# Parallel Crossed Chaotic Encryption for Hyperspectral Images
## 4 Results
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Name**} & \multirow{2}{*}{**Serial Time (s)**} & \multicolumn{4}{c}{**Parallel Time(s)**} & \multicolumn{2}{c}{**Entropy**} \\ \cline{3-8}  & & **Upload** & **Encrypt** & **Download** & **Total** & **Original** & **Encrypted** \\ \hline Female01 & 12.4671 & 0.0194 & 0.003338 & 0.0231 & 0.045838 & 7.6478 & 7.99995 \\ Female02 & 14.5577 & 0.0220 & 0.003502 & 0.0259 & 0.051482 & 6.9685 & 7.99994 \\ Female03 & 18.0801 & 0.0289 & 0.004160 & 0.0323 & 0.065360 & 7.7217 & 7.99994 \\ Female04 & 15.3995 & 0.0249 & 0.003745 & 0.0290 & 0.057645 & 7.4850 & 7.99994 \\ Female05 & 11.4269 & 0.0188 & 0.003177 & 0.0225 & 0.044477 & 6.0984 & 7.99994 \\ Female06 & 6.6332 & 0.0129 & 0.002135 & 0.0139 & 0.028935 & 7.5043 & 7.99996 \\ Female07 & 17.8849 & 0.0286 & 0.004158 & 0.0332 & 0.065958 & 7.7350 & 7.99997 \\ Female08 & 12.8754 & 0.0208 & 0.003407 & 0.0249 & 0.049107 & 7.5038 & 7.99994 \\ Female09 & 13.5488 & 0.0230 & 0.005120 & 0.0420 & 0.070120 & 6.0217 & 7.99995 \\ Female10 & 10.5763 & 0.0164 & 0.003324 & 0.0186 & 0.038324 & 7.0142 & 7.99996 \\ Female11 & 14.7164 & 0.0215 & 0.003804 & 0.0243 & 0.049604 & 6.9170 & 7.99994 \\ Female12 & 11.4762 & 0.0145 & 0.002545 & 0.0194 & 0.036445 & 7.2636 & 7.99994 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Female dataset encryption results. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Name**} & \multirow{2}{*}{**Serial Time (s)**} & \multicolumn{4}{c}{**Parallel Time(s)**} & \multicolumn{2}{c}{**Entropy**} \\ \cline{3-8}  & & **Upload** & **Encrypt** & **Download** & **Total** & **Original** & **Encrypted** \\ \hline Male01 & 16.6417 & 0.0253 & 0.00353 & 0.0304 & 0.05923 & 7.6170 & 7.99994 \\ Male02 & 16.9902 & 0.0249 & 0.00356 & 0.0301 & 0.05856 & 7.2491 & 7.99994 \\ Male03 & 15.0768 & 0.0243 & 0.00346 & 0.0298 & 0.05756 & 7.4629 & 7.99994 \\ Male04 & 14.8045 & 0.0239 & 0.00351 & 0.0301 & 0.05751 & 7.4662 & 7.99995 \\ Male05 & 10.4175 & 0.0186 & 0.00295 & 0.0275 & 0.04905 & 7.3869 & 7.99995 \\ Male06 & 9.8852 & 0.0187 & 0.00334 & 0.0256 & 0.04764 & 7.7191 & 7.99996 \\ Male07 & 11.8605 & 0.0225 & 0.00421 & 0.0261 & 0.05281 & 7.0507 & 7.99995 \\ Male08 & 14.7449 & 0.0246 & 0.00394 & 0.0311 & 0.05964 & 7.2739 & 7.99995 \\ Male09 & 13.2484 & 0.0225 & 0.00284 & 0.0294 & 0.05474 & 7.2322 & 7.99994 \\ Male10 & 22.14 & 0.0351 & 0.00353 & 0.0395 & 0.07813 & 7.4603 & 7.99996 \\ Male11 & 20.9537 & 0.0346 & 0.00467 & 0.0481 & 0.08737 & 7.3924 & 7.99995 \\ Male12 & 13.939 & 0.0253 & 0.00347 & 0.0331 & 0.06187 & 7.3524 & 7.99995 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Male data set encryption results. Figure 7: _Cont._Please note that the time in parallel is minimal compared with the serial time, this is due to the high parallelism in the cipher scheme. Furthermore, the information entropy is very close to the theoretical maximum entropy. This results overcome the results reported in [29; 30], for gray-scale and RGB images. The key of the proposed cipher is the parameters and the initial conditions of the chaotic systems, this can be improved with key establishment protocols [34] and chaotic-based hash functions [35]. Figure 8: Original and encrypted image (layer one) of Male03 HI. Figure 7: Original and encrypted image (layer one) of Female06 HI. In this manner, to test the strength against cryptanalytic differential attacks [36], we apply the NPCR, and UACI tests [16]. As we need two images of the same size, we trim the Female09 image to the Female10 image size. Then, we encrypt the two images with the same cipher and the same key and run NPCR and UACI test with the results displayed in Table 4. Please note that the result values approximate the expected values of a random image, then we can claim that the cipher is protected against differential attacks.