Image Security Based on Three-Dimensional Chaotic System and Random Dynamic Selection
<p>Bifurcation of different chaotic system: (<b>a</b>) bifurcation diagram of Logistic map; (<b>b</b>) bifurcation diagram of Hénon map; (<b>c</b>) bifurcation diagram of Sine map; (<b>d</b>) bifurcation diagram of proposed map.</p> "> Figure 2
<p>The effect of small initial changes.</p> "> Figure 3
<p>Lyapunov exponent: (<b>a</b>) Lyapunov exponent diagram of Logistic map; (<b>b</b>) Lyapunov exponent diagram of Hénon map; (<b>c</b>) Lyapunov exponent diagram of Sine map; (<b>d</b>) Lyapunov exponent diagram of Hénon map; (<b>e</b>) Lyapunov exponent diagram when a,b ∈ [0, 8], c = 0.23; (<b>f</b>) Lyapunov exponent diagram when b,c ∈ [0, 8], a = 56; (<b>g</b>) Lyapunov exponent diagram when a,c ∈ [0, 8], b = 78.</p> "> Figure 4
<p>Permutation entropy controlled by a, b, c parameters: (<b>a</b>) permutation entropy when a ∈ [0, 5], b = 56, c = 0.23; (<b>b</b>) permutation entropy when b ∈ [0, 5], a = 56, c = 0.23; (<b>c</b>) permutation entropy when c ∈ [0, 1], a = 56, b = 78.</p> "> Figure 5
<p>Encryption process.</p> "> Figure 6
<p>Permutation and diffusion example. (<b>a</b>) is a plaintext image; (<b>b</b>) is the result of row permutation with three permutation schemes from top to bottom; (<b>c</b>) is the result of column permutation with three permutation schemes from left to right; (<b>d</b>) is the result of row diffusion with three diffusion schemes from top to bottom; (<b>e</b>) is the result of column diffusion with three diffusion schemes from left to right; (<b>f</b>–<b>k</b>) is the adopted chaotic sequence.</p> "> Figure 7
<p>Encryption and decryption of gray-scale images. (<b>a</b>–<b>f</b>) are all kinds of plaintext images, (<b>g</b>–<b>l</b>) are corresponding encrypted images, (<b>m</b>–<b>r</b>) are corresponding decrypted images.</p> "> Figure 8
<p>Secret key sensitivity: (<b>a</b>) plaintext Airplane; (<b>b</b>) ciphertext of Airplane; (<b>c</b>) decryption result when x = 0.69, y = 0.83, z = 0.31; (<b>d</b>) decryption result when x = 0.68, y = 0.84, z = 0.31; (<b>e</b>) decryption result when x = 0.68, y = 0.83, z = 0.32; (<b>f</b>) original initial value decryption result when x = 0.68, y = 0.83, z = 0.31.</p> "> Figure 9
<p>Histograms of plain images and ciphered images: (<b>a</b>) Lena plaintext histogram; (<b>b</b>) Plane plaintext histogram; (<b>c</b>) Baboon plaintext histogram; (<b>d</b>) Lena cipher histogram; (<b>e</b>) Plane cipher histogram; (<b>f</b>) Baboon cipher histogram.</p> "> Figure 10
<p>Correlation coefficients of Lena: (<b>a</b>) plaintext horizontal direction; (<b>b</b>) plaintext vertical direction; (<b>c</b>) plaintext diagonal direction; (<b>d</b>) cipher text horizontal direction; (<b>e</b>) cipher text vertical direction; (<b>f</b>) cipher text diagonal direction.</p> "> Figure 11
<p>Cutting attacks of Lena: (<b>a</b>–<b>e</b>) are crop attacks at different clipping scales; (<b>f</b>–<b>j</b>) are the decryption results of (<b>a</b>–<b>e</b>).</p> "> Figure 12
<p>Noise attacks of Lena: (<b>a</b>) Gaussian noise attack when SNR = 25.3830; (<b>b</b>) Gaussian noise attack when SNR = 22.4203; (<b>c</b>) Gaussian noise attack when SNR = 20.7503; (<b>d</b>) decryption result of (<b>a</b>); (<b>e</b>) decryption result of (<b>b</b>); (<b>f</b>) decryption result of (<b>c</b>).</p> "> Figure 13
<p>Color image encryption and decryption results: (<b>a</b>–<b>c</b>) are the R, G, B components; (<b>d</b>–<b>f</b>) are cipher tests of R, G, B component; (<b>g</b>) colored Lena; (<b>h</b>) cipher test of (<b>g</b>); (<b>i</b>) decryption result of (<b>g</b>).</p> "> Figure 14
<p>Histogram of each component before and after color image encryption: (<b>a</b>) horizontal of R component; (<b>b</b>) horizontal of G component; (<b>c</b>) horizontal of B component; (<b>d</b>) horizontal of R component; (<b>e</b>) horizontal of G component; (<b>f</b>) horizontal of B component.</p> "> Figure 15
<p>Correlation of color images before and after encryption: (<b>a</b>–<b>c</b>) are distribution of R G B component; (<b>d</b>–<b>f</b>) are distribution of encrypted R G B component.</p> "> Figure 16
<p>Cropping and the corresponding decryption images: (<b>a</b>–<b>e</b>) are crop attacks at different clipping scales; (<b>f</b>–<b>j</b>) are decryption results of (<b>a</b>–<b>e</b>).</p> ">
Abstract
:1. Introduction
- A three-dimensional hyperchaotic system with wide parameter range and good randomness is designed.
- The block-divided methods make the image blocks overlap, which enables the algorithm to become more sensitive to plaintext. The pixel values in each image block are encrypted by different permutation and diffusion methods.
- The single permutation-diffusion process of the traditional methods is optimized. It uses 9n (n > 100) combinations of encryption algorithms to obtain the final encrypted image.
2. Chaotic System
2.1. Definitions
2.2. Performance Analysis of PHSL Chaotic System
2.2.1. Initial Value Sensitivity Analysis
2.2.2. Bifurcation Diagram Analysis
2.2.3. Lyapunov Exponent Analysis
2.2.4. Permutation Entropy
2.2.5. NIST Test
3. Encryption Procedure
- Step 1:
- Step 2:
- Step 3:
Algorithm 1 Permutation |
Input: |
Plain image blocks P, sequences S (S is half the size of P) |
Output: Scrambled Image Block K |
1: K ← []; |
2: K ← [S P]; %Combine S and P into one matrix |
3: K ← sortrows(K,1); %Move rows in ascending order according to the first column |
4: K ← K(:, 2:3); |
5: Output Scrambled Image Block K |
Algorithm 2 Permutation |
Input: |
Plain image blocks P, sequences S, M (S and M are half the size of P) |
Output: Scrambled Image Block K |
1: Q, X ← sort (S), sort (M); %Ascending order |
2: f = length(S); |
3: for i = 1 to f do %Quantify the elements in S to [1,f] |
4: for j = 1 to f do |
5: if Q(i) = = S(j) then |
6: S(j)←i; |
7: end |
8: end |
9: end |
10: for i = 1 to f do Quantify the elements in M to [1,f] |
11: for j = 1 to f do |
12: if X(i) = = M(j) then |
13: M(j)←i; |
14: end |
15: end |
16: end |
17: for i = 1 to f do %Scramble two columns of P according to the quantized elements in S and M |
18: K(i, 1)←P(S(i), 1); |
19: K(i, 2)←P(M(i), 2); |
20: end |
21: Output Scrambled Image Block K |
Algorithm 3 Permutation |
Input: |
Plain image blocks P, sequences S, M (The size of S is f and the size of M is N.) |
Output: Scrambled Image Block K |
1: [F, N]←size(P); % Image Block Size |
2: for i = 1 to F do %The distance to shift each row is determined by the value of the S sequence. |
3: K(i, :)←circshift(P(i, :), S(i), 2); |
4: end |
5: for i = 1 to N do %The distance to shift each column is determined by the value of the M sequence. |
6: K(:, i)←circshift(P(:, i), M(i), 1); |
7: end |
8: Output Scrambled Image Block K |
- Step 4:
- Step 5:
- Diffusion Algorithm 1:
- Diffusion Algorithm 2:
- Diffusion Algorithm 3:
4. Experimental Results and Performance Analysis
4.1. Encryption and Decryption Results
4.2. Security Analysis
4.2.1. Key Security Analysis
4.2.2. Histogram Analysis
4.2.3. Adjacent Pixel Correlation
4.2.4. Anti-Differential Attack
4.2.5. Information Entropy
4.2.6. Robustness Analysis
4.2.7. Test Analysis
4.2.8. Encryption Speed
4.2.9. Key Space
4.2.10. Time Complexity
5. Application of Color Image
5.1. Color Image Encryption and Decryption Results
5.2. Test and Analysis of Color Encrypted Image
5.2.1. Histogram Analysis
5.2.2. Correlation Analysis
5.2.3. Cropping and Decryption Results of Color Image
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Standard, D.E. Data encryption standard. In Federal Information Processing Standards Publication; Information Technology Laboratory: Gaithersburg, MD, USA, 1999; Volume 112. [Google Scholar]
- Heron, S. Advanced encryption standard (AES). Netw. Secur. 2009, 2009, 8–12. [Google Scholar] [CrossRef]
- Pak, C.; Huang, L. A new color image encryption using combination of the 1D chaotic map. Signal Processing 2017, 138, 129–137. [Google Scholar] [CrossRef]
- Jia, M. Image encryption with cross colour field algorithm and improved cascade chaos systems. IET Image Process 2020, 14, 973–981. [Google Scholar] [CrossRef]
- Yavuz, E. A novel chaotic image encryption algorithm based on content-sensitive dynamic function switching scheme. Opt. Laser Technol. 2019, 114, 224–239. [Google Scholar] [CrossRef]
- Liu, L.; Hao, S.; Lin, J. Image block encryption algorithm based on chaotic maps. IET Signal Processing 2018, 12, 22–30. [Google Scholar] [CrossRef]
- Wu, J.; Liao, X.; Yang, B. Color image encryption based on chaotic systems and elliptic curve ElGamal scheme. Signal Processing 2017, 141, 109–124. [Google Scholar] [CrossRef]
- Niyat, A.Y.; Moattar, M.H.; Torshiz, M.N. Color image encryption based on hybrid hyper-chaotic system and cellular automata. Opt. Lasers Eng. 2017, 90, 225–237. [Google Scholar] [CrossRef]
- Artiles, J.A.P.; Chaves, D.P.B.; Pimentel, C. Image encryption using block cipher and chaotic sequences. Signal Processing Image Commun. 2019, 79, 24–31. [Google Scholar] [CrossRef]
- Peng, Z.; Wang, C.; Lin, Y. A novel four-dimensional multi-wing hyper-chaotic attractor and its application in image encryption. Acta Phys. Sin. 2014, 63, 240506. [Google Scholar] [CrossRef]
- Enayatifar, R.; Abdullah, A.H.; Isnin, I.F. Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence. Opt. Lasers Eng. 2014, 56, 83–93. [Google Scholar] [CrossRef]
- Chen, J.; Zhu, Z.; Zhang, L. Exploiting self-adaptive permutation–diffusion and DNA random encoding for secure and efficient image encryption. Signal Processing 2018, 142, 340–353. [Google Scholar] [CrossRef]
- Zhou, G.; Zhang, D.; Liu, Y. A novel image encryption algorithm based on chaos and Line map. Neurocomputing 2015, 169, 150–157. [Google Scholar] [CrossRef]
- Luo, H.; Ge, B. Image encryption based on Henon chaotic system with nonlinear term. Multimed. Tools Appl. 2019, 78, 34323–34352. [Google Scholar] [CrossRef]
- Huang, X.; Liu, L.; Li, X. A new two-dimensional mutual coupled logistic map and its application for pseudorandom number generator. Math. Probl. Eng. 2019, 2019, 7685359. [Google Scholar] [CrossRef] [Green Version]
- Liu, Y.; Wang, J.; Fan, J. Image encryption algorithm based on chaotic system and dynamic S-boxes composed of DNA sequences. Multimed. Tools Appl. 2016, 75, 4363–4382. [Google Scholar] [CrossRef]
- Zheng, J.; Liu, L.F. Novel image encryption by combining dynamic DNA sequence encryption and the improved 2D logistic sine map. IET Image Processing 2020, 14, 2310–2320. [Google Scholar] [CrossRef]
- Ma, Y.; Li, C.; Ou, B. Cryptanalysis of an image block encryption algorithm based on chaotic maps. J. Inf. Secur. Appl. 2020, 54, 102566. [Google Scholar] [CrossRef]
- Li, C.; Feng, B.; Li, S. Dynamic analysis of digital chaotic maps via state-mapping networks. IEEE Trans. Circuits Syst. I Regul. Pap. 2019, 66, 2322–2335. [Google Scholar] [CrossRef] [Green Version]
- Wang, X.; Gao, S. Image encryption algorithm based on the matrix semi-tensor product with a compound secret key produced by a Boolean network. Inf. Sci. 2020, 539, 195–214. [Google Scholar] [CrossRef]
- Wu, Y.; Noonan, J.P.; Yang, G. Image encryption using the two-dimensional logistic chaotic map. J. Electron. Imaging 2012, 21, 013014. [Google Scholar] [CrossRef]
- Hua, Z.; Zhou, Y.; Pun, C.M. 2D Sine Logistic modulation map for image encryption. Inf. Sci. 2015, 297, 80–94. [Google Scholar] [CrossRef]
- Li, C.; Luo, G.; Qin, K. An image encryption scheme based on chaotic tent map. Nonlinear Dyn. 2017, 87, 127–133. [Google Scholar] [CrossRef]
- Rashmi, P.; Supriya, M.C.; Kiran, K. Image Encryption Algorithm based on 2D Hyper Chaotic Map and Trigonometric Functions. In Proceedings of the 2021 IEEE International Conference on Mobile Networks and Wireless Communications (ICMNWC), Tumkur, India, 3–4 December 2021; pp. 1–4. [Google Scholar]
- Hua, Z.; Zhou, Y. Image encryption using 2D Logistic-adjusted-Sine map. Inf. Sci. 2016, 339, 237–253. [Google Scholar] [CrossRef]
- Chen, Z.; Yuan, X.; Yuan, Y. Parameter identification of chaotic and hyper-chaotic systems using synchronization-based parameter observer. IEEE Trans. Circuits Syst. I Regul. Pap. 2016, 63, 1464–1475. [Google Scholar] [CrossRef]
- Hua, Z.; Zhou, B.; Zhou, Y. Sine-transform-based chaotic system with FPGA implementation. IEEE Trans. Ind. Electron. 2017, 65, 2557–2566. [Google Scholar] [CrossRef]
- Xie, E.Y.; Li, C.; Yu, S. On the cryptanalysis of Fridrich’s chaotic image encryption scheme. Signal Processing 2017, 132, 150–154. [Google Scholar] [CrossRef] [Green Version]
- Jeng, F.G.; Huang, W.L.; Chen, T.H. Cryptanalysis and improvement of two hyper-chaos-based image encryption schemes. Signal Processing: Image Commun. 2015, 34, 45–51. [Google Scholar] [CrossRef]
- Wang, X.; Chen, S.; Zhang, Y. A chaotic image encryption algorithm based on random dynamic mixing. Opt. Laser Technol. 2021, 138, 106837. [Google Scholar] [CrossRef]
- Wang, X.; Chen, F.; Wang, T. A new compound mode of confusion and diffusion for block encryption of image based on chaos. Commun. Nonlinear Sci. Numer. Simul. 2010, 15, 2479–2485. [Google Scholar] [CrossRef]
- Xian, Y.; Wang, X.; Yan, X. Image encryption based on chaotic sub-block scrambling and chaotic digit selection diffusion. Opt. Lasers Eng. 2020, 134, 106202. [Google Scholar] [CrossRef]
- Khan, J.S.; Ahmad, J. Chaos based efficient selective image encryption. Multidimens. Syst. Signal Processing 2019, 30, 943–961. [Google Scholar] [CrossRef]
- Wolf, A.; Swift, J.B.; Swinney, H.L. Determining Lyapunov exponents from a time series. Phys. D Nonlinear Phenom. 1985, 16, 285–317. [Google Scholar] [CrossRef] [Green Version]
- Bandt, C.; Pompe, B. Permutation entropy: A natural complexity measure for time series. Phys. Rev. Lett. 2002, 88, 174102. [Google Scholar] [CrossRef] [PubMed]
- Wang, G.Y.; Yuan, F. Cascade chaos and its dynamic characteristics. Acta Phys. Sin. 2013, 62, 020506. [Google Scholar] [CrossRef]
- He, D.; He, C.; Jiang, L.G. A chaotic map with infinite collapses. In Proceedings of the Intelligent Systems and Technologies for the New Millennium (Cat. No. 00CH37119), Kuala Lumpur, Malaysia, 24–27 September 2000; Volume 3, pp. 95–99. [Google Scholar]
- Khaitan, S.; Sagar, S.; Agarwal, R. Chaos based image encryption using 3-Dimension logistic map. Mater. Today Proc. 2021; in press. [Google Scholar] [CrossRef]
- Ramakrishnan, A.; Ramanujam, K. Designing a fast image encryption scheme using fractal function and 3D Henon map. J. Inf. Secur. Appl. 2019, 49, 102390. [Google Scholar]
- Enayatifar, R.; Abdullah, A.H.; Isnin, I.F. Image encryption using a synchronous permutation-diffusion technique. Opt. Lasers Eng. 2017, 90, 146–154. [Google Scholar] [CrossRef]
- Kaur, M.; Kumar, V. Efficient image encryption method based on improved Lorenz chaotic system. Electron. Lett. 2018, 54, 562–564. [Google Scholar] [CrossRef]
- Wu, J.; Liao, X.; Yang, B. Image encryption using 2D Hénon-Sine map and DNA approach. Signal Processing 2018, 153, 11–23. [Google Scholar] [CrossRef]
- Wang, X.; Zhang, M. An image encryption algorithm based on new chaos and diffusion values of a truth table. Inform. Sci. 2021, 579, 128–149. [Google Scholar] [CrossRef]
- Xingyuan, W.; Chuanming, L.; Dahai, X. Image encryption scheme using chaos and simulated annealing algorithm. Nonlinear Dyn. 2016, 84, 1417–1429. [Google Scholar]
- Farah, M.A.; Farah, A.; Farah, T. An image encryption scheme based on a new hybrid chaotic map and optimized substitution box. Nonlinear Dyn. 2020, 99, 3041–3064. [Google Scholar] [CrossRef]
- Amira, G.M.; Noha, O.K.; Said, E.E. New DNA Coded Fuzzy Based(DNAFZ) S-Boxes: Application to Robust Image Encryption Using Hyper Chaotic Maps. IEEE Access 2021, 9, 14284–14305. [Google Scholar]
- Liao, X.; Kulsoom, A.; Abbas, S.A. Selective encryption for gray images based on chaos and DNA complementary rules. Multimed. Tools Appl. 2015, 74, 4655–4677. [Google Scholar]
- Wang, X.; Zhao, M. An image encryption algorithm based on hyperchaotic system and DNA coding. Opt. Laser Technol. 2021, 143, 107316. [Google Scholar] [CrossRef]
- Teng, L.; Wang, X. A bit-level image encryption algorithm based on spatiotemporal chaotic system and self-adaptive. Opt. Commun. 2012, 285, 4048–4054. [Google Scholar] [CrossRef]
- Chai, X.; Zheng, X.; Gan, Z.; Han, D.; Chen, Y. An image encryption algorithm based on chaotic system. Signal Processing 2018, 148, 124–144. [Google Scholar] [CrossRef]
- Hua, Z.; Zhou, Y. Design of image cipher using block-based scrambling and image filtering. Inf. Sci. 2017, 396, 97–113. [Google Scholar] [CrossRef]
System | Parameter | PE |
---|---|---|
PHSL | a = 4.99 b = 57 c = 0.23 | 0.995 |
Logistic [21] | μ = 4 | 0.679 |
Sine [22] | μ = 1 | 0.669 |
LT [36] | μ = 4 a = 2 | 0.943 |
ICMIC [37] | c = 3 | 0.942 |
3D Logistic [38] | Γ = 3.8 β = 0.021 α = 0.014 | 0.987 |
3D Hénon [39] | m = 1.7 p = 1.0 q = 0.4 | 0.989 |
The Items Used for Testing | Success Rate | The Items Used for Testing | Success Rate | The Items Used for Testing | Success Rate |
---|---|---|---|---|---|
Approximate Entropy | 100% | Linear Complexity | 95% | Random Excursions Variant | 99.5% |
Block Frequency | 98.5% | Longest Run | 96.5% | Rank | 99% |
CumulativeSums | 96.5% | NonOverlapping Template | 98.5% | Runs | 99% |
FFT | 99.5% | Overlapping Template | 98.5% | Serial | 98% |
Frequency | 95.5% | Random Excursions | 99% | Universal | 100% |
Image | Plain | Proposed | Ref. [8] | Ref. [30] | Ref. [38] | Ref. [40] | Ref. [41] | Ref. [42] | |
---|---|---|---|---|---|---|---|---|---|
Lena | Horizontal | 0.93853 | −0.0018 | 0.0061 | 0.0083 | 0.0054 | 0.0023 | — | 0.0056 |
Vertical | 0.9702 | −0.0017 | 0.0116 | −0.0021 | 0.0063 | 0.0019 | — | 0.0037 | |
Diagonal | 0.91697 | 0.0001 | 0.0018 | −0.0025 | 0.0023 | 0.0011 | — | 0.0032 | |
Plane | Horizontal | 0.94437 | 0.0003 | 0.0054 | −0.0209 | — | 0.0062 | 0.0012 | 0.0028 |
Vertical | 0.93332 | −0.0064 | 0.0089 | 0.0083 | — | 0.0074 | −0.0063 | 0.0041 | |
Diagonal | 0.89198 | −0.0033 | 0.0021 | −0.0070 | — | 0.0009 | 0.0058 | 0.0010 | |
Pepper | Horizontal | 0.96038 | 0.0039 | 0.0049 | 0.0067 | — | 0.0037 | 0.0001 | 0.0016 |
Vertical | 0.97153 | −0.0026 | 0.0031 | −0.0050 | — | 0.0258 | −0.0008 | 0.0059 | |
Diagonal | 0.93645 | −0.0034 | 0.0079 | −0.0059 | — | 0.0079 | 0.0002 | 0.0034 | |
Baboon | Horizontal | 0.86456 | −0.0066 | 0.0060 | — | — | 0.0059 | — | 0.0026 |
Vertical | 0.82162 | 0.0007 | 0.0058 | — | — | 0.0041 | — | 0.0009 | |
Diagonal | 0.77757 | −0.0024 | 0.0016 | — | — | 0.0028 | — | 0.0052 |
Image | Proposed | Ref. [8] | Ref. [38] | Ref. [40] | Ref. [41] | Ref. [42] |
---|---|---|---|---|---|---|
Lena | 0.996048 | 0.996152 | 0.9961 | 0.996304 | — | 0.996002 |
Plane | 0.996025 | 0.994350 | — | 0.994883 | 0.9967 | 0.996261 |
Pepper | 0.996071 | 0.996202 | — | 0.993017 | 0.9970 | 0.996112 |
Cameraman | 0.996084 | 0.996405 | — | 0.992052 | — | 0.996082 |
Baboon | 0.996155 | 0.995966 | — | 0.992394 | — | 0.995903 |
Average value | 0.996077 | 0.995815 | — | 0.99373 | 0.9969 | 0.996072 |
Image | Proposed | Ref. [8] | Ref. [38] | Ref. [40] | Ref. [41] | Ref. [42] |
---|---|---|---|---|---|---|
Lena | 0.334389 | 0.335024 | 0.3343 | 0.335989 | — | 0.335079 |
Plane | 0.334199 | 0.334109 | — | 0.333562 | 0.3361 | 0.335782 |
Pepper | 0.335157 | 0.335323 | — | 0.330026 | 0.3358 | 0.335265 |
Cameraman | 0.333959 | 0.334109 | — | 0.334390 | — | 0.335574 |
Baboon | 0.335558 | 0.335016 | — | 0.333144 | — | 0.335281 |
Average value | 0.3346524 | 0.3347162 | — | 0.3334222 | 0.3360 | 0.3353962 |
Image | Plain | Proposed | Ref. [8] | Ref. [23] | Ref. [38] | Ref. [40] | Ref. [41] | Ref. [42] |
---|---|---|---|---|---|---|---|---|
512 × 512 | ||||||||
Cameraman | 7.0480 | 7.9993 | 7.9993 | 7.9923 | - | 7.9972 | - | 7.9993 |
Lena | 7.4451 | 7.9992 | 7.9995 | 7.9924 | 7.9974 | 7.9994 | - | 7.9994 |
Plane | 6.7135 | 7.9993 | 7.9991 | 7.9925 | - | 7.9991 | 7.9990 | 7.9992 |
Pepper | 6.7624 | 7.9993 | 7.9990 | 7.9921 | - | 7.9983 | - | 7.9993 |
Baboon | 7.2925 | 7.9992 | 7.9990 | 7.9922 | - | 7.9981 | 7.9989 | 7.9992 |
Image | Lena | Plane | Pepper | Baboon | Black | White |
---|---|---|---|---|---|---|
Plain | 158,345 | 17,446 | 31,989 | 42,256 | 16,711,680 | 16,711,680 |
Proposed | 255.8 | 265.1 | 250.32 | 252.3 | 261.7 | 264.9 |
Encryption Time (s) | Decryption Time (s) | |
---|---|---|
Ours (256 × 256) | 0.176182 | 0.189482 |
Ours (512 × 512) | 0.526771 | 0.514788 |
Proposed | Ref. [51] | Ref. [49] | Ref. [50] |
---|---|---|---|
O(m2 + n2 + m + n) | ) | O(MNlog(MN) + 4MNlog(4MN)) + 3O(4MN) | O(M^2*N^2) |
Plain Image | Horizontal | Vertical | Diagonal |
---|---|---|---|
R | 0.9411 | 0.9705 | 0.9164 |
G | 0.9434 | 0.9719 | 0.9204 |
B | 0.88989 | 0.9433 | 0.8493 |
Cipher image | |||
R | −0.0035 | 0.0010 | 0.0008 |
G | 0.0006 | −0.0062 | 0.0033 |
B | 0.0006 | −0.0068 | 0.0023 |
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Ran, B.; Zhang, T.; Wang, L.; Liu, S.; Zhou, X. Image Security Based on Three-Dimensional Chaotic System and Random Dynamic Selection. Entropy 2022, 24, 958. https://doi.org/10.3390/e24070958
Ran B, Zhang T, Wang L, Liu S, Zhou X. Image Security Based on Three-Dimensional Chaotic System and Random Dynamic Selection. Entropy. 2022; 24(7):958. https://doi.org/10.3390/e24070958
Chicago/Turabian StyleRan, Bo, Tianshuo Zhang, Lihong Wang, Sheng Liu, and Xiaoyi Zhou. 2022. "Image Security Based on Three-Dimensional Chaotic System and Random Dynamic Selection" Entropy 24, no. 7: 958. https://doi.org/10.3390/e24070958