## 6 Discussion  
Since security is vital for any cryptosystem, it starts with the AICLDH resistance against different known attacks. With this objective in mind, attacks are divided into three categories. Those that apply to the ElGamal cryptosystem, those that impact the proposed symmetric cryptosystem, and those that damage encrypted images. The attack on the ElGamal cryptosystem aims to obtain the private key, \(a\), when the public key, \(\beta\), is known. In this sense, some generic algorithms have been realized, which have a complexity of \(O(\sqrt{p})\), to obtain a solution. In addition, there is another well-known procedure to obtain the private key known as the Pohlig-Hellman attack, and also, in this case, the complexity is \(O(\sqrt{p})\)[55]. On the other hand, the value of \(p\) used in this investigation is approximately \(2^{1024}\). As a result, the attack complexity would be \(O(2^{512})\). In conclusion, this type of attack, at least for the moment, does not affect the proposed cryptosystem [56]. The security benefits of the proposed AICLDH symmetric algorithm are described below. The substitution boxes, \(8\times 8\)\(S-box\), used in the encryption procedure are dynamic. In other words, they are unknown before encryption. In addition, each round employs a different box. In conclusion, it is impossible to accomplish linear and algebraic attacks; at least as we know it [57]. On the other hand, a brute-force attack requires knowing \(C^{1},C^{2}\). However, that problem has a complexity of \(2^{1024}\). Hence, the brute-force attack cannot be performed successfully. It is important to remember that AES has at most \(2^{256}\) and has not been broken yet. In addition, it has been reported that in private key algorithms, the impact due to the appearance of quantum computers will be less drastic [7]. Moreover, because \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Color** & **Noise Type** & **Peppers** & **Donkey** & **Lena** & **Barbara** \\ \hline \multirow{4}{*}{Red} & Occlusion & 91.30 & 69.41 & 88.18 & 83.45 \\  & Additive & 91.35 & 69.78 & 88.30 & 83.20 \\  & Multiplicative & 91.51 & 69.76 & 89.12 & 83.95 \\  & Chi-square & 91.56 & 68.53 & 87.57 & 83.66 \\ \hline \multirow{4}{*}{Green} & Occlusion & 86.54 & 68.84 & 87.83 & 83.38 \\  & Additive & 86.52 & 69.02 & 87.78 & 83.24 \\  & Multiplicative & 87.16 & 69.22 & 88.45 & 83.94 \\  & Chi-square & 87.26 & 67.67 & 87.50 & 83.57 \\ \hline \multirow{4}{*}{Blue} & Occlusion & 86.11 & 69.46 & 90.70 & 83.45 \\  & Additive & 86.04 & 69.71 & 90.75 & 83.33 \\ \cline{1-1}  & Multiplicative & 86.87 & 70.00 & 90.94 & 84.02 \\ \cline{1-1}  & Chi-square & 86.95 & 68.40 & 90.48 & 83.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: SP after a \(5\times 5\) median filter was applied to encrypted images with 50% damage from different noise sources. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Color** & **Size Noise** & **Peppers** & **Donkey** & **Lena** & **Barbara** \\ \hline \multirow{4}{*}{Red} & 20\% & 82.77 & 72.24 & 80.19 & 82.06 \\  & 30\% & 73.70 & 57.74 & 70.60 & 73.20 \\  & 40\% & 66.17 & 44.65 & 60.42 & 64.31 \\  & 50\% & 57.69 & 30.30 & 50.11 & 55.78 \\ \hline \multirow{4}{*}{Green} & 20\% &  
the proposed symmetric cryptosystem was built using the ElGamal cryptosystem, it makes it possible for ElGamal to distribute its keys. In the same way, Table 11 shows that the values of the NPCR, UACI, and AC parameters are adequate to avoid the differential attack. Other attacks tested on encrypted images are the noises: additive, multiplicative, occlusion, and the \(\chi^{2}\) proposed. Moreover, the affected area is available in four sizes; 20%, 30%, 40%, and 50%. In addition, the SP parameter evaluates the sharpness loss of decrypted images with damage. The result appears in Table 12. Furthermore, Figure 5a shows the decrypted image when the original was encrypted with the proposed algorithm and then \(\chi^{2}\) noise application of size 50%.