# Remote-Sensing Image Encryption Algorithm Using the Advanced Encryption Standard
## 6 Algorithm Analyses
### Encryption Efficiency Analysis  
The encryption efficiency is the significant performance for an encryption algorithm. The core encryption times can directly affect the encryption speed. For the proposed algorithm, [PERSON]'s algorithm, [PERSON]'s algorithm, and [PERSON]'s algorithm have their core operation is AES encryption times. The AES encryption times for these algorithms are given in Table 6. The unit is times. A 128-bit data block is encrypted with the encryption function of AES, i.e., AES\({}_{\mathrm{e}}(\cdot)\), viewed as once AES encryption times. The data in Table 6 view that the proposed algorithm can obviously reduce AES encryption times. We analyze the AES encryption times of these algorithms in detail as follows.  
(1) In [PERSON]'s algorithm, authors divide the pixel values into pixel blocks, and then encrypt them with AES. For the plain image with the size \(512\times 512\), it has 262,144 (i.e., \(512\times 512\)) pixel values. These pixel values can be converted into 16,384 (i.e., 262,144/16) pixel blocks. Therefore, to protect the plain image, this algorithm should encrypt 16,384 pixel blocks with Equation (11) or (12), i.e., 16,384 AES encryption times;  
(2) In [PERSON]'s algorithm, authors encode the plain image with the Base64 standard. And then they encrypt the Base64 encoded text with AES. For the plain image with the size \(512\times 512\), it has 262,144 pixel values. Each Base64 code represents with 6 bits of the pixel value, so three 8-bit pixel values can be represented by four 6-bit Base64 codes. If there are only two pixel values, they can be represented by three Base64 codes. If there is only one pixel value, it can be represented by two Base64 codes [24]. Therefore, for the plain image, 262,144 pixel values can be encoded with 349,526 (i.e., (62,143/3 \(\times\) 4) + 2) Base64 codes, where 262,143 is multiples of 3,262,143 pixel values can be encoded with 349,524 Base64 codes, and the last pixel value can be encoded with 2 Base64 codes. The plain  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithms** & **AES Encryption Times** \\ \hline [PERSON]’s algorithm & 16,384 \\ [PERSON]’s algorithm & 21,846 \\ [PERSON]’s algorithm & 16,384 \\ The proposed algorithm & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison on the AES encryption times (unit: times).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithms** & **Entropy** \\ \hline The proposed algorithm & 7.9991 \\ [PERSON]’s algorithm & 7.9994 \\ [PERSON]’s algorithm & 7.9994 \\ [PERSON]’s algorithm & 7.9991 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Entropy values.  
image can be encoded with 349,526 Base64 codes in total. These Base64 codes can be converted into 21,846 (i.e., (349,520/16) + 1) 128-bit data blocks, where 349,520 is multiples of 16. The 349,520 Base64 codes can be converted with 21,845 128-bit data blocks, and the last 6 Base64 codes can be converted with one 128-bit data block. Therefore, to protect the plain image, this algorithm should encrypt 21,846 128-bit data blocks with \(\text{AES}_{\text{e}}(\cdot)\), i.e., 21,846 AES encryption times;  
(3) In [PERSON]'s algorithm, authors divide the image into \(4\times 4\) pixel blocks, and then encrypt them with AES directly. The plain image with the size \(512\times 512\) can be divided into 16,384 (i.e., \((512\times 512)/16\)) pixel blocks. Therefore, to protect the plain image, this algorithm should encrypt 16,384 pixel blocks with \(\text{AES}_{\text{e}}(\cdot)\), i.e., 16,384 AES encryption times;  
(4) In the proposed algorithm, [PERSON] groups 16 pixel values together to form a big integer number with the 128-bit length. We consider that the AES operation is more complex than the XOR operation. The proposed algorithm only encrypts the first big integer with Equation (7), i.e., only once AES encryption times, and encrypt other big integers with the previous encrypted big integer and chaotic big integers, i.e., Equation (8).