An Innovative Algorithm Based on Chaotic Maps Amalgamated with Bit-Level Permutations for Robust S-Box Construction and Its Application in Medical Image Privacy
Abstract
:1. Introduction
1.1. Motivation
1.2. Contribution
- The proposed cryptographic solution deals with chaos theory and an approach that combines the complexity and natural unpredictability of chaotic systems to create security models.
- This paper presents a symmetric block encryption technique using a permutation group to operate a set of pseudo-random numbers generated by the chaotic maps.
- The technique iterates the chaotic map between a pair’s changes to produce a binary output. Furthermore, we adjust these sequences to construct a solid substitution box (S-box), a crucial aspect of cryptographic systems.
- Furthermore, block substitution in the encryption process involves unique permutations that are critical for strong encryption because they create confusion and diffusion.
- The proposed method effectively demonstrates its application of medical image confidentiality through a thorough analysis based on several metrics compared to the existing methodologies.
2. Chaos Theory
2.1. Tent Map
2.2. May Map
3. Novel Tent–May Map
3.1. Detailed Analysis of the Novel Tent-May Map
Conversion between Tent and May Maps
- a.
- Tent Map Region
- b.
- May Map Region
4. Cryptographic Applications
Algorithm 1: Construction of | |
00 | Input: |
01 | Initialize parameter and iterations |
02 | |
03 | Output: |
04 | |
05 | |
06 | Iterate Tent–May Map: |
07 | from to iterations |
08 | Calculate by Tent–May Map |
09 | |
10 | Store each value in array (say) |
11 | |
12 | Initialize arrays and : |
13 | for from to iterations: |
14 | Calculate by converting each value to binary |
15 | End |
16 | |
17 | for from to iterations: |
18 | Calculate by Transforming values of to binary |
19 | End |
20 | |
21 | Perform the operation between and |
22 | Convert to binary string |
23 | |
24 | Make segments of bits: |
25 | Convert each segment to decimal |
26 | |
27 | Find unique values: |
28 | Store the unique values in array |
29 | |
30 | Update Array : |
31 | Add fixed integer to each value and restrict between |
32 | Convert each to binary |
33 | Reordered the bits with unique pattern. |
34 | Convert the rearranged binary string back to decimal. |
35 | |
36 | Find : |
37 | is generated by updated values. |
38 | Interchange the position of fix point with first element in |
39 | |
40 | Tweaking the Nonlinearity: |
41 | Take the Action of a permutation group |
with generators and of order on , through | |
right mutilation. | |
42 | |
43 | Update : |
44 | |
45 | End |
5. Performance Analysis for Proposed S-Box
- —Nonlinearity;
- —Strict Avalanche Criterion;
- —Bit Independent Criterion;
- —Linear Approximation Probability;
- —Differential Approximation Probability.
5.1. Nonlinearity (NL)
5.2. Strict Avalanche Criterion (SAC)
5.3. Bit Independence Criterion (BIC)
5.4. Linear Approximation Probability
5.5. Differential Approximation Probability
6. Proposed Algorithm of Image Encryption
Algorithm 2: Image Encryption Algorithm | ||
00. | Input: | Input image |
01. | Substitution box | |
02. | Key (8-byte key) | |
03. | Output: | Encrypted image |
04. | Step 1: | |
05. | Perform block-wise substitution for the first round: | |
06. | Divide the image into blocks of size | |
07. | For each block: | |
08. | Extract the block. | |
09. | Perform substitution for each pixel in the block using the key. | |
10. | Update the encrypted image with the substituted block. | |
11. | Write the encrypted image to file Enc_round_1 | |
12. | Step 2: | |
13. | Perform permutation for the second round: | |
14. | Reshape the encrypted image into a vector. | |
15. | ||
16. | Permute the reshaped vector according to the permutation vector. | |
17. | Reshape the permuted vector back into the image shape. | |
18. | Write the encrypted image to file Enc_round_2 |
7. Proposed Technique Analysis
Histogram
8. Majority Logical Criterion (MLC)
8.1. Homogeneity Analysis
8.2. Energy
8.3. Contrast
9. Adjacent Pixel Correlation
10. Information Entropy
11. Encrypted Image Quality Measure
11.1. Mean Square Error (MSE)
11.2. Peak Signal-To-Noise Ratio (PSNR)
11.3. Structural Similarity Index Method (SSIM)
11.4. Average and Maximum Difference (AD and MD)
11.5. Structural Content (SC)
11.6. Normalized Cross-Correlation (NCC)
11.7. Normalized Absolute Error (NAE)
11.8. Root Mean Square Error (RMSE)
12. NPCR, UACI, and & BACI Analysis
13. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Boolean Function | ||||||||
NL Score |
S-Box | Minimum NL | Maximum NL | Average NL |
---|---|---|---|
Proposed | |||
[32] | |||
[33] | |||
[34] | |||
[35] | |||
[36] | |||
[37] | |||
[38] | |||
[39] | |||
[40] | |||
[41] | |||
[42] | |||
[43] | |||
[44] | |||
[45] |
S-Box | SAC | SAC-Offset | BIC-NL | LP | DP |
---|---|---|---|---|---|
Proposed | |||||
[32] | |||||
[33] | |||||
[34] | |||||
[35] | |||||
[36] | |||||
[37] | |||||
[38] | |||||
[39] | |||||
[40] | |||||
[41] | |||||
[42] | |||||
[43] | |||||
[44] | |||||
[45] |
Images | Approach | Contrast | Correlation | Energy | Homogeneity | |
---|---|---|---|---|---|---|
Medical_Image_1 | Original | |||||
Proposed | ||||||
Ref. [36] | ||||||
Ref. [53] | ||||||
Ref. [54] | ||||||
Ref. [55] | ||||||
Medical_Image_2 | Original | |||||
Proposed | ||||||
Ref. [36] | ||||||
Ref. [53] | ||||||
Ref. [54] | ||||||
Ref. [55] | ||||||
Medical_Image_3 | Original | |||||
Proposed | ||||||
Ref. [36] | ||||||
Ref. [53] | ||||||
Ref. [54] | ||||||
Ref. [55] | ||||||
Original | ||||||
Proposed | ||||||
Ref. [36] | ||||||
Medical_Image_4 | Ref. [53] | |||||
Ref. [54] | ||||||
Ref. [55] |
Images | Information Entropy Values |
---|---|
Medical_Image_1 Org | |
Medical_Image_1 Enc | |
Medical_Image_2 Org | |
Medical_Image_2 Enc | |
Medical_Image_3 Org | |
Medical_Image_3 Enc | |
Medical_Image_4 Org | |
Medical_Image_4 Enc |
Images | MSE | PSNR | MD | AD | UQI | SSIM | NCC | NAE | SC | RMSC |
---|---|---|---|---|---|---|---|---|---|---|
Med_Imege_1 | ||||||||||
Med_Imege_2 | ||||||||||
Med_Imege_3 | ||||||||||
Med_Imege_4 |
Images | UACI% | NPCR% | BACI% |
---|---|---|---|
Medical_Image_1 | 43.6086 | 26.6778 | |
Medical_Image_2 | 99.4961 | ||
Medical_Image_3 | |||
Medical_Image_4 |
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Hazzazi, M.M.; Baowidan, S.A.; Yousaf, A.; Adeel, M. An Innovative Algorithm Based on Chaotic Maps Amalgamated with Bit-Level Permutations for Robust S-Box Construction and Its Application in Medical Image Privacy. Symmetry 2024, 16, 1070. https://doi.org/10.3390/sym16081070
Hazzazi MM, Baowidan SA, Yousaf A, Adeel M. An Innovative Algorithm Based on Chaotic Maps Amalgamated with Bit-Level Permutations for Robust S-Box Construction and Its Application in Medical Image Privacy. Symmetry. 2024; 16(8):1070. https://doi.org/10.3390/sym16081070
Chicago/Turabian StyleHazzazi, Mohammad Mazyad, Souad Ahmad Baowidan, Awais Yousaf, and Muhammad Adeel. 2024. "An Innovative Algorithm Based on Chaotic Maps Amalgamated with Bit-Level Permutations for Robust S-Box Construction and Its Application in Medical Image Privacy" Symmetry 16, no. 8: 1070. https://doi.org/10.3390/sym16081070