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13 |                                                              Yousif, Hameed & Al-Zuhairi

                                                                TABLE V.
      RESULTS OF ENCRYPTION/DECRYPTION TIME MEASURED FOR TEST IMAGES WITH DIFFERENT SIZES

      Image                     Size    Encryption time (Second)  Decryption time (Second)
      Cameraman              256x256             0.154946                   0.670657
      Lena                   512x512             0.527656                   1.686384
      Baboon                1024x1024            1.580442                   2.502797
      Barbara                256x256             0.162288                   0.643419
      Boat                   512x512             0.378125                   1.590626
      Peppers               1024x1024            1.466533                   2.325564
                             256x256             0.131102                   0.697361
                             512x512             0.384833                   1.627816
                            1024x1024            1.453171                   2.238646
                             256x256             0.132878                   0.728806
                             512x512             0.390394                   1.66202
                            1024x1024            1.426099                   2.303133
                             256x256             0.149949                   0.672086
                             512x512             0.339793                   1.670934
                            1024x1024            1.508857                   2.39036
                             256x256             0.143553                   0.650492
                             512x512             0.356593                   1.628605
                            1024x1024            1.462144                   2.261963

                             TABLE VI.                            information entropy, correlation coefficient in horizontal di-
RESULTS OF PSNR AND CORRELATION BETWEEN INPUT                     rection, MSE, PSNR, UACI, and NPCR. The results of these
                                                                  metrics are computed for Lena image of size 256 × 256. It
   AND RECONSTRUCTED IMAGES UNDER CROPPING                        can be noticed from the outcomes in this table that the entropy
                              ATTACK.                             score after the zigzag scan stage remains constant (7.4318
                                                                  in Table II, while this value increases after the second and
      Size of Cropping      PSNR (dB))  Correlation               third encryption stages to: 7.9950 and 7.9971, respectively.
         Cropping ½           10.0189     0.3957                  Also, the correlation value decreases from 0.9492 (Table III
                              12.9694     0.6001                  to: 0.1330, 0.0204 and 4.9266 × 10-4, respectively after the
Cropping ¼ in bottom right    13.1048     0.6026                  first, second and third ciphering stages. Further, the value of
   Cropping ¼ in top left     13.1152     0.6241                  MSE after the zigzag scan is 4.5449 × 103 . Then, this value
   Cropping ¼ in center       18.9409     0.8577                  increases to: 7.7540 × 103 and 1.3962 × 104, respectively
  Cropping 1/8 in top left                                        after applying the RSA and chaotic systems. Contrariwise,
                                                                  the PSNR score decreases from 11.5556 at the first layer
and 0.8577, respectively for PSNR and correlation. Also,          (zigzag scan) to: 9.2356 and 6.6813, respectively after em-
different outcomes are obtained when changing the cropping        ploying the other encryption phases. Finally, for the UACI
location. For instance, cropping 1/4 from the bottom right of     and NPCR, their values increase gradually from 27.4992 and
the cipher image yields 12.9694 dB and 0.6001 for PSNR and        99.37, respectively to: 33.3258 and 100, respectively after
correlation, respectively, cropping 1/4 from the top left yields  implementing the RSA and chaotic maps.
13.1048 dB and 0.6026 for PSNR and correlation, respectively,
while cropping 1/4 from the center part yields 13.1152 dB and         From Table VII, it can be concluded that each technique
0.6241 for PSNR and correlation, respectively. Hence, the         has a significant role in the encryption process. The modified
reconstructed image conserves the significant data included       zigzag scan does not effect on the entropy value, but it is
in the original image even if the cutting size reaches to half    obviously effect on the other metrics. The impact of RSA
size of the cipher image thereby the TIC endures efficiently      mechanism on the increasing the entropy, MSE, UACI, NPCR
the cropping attack.                                              values, and decreasing the correlation and PSNR values is
                                                                  extremely clear. Finally, the high dimension chaotic maps
F. Case Study of the Proposed TIC Method                          with confusion/diffusion processes can further improve the
Table VII is presented in order to show the effect of each
encryption stage of the proposed TIC algorithm in terms of
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