Image encryption algorithm with matrix semi-tensor product. (English) Zbl 1537.94076
Summary: This article proposed an improved 2D-logistic-adjusted-Sine map, which has better ergodicity, pseudo-randomness, unpredictability and wider chaotic range than many existing 2D-chaotic maps. Utilizing improved 2D-logistic-adjusted-Sine map generates chaotic sequences, where the initial values of the system are assigned based on SHA 512 hash function. Compared with traditional encryption scheme, the size of cipher image is different to plain image, because multiply can be applied between mismatched dimensional matrices through semi-tensor product, and therefore, attackers cannot obtain the size of plain image from encryption image. In order to lighten transmission and storage burden, we reduce the results of semi-tensor product by data process. Keys security, correlation coefficient, information entropy and ability of defending differential attack are analyzed to confirm the security of our encryption scheme. Experimental results confirm that the proposed algorithm can encrypt image effectively and securely.
MSC:
| 94A60 | Cryptography |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 37N99 | Applications of dynamical systems |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
Keywords:
encryption algorithm; 2D-logistic-adjusted-sine map; SHA 512 hash function; matrix semi-tensor productReferences:
| [1] | Gan, ZH; Chai, XL; Han, DJ, A chaotic image encryption algorithm based on 3-D bit-plane permutation, Neural Comput. Appl., 31, 11, 7111-7130 (2019) |
| [2] | Li, YP; Wang, CH; Chen, H., A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation, Opt. Lasers Eng., 90, 238-246 (2017) |
| [3] | Zou, CY; Zhang, Q.; Wei, XP, Image encryption based on improved Lorenz system, IEEE Access, 8, 75728-75740 (2020) |
| [4] | Khan, M.; Masood, F., A novel chaotic image encryption technique based on multiple discrete dynamical maps, Multimedia Tools Appl., 78, 18, 26203-26222 (2019) |
| [5] | Khan, FA; Ahmed, J.; Khan, JS, A novel image encryption based on Lorenz equation, Gingerbreadman chaotic map and S-8 permutation, J. Intell. Fuzzy Syst., 33, 6, 3753-3765 (2017) |
| [6] | Arshad, U.; Batool, SI; Amin, M., A novel image encryption scheme based on Walsh compressed quantum spinning chaotic Lorenz system, Int. J. Theor. Phys., 58, 10, 3565-3588 (2019) · Zbl 1428.81068 |
| [7] | Aqeel-ur-Rehman, Liao, X. F., Hahsmi, M. A.: An efficient mixed inter-intra pixels substitution at 2bits-level for image encryption technique using DNA and chaos. Optik 153: 117-134 (2018). |
| [8] | Wang, XY; Gao, S., Image encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory, Inf. Sci., 507, 16-36 (2020) · Zbl 1456.68034 |
| [9] | Suri, S.; Vijay, R., A Pareto-optimal evolutionary approach of image encryption using coupled map lattice and DNA, Neural Comput. Appl., 32, 15, 11859-11873 (2020) |
| [10] | Zhu, SQ; Zhu, CX, Secure image encryption algorithm based on hyperchaos and dynamic DNA coding, Entropy, 22, 7, 772 (2020) |
| [11] | Luo, YQ; Yu, J.; Lai, WR, A novel chaotic image encryption algorithm based on improved baker map and logistic map, Multimedia Tools Appl., 78, 18, 26203-26222 (2019) |
| [12] | Sui, LS; Du, C.; Tian, AL, Double-image encryption based on interference and logistic map under the framework of double random phase encoding, Opt. Lasers Eng., 112, 113-122 (2019) |
| [13] | Wu, JH; Liao, XF; Yang, B., Image encryption using 2D Henon-Sine map and DNA approach, Signal Process., 153, 11-23 (2018) |
| [14] | Jiang, N.; Dong, X.; Hu, H., Quantum image encryption based on Henon mapping, Int. J. Theor. Phys., 58, 3, 979-991 (2019) · Zbl 1415.37113 |
| [15] | Lv, XP; Liao, XF; Yang, B., Bit-level plane image encryption based on coupled map lattice with time-varying delay, Modern Phys. Lett. B, 32, 10, 1850124 (2018) |
| [16] | Zhang, YQ; Wang, XY, A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice, Inf. Sci., 273, 329-351 (2014) |
| [17] | Hua, ZY; Zhou, YC, Image encryption using 2D Logistic-adjusted-Sine map, Inf. Sci., 339, 237-253 (2016) |
| [18] | Wang, XY; Feng, L.; Li, R., A fast image encryption algorithm based on non-adjacent dynamically coupled map lattice model, Nonlinear Dyn., 95, 4, 2797-2824 (2019) · Zbl 1439.94067 |
| [19] | Gu, GS; Ling, J., A fast image encryption method by using chaotic 3D cat maps, Optik, 125, 17, 4700-4705 (2014) |
| [20] | Tang, J.; Yu, ZN; Liu, LF, A delay coupling method to reduce the dynamical degradation of digital chaotic maps and its application for image encryption, Multimedia Tools Appl., 78, 17, 24765-24788 (2019) |
| [21] | Tutueva, AV; Nepomuceno, EG; Karimov, AI, Adaptive chaotic maps and their application to pseudo-random numbers generation, Chaos Soliton Fractal, 133, 109615 (2020) · Zbl 1483.37112 |
| [22] | Nepomuceno, EG; Lima, AM; Arias-Garcia, J., Minimal digital chaotic system, Chaos, Soliton Fractal, 120, 62-66 (2020) · Zbl 1448.65269 |
| [23] | Wang, XY; Gao, S., Application of matrix semi-tensor product in chaotic image encryption, J. Franklin Inst. Eng. Appl. Math., 356, 18, 11638-11667 (2019) · Zbl 1455.94038 |
| [24] | Wang, J. M., Wang, J., Jiang, Y. J.: Image encryption algorithm based on the semi-tensor product. Journal of Image and Graphics 21(3), 282-296 (2016) |
| [25] | Wang, JM; Ye, SP; Xu, ZY, Low storage space of random measurement matrix for compressed sensing with semi-tensor product, ACTA Electr. Sinica, 46, 4, 797-804 (2018) |
| [26] | Wang, XY; Feng, L.; Zhao, HY, Fast image encryption algorithm based on parallel computing system, Inf. Sci., 486, 340-358 (2019) · Zbl 1451.68308 |
| [27] | Wang, XY; Zhang, YQ; Bao, XM, A novel chaotic image encryption scheme using DNA sequence operations, Opt. Lasers Eng., 73, 53-61 (2015) |
| [28] | Cheng, DZ; Qi, HS, Principle and range of possible applications of semi-tensor product of matrices, Syst. Sci. Math., 32, 12, 1488-1496 (2012) · Zbl 1289.15045 |
| [29] | May, RM, Simple mathematical models with very complicated dynamics, Nature, 261, 5560, 459-467 (1976) · Zbl 1369.37088 |
| [30] | Wu, Y.; Yang, GL; Jin, HX, Image encryption using the two-dimensional logistic chaotic map, J. Electr. Imaging, 20, 1, 013014 (2012) |
| [31] | Hua, ZY; Zhou, YC; Pun, CM, 2D Sine Logistic modulation map for image encryption, Inf. Sci., 297, 80-94 (2015) |
| [32] | Hua, ZY; Zhou, YC, Image encryption using 2D Logistic-adjusted-Sine map, Inf. Sci., 339, 237-253 (2016) |
| [33] | Cardoso, V.; Miranda, AS; Berti, E., Geodesic stability, Lyapunov exponents, and quasinormal modes, Phys. Rev. D, 79, 6, 064016 (2009) |
| [34] | Pincus, SM, Approximate entropy as a measure of system-complexity, Proc. Natl. Acad. Sci. USA, 88, 6, 2297-2301 (1991) · Zbl 0756.60103 |
| [35] | Alvarez, G.; Li, SJ, Some basic cryptographic requirements for chaos-based cryptosystems, Int. J. Bifurc. Chaos, 18, 6, 2129-2151 (2006) · Zbl 1192.94088 |
| [36] | Wang, Y.; Wong, KW; Liao, XF, A new chaos-based fast image encryption algorithm, Appl. Soft Comput., 11, 1, 514-522 (2011) |
| [37] | Wen, WY; Hong, YK; Fang, YM, A visually secure image encryption scheme based on semi-tensor product compressed sensing, Signal Process., 173, 107580 (2020) |
| [38] | Seyedzadeh, SM; Mirzakuchaki, S., A fast color image encryption algorithm based on coupled two-dimensional piecewise chaotic map, Signal Process., 92, 5, 1202-1215 (2012) |
| [39] | Wang, T.; Wang, MH, Hyperchaotic image encryption algorithm based on bit-level permutation and DNA encoding, Opt. Laser Technol., 132, 106355 (2020) |
| [40] | Asgari-Chenaghlu, M.; Feizi-Derakhshi, MR; Nikzad-Khasmakhi, N., C-y: Chaotic yolo for user intended image encryption and sharing in social media, Inf. Sci., 542, 212-227 (2021) |
| [41] | Abbasi, AA; Mazinani, M.; Hosseini, R., Chaotic evolutionary-based image encryption using RNA codons and amino acid truth table, Opt. Laser Technol., 132, 106465 (2020) |
| [42] | Kaur, G.; Agarwal, R.; Patidar, V., Chaos based multiple order optical transform for 2D image encryption, Eng. Sci. Technol. Int. J. Jestech, 23, 5, 998-1014 (2020) |
| [43] | Hua, ZY; Jin, F.; Xu, BX, 2D Logistic-Sine-coupling map for image encryption, Signal Process., 149, 148-161 (2018) |
| [44] | Diaconu, AV, Circular inter-intra pixels bit-level permutation and chaos-based image encryption, Inf. Sci., 355, 314-327 (2016) |
| [45] | Wang, XY; Liu, CM; Xu, DH, Image encryption scheme using chaos and simulated annealing algorithm, Nonlinear Dyn., 84, 3, 1417-1429 (2016) |
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