Parallel and Practical Approach of Efficient Image Chaotic Encryption Based on Message Passing Interface (MPI)
Abstract
:1. Introduction
2. Related Work
2.1. Stream Ciphers Algorithms
2.2. Related Papers
3. Parallel Programming Models and Techniques
4. Proposed Parallel Chaos Crypto System
Algorithm 1 PARALLEL IMAGE CHAOS ENCRYPTION ALGORITHM 
Input: clear image Output: Scrambled Encrypted image

5. Performance Computation of Proposed Parallel Computing
5.1. SpeedUp Calculations
5.2. Amdahl’s Law
6. Security
6.1. Keyspace
6.2. Key Security and Sensitivity Attack
6.3. Information Entropy
7. Statistical Analysis
7.1. NIST Test
7.2. ChiSquare Test and Histogram
8. Correlation Analysis
9. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Data  NCpB_Seq  NCpB_Pthread  NCpB_MPI 

64  242.1  13,463.2  48.4 
128  184.0  6726.8  53.3 
256  114.6  2791.9  53.3 
512  127.1  1326.9  23.0 
1024  292.0  9879.8  44.0 
2048  155.9  8295.0  44.9 
4096  82.1  3586.4  27.1 
16,384  44.9  649.9  24.6 
32,768  37.6  443.6  24.1 
65,536  34.7  189.8  23.6 
125,000  34.6  141.4  24.8 
196,608  34.7  78.0  23.3 
3,145,728  32.0  26.3  22.2 
Data  Gen_Time_Seq  Gen_Time_Pthread  Gen_Time_MPI 

64  25  1390  5 
128  38  1389  11 
256  49  1153  22 
512  105  1096  19 
1024  471  15,938  71 
2048  503  26,763  145 
4096  530  23,142  175 
16,384  1180  17,090  646 
32,768  1982  23,400  1271 
65,536  3665  20,052  2489 
125,000  6973  28,523  5008 
196,608  10,990  24,748  7391 
3,145,728  162,322  133,493  116,401 
Algorithm  Image Size  Enc_Time (Ms)  ET (Mbit/s)  NCpB 

Rabbit  $256\times 256\times 3$  811.3  1848.8  9.5 
$512\times 512\times 3$  3256  1842.6  9.5  
$1024\times 1024\times 3$  12,950  1853.9  9.5  
HC128  $256\times 256\times 3$  1221  1228.1  14.4 
$512\times 512\times 3$  4895  1225.6  14.4  
$1024\times 1024\times 3$  19,647  1221.5  14.4  
Salsa 20/12  $256\times 256\times 3$  836.4  1793.4  9.8 
$512\times 512\times 3$  3389  1770  9.8  
$1024\times 1024\times 3$  13,483  1779.9  9.8  
AbuTaha Chaos Stream Cipher(Seq)  $256\times 256\times 3$  5838  1077.63  18.4 
$512\times 512\times 3$  —  —  —  
$1024\times 1024\times 3$  97,584  1031.55  19.2  
AbuTaha Chaos Stream Cipher(Pthread)  $256\times 256\times 3$  17,148  366.88  54.1 
$512\times 512\times 3$  —  —  —  
$1024\times 1024\times 3$  80,568  1249.41  16.7  
Parallel Proposed Chaos CryptoSystem(MPI)  $256\times 256\times 3$  4387  1434.06  13.8 
$512\times 512\times 3$  —  —  21.2  
$1024\times 1024\times 3$  69,631  1445.65  13.2 
Data  BR_Seq  BR_Pthread  BR_MPI 

64  81.92  1.47  409.60 
128  107.79  2.95  372.36 
256  173.06  7.10  372.36 
512  156.04  14.95  862.32 
1024  67.94  2.01  450.70 
2048  127.24  2.39  441.38 
4096  241.51  5.53  731.43 
16,384  442.03  30.52  807.43 
32,768  527.95  44.72  823.29 
65,536  571.90  104.53  842.11 
125,000  573.64  140.24  798.72 
196,608  572.45  254.21  851.20 
3,145,728  620.14  754.07  864.79 
Data  NCpB_Seq  NCpB_Pthread  NCpB_MPI 

64  164.7  9065.9  96.9 
128  116.2  4663.7  33.9 
256  96.9  2767.7  31.5 
512  89.6  1348.7  24.2 
1024  78.7  638.0  23.6 
2048  116.5  2532.9  21.4 
4096  58.1  1215.3  18.0 
16,384  27.2  510.9  15.1 
125,000  18.4  71.5  14.1 
196,608  18.4  54.1  13.8 
3,145,728  19.2  16.7  13.2 
Data  Gen_Time_Seq  Gen_Time_Pthread  Gen_Time_MPI 

64  17  936  10 
128  24  963  7 
256  40  1143  13 
512  1114  1114  20 
1024  130  1054  39 
2048  376  8172  69 
4096  375  7842  116 
16,384  715  13,435  398 
125,000  3714  14,416  2844 
19,6608  5838  17,148  4387 
3,145,728  97,584  80,568  69,631 
Data  BR_Seq  BR_Pthread  BR_MPI 

64  120.47  2.19  204.80 
128  170.67  4.25  585.14 
256  204.80  7.17  630.15 
512  221.41  14.71  819.20 
1024  252.06  31.09  840.21 
2048  170.21  7.83  927.54 
4096  341.33  16.32  1103.45 
16,384  729.51  38.82  1310.55 
125,000  1077.01  277.47  1406.47 
196,608  1077.63  366.88  1434.06 
3,145,728  1031.55  1249.41  1445.65 
Encryption Algorithm  Keyspace 

Proposed Algorithm  ${2}^{555}$ 
Wange et al.’s Algorithm [35]  ${2}^{149}$ 
Guesmi et al.’s Algorithm [36]  ${2}^{256}$ 
Curiac et al.’s Algorithm [37]  ${2}^{128}$ 
Curiacet al.’s Algorithm [38]  ${2}^{357}$ 
Zhu et al.’s Algorithm [39]  ${2}^{339}$ 
Cryptosystem  NPCR  UACI 

Proposed Cipher Cryptosystem  99.665  33.459 
[41]  99.4  32.7 
[42]  99.1  32.8 
[43]  98.8  31.7 
[44]  99.1  32.8 
[45]  99.6  33.1 
[46]  99.6  33.3 
[47]  99.6  33.3 
[47]  99.6  33.3 
[48]  99.64  33.4 
[49]  99.66  33.43 
Ciphered Image  Sharukhan  Titanic  Photographer  Manhattan  Cameraman  Boat  Lena 

entropy  7.9999  7.9999  7.9999  7.9999  7.9998  7.9997  7.9999 
Encryption Method  Information Entropy 

Proposed Algorithm  7.9999 
[41]  7.9973 
[42]  7.9975 
[43]  7.9977 
[44]  7.9973 
[45]  7.9982 
[46]  7.99 
[47]  7.990 
[48]  7.908 
Test  p_Value  Proportion 

Frequency test  0.494  97.000 
Blockfrequency test  0.760  100.000 
Cumulativesums test  0.797  97.000 
Runs test  0.596  99.000 
Longestrun test  0.699  98.000 
Rank test  0.029  100.000 
FFT test  0.834  98.0000 
Nonperiodictemplates  0.479  99.000 
Overlappingtemplates  0.237  96.000 
Universal  0.494  98.000 
Approximate entropy  0.740  99.000 
Randomexcursions  0.223  99.375 
Randomexcursionsvariant  0.428  98.925 
Serial test  0.828  99.500 
Linearcomplexity  0.834  100.000 
Image  Experimental Value  Theoretical Value 

Titanic $256\times 256\times 3$  245.8750  293.247835 
Titanic $512\times 512\times 3$  279.1621  293.247835 
Titanic $1024\times 1024\times 3$  283.5923  293.247835 
Photographer $256\times 256\times 3$  252.1406  293.247835 
Photographer $512\times 512\times 3$  243.8066  293.247835 
Photographer $1024\times 1024\times 3$  251.6162  293.247835 
Manhattan $256\times 256\times 3$  264.6719  293.247835 
Manhattan $512\times 512\times 3$  254.6660  293.247835 
Manhattan $1024\times 1024\times 3$  257.3975  293.247835 
Sharukhan $256\times 256\times 3$  252.9531  293.247835 
Sharukhan $512\times 512\times 3$  228.9316  293.247835 
Sharukhan $1024\times 1024\times 3$  245.7544  293.247835 
Plain/Ciphered Image  Horizontal  Vertical  Diagonal 

Lena  0.96606/0.035  0.96613/0.026  0.96619/0.027 
Boat  0.99605/0.022  0.99703/0.019  0.99671/0.020 
Cameraman  0.96618/0.036  0.96771/0.028  0.96767/0.022 
Peppers  0.96608/0.019  0.96612/0.031  0.96647/0.011 
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Abutaha, M.; Amar, I.; AlQahtani, S. Parallel and Practical Approach of Efficient Image Chaotic Encryption Based on Message Passing Interface (MPI). Entropy 2022, 24, 566. https://doi.org/10.3390/e24040566
Abutaha M, Amar I, AlQahtani S. Parallel and Practical Approach of Efficient Image Chaotic Encryption Based on Message Passing Interface (MPI). Entropy. 2022; 24(4):566. https://doi.org/10.3390/e24040566
Chicago/Turabian StyleAbutaha, Mohammed, Islam Amar, and Salman AlQahtani. 2022. "Parallel and Practical Approach of Efficient Image Chaotic Encryption Based on Message Passing Interface (MPI)" Entropy 24, no. 4: 566. https://doi.org/10.3390/e24040566