# Parallel Crossed Chaotic Encryption for Hyperspectral Images
## 4 Results  
To demonstrate the performance of the proposed algorithm, we offer the following results. These experiments were carried out in an Intel Xeon(r) E31225 3.10 GHz, with a 16 GB of RAM and a GTX 1050 Ti. The algorithm was implemented in Matlab(r) programming language and with GPU computing support for Nvidia CUDA(r). The GTX 1050 Ti have 768 cores and 4 GB of memory. In Figure 5, we present an encryption over \"San Francisco with Polarizing filter\" HI, from the Scene Database 4 of ImageVal Consulting(r) (Database from [[http://www.imageval.com](http://www.imageval.com)]([http://www.imageval.com](http://www.imageval.com))). The image size is \(702\times 1000\times 148\) (we show in Figure 5 the layer 50) and the light-wave is 415-915 nm. The entropy of the original image is 6.1057 and the encrypted entropy is 7.99997, very close to the theoretical maximum entropy. We also show in Figure 6, the normalized hyperhistogram where we calculate the histogram of every layer. Please note that the encrypted image has a hyperhistogram approximately uniform. Figure 5: Experiment 1. Original and encrypted images. In this way, to show the time advantage of using an ad hoc encryption technique for HI, consider the data set shown in Table 1, where the sizes of 24 HI of women and men faces (this data set is taken from Hyperspectral High-Resolution Faces of the Scene Database of ImageVal Consulting(r) (Taken from [[http://www.imageval.com/scene-database/](http://www.imageval.com/scene-database/)]([http://www.imageval.com/scene-database/](http://www.imageval.com/scene-database/)))). The dataset consists of 12 portraits of women and 12 of men with a light-wave spectrum of 415-915 nm. We show the file size and the image size. In Tables 2 and 3, we present the results of the encryption of the female and male faces datasets, respectively. We show the serial time and the parallel time. In the parallel time, we also include the upload to GPU and the download to CPU times, such time is achieve thanks to the high parallelism of the scheme. We also show the original and encrypted entropy. In Figure 7, we show an example of the Female06 image with the respective hyperhistograms. In the same way, and Figure 8 shows an example of the Male03 image with the respective hyperhistograms. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{3}{c}{**Female Dataset**} & \multicolumn{6}{c}{**Male Dataset**} \\ \hline \multirow{2}{*}{**Name**} & \multirow{2}{*}{**Size (MB)**} & \multicolumn{2}{c}{**Dimensions**} & \multicolumn{3}{c}{**Dimensions**} \\ \cline{3-10}  & & \(n\) & \(m\) & \(l\) & & & \(n\) & \(m\) & \(l\) \\ \hline Female01 & 922 & 1403 & 975 & 29 & Male01 & 993 & 1349 & 965 & 41 \\ Female02 & 820 & 1169 & 912 & 42 & Male02 & 974 & 1294 & 969 & 43 \\ Female03 & 993 & 1346 & 935 & 46 & Male03 & 949 & 1337 & 948 & 39 \\ Female04 & 906 & 1279 & 912 & 43 & Male04 & 927 & 1322 & 981 & 35 \\ Female05 & 802 & 1260 & 904 & 33 & Male05 & 851 & 1379 & 969 & 24 \\ Female06 & 651 & 1237 & 855 & 21 & Male06 & 894 & 1317 & 1066 & 24 \\ Female07 & 1014 & 1368 & 942 & 45 & Male07 & 986 & 1447 & 1044 & 26 \\ Female08 & 883 & 1322 & 955 & 33 & Male08 & 1013 & 1423 & 1059 & 30 \\ Female09 & 952 & 1323 & 1043 & 31 & Male09 & 920 & 1366 & 938 & 35 \\ Female10 & 763 & 1197 & 970 & 27 & Male10 & 1085 & 1271 & 1038 & 50 \\ Female11 & 867 & 1213 & 929 & 42 & Male11 & 1105 & 1414 & 975 & 47 \\ Female12 & 771 & 1214 & 914 & 32 & Male12 & 937 & 1317 & 981 & 36 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: HI face images dataset. Figure 6: Experiment 1. Hyperhistogram of original an encrypted images.