1 Introduction
2 Literature Review
3 Contributions
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Designing an effective multi-stage cryptographic algorithm for medical images encryption using substitution-permutation technique. This multi-stage cryptographic algorithm uses random numbers generated from chaos maps which reduces correlation among the pixels of the digital medical images.
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Designing a contemporary variant of the chaos-based confusion-diffusion approach that is capable of achieving a significant higher entropy and NIST-based randomness results as compared to existing methods. The results demonstrate that the proposed encryption algorithm is able to generate highly secured medical encrypted images.
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Analysing the performance of the proposed system and comparing it with several existing approaches used in cryptosystems. The efficiency of each algorithm is analyzed in terms of histogram consistency analysis and its variance (HCAV), adjacent pixels correlation analysis (APCA), contrast analysis (CA), homogeneity analysis (HA), energy analysis (EA), NIST analysis, information entropy (IE), a number of pixels changing rate (NPCR), unified average changing intensity (UACI), mean square error (MSE), peak to signal noise ratio (PSNR), and time complexity (TC).
4 Proposed Algorithm
4.1 Henon Chaotic Map (HCM)
4.1.1 Brownian Motion (BM)
4.1.2 Chaotic Chen System (CSS)
4.2 The Proposed Algorithm
5 Experimental Results
5.1 Histogram Analysis
5.2 Adjacent Pixels Correlation Analysis
Images | Plain image dimensions | Encrypted image dimensions | |||||||
---|---|---|---|---|---|---|---|---|---|
H-D | D-D | V-D | A-V | H-D | D-D | V-D | A-V | ||
1 | Chest-X direction | 0.9988 | 0.9975 | 0.9985 | NA | 0.0023 | − 0.0008 | 0.0007 | NA |
2 | Chest-Y direction | 0.9988 | 0.9975 | 0.9985 | NA | − 0.0012 | 0.0021 | − 0.0002 | NA |
3 | Chest-Z direction | 0.9988 | 0.9975 | 0.9985 | NA | − 0.0035 | 0.0016 | 0.0003 | NA |
4 | Brain-X direction | 0.9831 | 0.9566 | 0.9713 | NA | 0.0000 | − 0.0030 | − 0.0029 | NA |
5 | Brain-Y direction | 0.9831 | 0.9566 | 0.9713 | NA | 0.0014 | 0.0002 | − 0.0009 | NA |
6 | Brain-Z direction | 0.9831 | 0.9566 | 0.9713 | NA | − 0.0004 | 0.0020 | 0.0002 | NA |
7 | MR-X direction | 0.9850 | 0.9783 | 0.9881 | NA | 0.0021 | − 0.0016 | 0.0065 | NA |
8 | MR-Y direction | 0.9850 | 0.9783 | 0.9881 | NA | 0.0010 | 0.0007 | 0.0058 | NA |
9 | MR-Z direction | 0.9850 | 0.9783 | 0.9881 | NA | 0.0020 | − 0.0022 | 0.0050 | NA |
6 | [5] | 0.9727 | 0.9204 | 0.9573 | - | − 0.0394 | − 0.0194 | − 0.0223 | – |
7 | [35] | – | – | – | – | 0.0681 | 0.0128 | 0.0049 | – |
8 | [25] | – | – | – | – | 0.0965 | 0.0362 | − 0.0581 | – |
9 | [18] | – | – | – | – | 0.1257 | 0.0226 | 0.0581 | – |
5.3 Homogeneity, Energy and Contrast Analyses
S. no. | Algorithms | Homogeneity | Energy | Contrast |
---|---|---|---|---|
1 | Chest | 0.3890 | 0.0156 | 10.5305 |
2 | Brain | 0.3895 | 0.0156 | 10.5081 |
3 | MR | 0.3933 | 0.0157 | 10.2801 |
S. no. | Algorithms | Homogeneity | Energy | Contrast |
---|---|---|---|---|
1 | Chest | 0.3894 | 0.0156 | 10.4844 |
2 | Brain | 0.3888 | 0.0156 | 10.5022 |
3 | MR | 0.3936 | 0.0157 | 10.2778 |
S. no. | Algorithms | Homogeneity | Energy | Contrast |
---|---|---|---|---|
1 | Chest | 0.3899 | 0.0156 | 10.4780 |
2 | Brain | 0.3894 | 0.0156 | 10.4716 |
3 | MR | 0.3932 | 0.0157 | 10.2948 |
5.4 NIST Analyses
Test | p values for grey medical Chest image along three direction | Results | |||||
---|---|---|---|---|---|---|---|
Plain | X direction | Y direction | Z direction | ||||
Frequency | \(3.5568\times 10^{-07}\) | 0.72795 | 0.48662 | 0.65797 | Success | ||
Block frequency | \(4.9729\times 10^{-09}\) | 0.80617 | 0.82067 | 0.53435 | Success | ||
Rank | 0.29191 | 0.29191 | 0.29191 | 0.29191 | Success | ||
Runs (M = 10,000) | 0.75417 | 0.97325 | 0.35506 | 0.75417 | Success | ||
Long runs of ones | 0.035752 | 0.035752 | 0.035752 | 0.035752 | Success | ||
Overlapping templates | 0.85988 | 0.85988 | 0.85988 | 0.85988 | Success | ||
No overlapping templates | 0.99999 | 0.99995 | 0.93985 | 0.99999 | Success | ||
Spectral DFT | 0.66336 | 0.77167 | 0.77167 | 0.66336 | Success | ||
Approximate entropy | 0.39444 | 0.26251 | 0.85323 | 0.39444 | Success | ||
Universal | 0.99931 | 0.99574 | 0.98619 | 0.99931 | Success | ||
Serial | p values 1 | 0.70248 | 0.37715 | 0.22973 | 0.70248 | Success | |
Serial | p values 2 | 0.49286 | 0.12465 | 0.21782 | 0.49286 | Success | |
Cumulative sums forward | 0.27679 | 0.24206 | 0.23771 | 0.27679 | Success | ||
Cumulative sums reverse | 0.77056 | 1.1217 | 0.85465 | 0.77506 | Success |
5.5 Differential Attack Analysis
5.5.1 Number of Pixels Changing Rate
5.5.2 Unified Average Changing Intensity
S. no. | Images | Direction | NPCR values | UACI values |
---|---|---|---|---|
1 | Chest | X-direction | 99.62 | 33.65 |
2 | Chest | Y-direction | 99.63 | 33.60 |
3 | Chest | Z-direction | 99.63 | 33.54 |
4 | Brain | X-direction | 99.60 | 33.61 |
5 | Brain | Y-direction | 99.62 | 33.59 |
6 | Brain | Z-direction | 99.59 | 33.64 |
7 | MR | X-direction | 99.62 | 33.36 |
8 | MR | Y-direction | 99.61 | 33.27 |
9 | MR | Z-direction | 99.60 | 33.32 |
5.6 Pixel’s Inconsistency Analysis
5.6.1 Mean Square Error
5.6.2 Peak to Signal Noise Ratio
S. no. | Algorithms | X-direction | Y-direction | Z-direction | X-direction | Y-direction | Z-direction |
---|---|---|---|---|---|---|---|
1 | Chest | 11025.61 | 10998.49 | 11028.51 | 7.74 | 7.75 | 7.74 |
2 | Brain | 12352.67 | 12318.60 | 12291.03 | 7.25 | 7.26 | 7.27 |
3 | MR | 11484.95 | 11495.07 | 11425.25 | 7.56 | 7.56 | 7.58 |
5.7 Entropy Analysis
S. no | Name | Along X | Along Y | Along Z |
---|---|---|---|---|
1 | Actual entropy | 7.0899 | 7.0899 | 7.0899 |
2 | Ideal entropy | 8.0000 | 8.0000 | 8.0000 |
3 | Ciphered | 7.9994 | 7.9993 | 7.9993 |
S. no | Name | Along X | Along Y | Along Z |
---|---|---|---|---|
1 | Actual entropy | 7.0634 | 7.0634 | 7.0634 |
2 | Ideal entropy | 8.0000 | 8.0000 | 8.0000 |
3 | Ciphered | 7.9986 | 7.9986 | 7.9986 |
S. No | Name | Along X | Along Y | Along Z |
---|---|---|---|---|
1 | Actual entropy | 7.2399 | 7.2399 | 7.2399 |
2 | Ideal entropy | 8.0000 | 8.0000 | 8.0000 |
3 | Ciphered | 7.9993 | 7.9993 | 7.9993 |