Int J Syst Sci 49:537–545
Zhou NR, Wang YX, Gong LH, He H, Wu JH (2011) Novel single–channel color image encryption algorithm based on chaos and fractional Fourier transform. Opt Commun 12:89–96
Zhu C (2012) A novel image encryption scheme based on improved hyperchaotic sequences. Opt Commun 285:29–37
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Bouridah, M.S., Bouden, T. & Yalçin, M.E. Delayed outputs fractional-order hyperchaotic systems synchronization for images encryption. Multimed Tools Appl 80, 14723–14752 (2021). https://doi.org/10.1007/s11042-020-10425-3
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DOI: https://doi.org/10.1007/s11042-020-10425-3