# A Novel Image Encryption Algorithm Based on Voice Key and Chaotic Map
## 2 Principles of the Proposed Method
### Proposed Image Encryption and Decryption Algorithm
#### 2.2.1 Encryption Process
The experiments show that the NPCR value of Lena ciphertext image fine-tuned by \(Fp\) or \(n_{w1}\)-\(n_{w}6\) is very close to the ideal value of 99.6094%. It can be seen from the experimental data that there is a certain gap between the UACI value obtained using the proposed method and the values provided in the existing literature. This is caused by the uneven gray-scale distribution of the experimental images. Histogram equalization could be added to the experiment to optimize the UACI. Table 8 shows the optimized UACI, which is close to the ideal value and is equivalent to the UACI values given in other references. Figure 9 shows the optimized images and Figure 10 depicts the histogram of the original image and the decrypted image before and after equalization. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**F\(p\) (Hz)**} & \multirow{2}{*}{\(n_{w}1\)-\(n_{w}6\)} & \multirow{2}{*}{**R**} & \multicolumn{3}{c}{**G**} & \multicolumn{3}{c}{**B**} \\ \cline{3-8}  & & & **NPCR** & **UACI** & **NPCR** & **UACI** & **NPCR** & **UACI** \\ \hline
55 & 5, 4, 2, 3, 2, 4 & 0.9938 & 0.2271 & 0.9951 & 0.2411 & 0.9916 & 0.1521 \\
55 & 5, 4, 3, 3, 2, 4 & 0.9920 & 0.2139 & 0.9946 & 0.2377 & 0.9908 & 0.1497 \\
56 & 5, 4, 2, 3, 2, 4 & 0.9893 & 0.2105 & 0.9940 & 0.2287 & 0.9891 & 0.1376 \\
1200 & 3, 2, 4, 3, 5, 2 & 0.9925 & 0.2138 & 0.9943 & 0.2375 & 0.9909 & 0.1496 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The NPCR and UACI for the cipher images. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Ref. [35]** & **Ref. [36]** & **Ref. [37]** & **Ref. [38]** & **Ref. [39]** \\ \hline NPCR (\%) & 99.54 & 99.6146 & 99.6048 & 99.4602 & 99.655 \\ UACI (\%) & 28.27 & 33.5113 & 33.2966 & 33.2161 & 33.516 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The comparison results of NPCR and UACI. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**F\(p\) (Hz)**} & \multirow{2}{*}{\(n_{w}\)**1-\(n_{w}\)6**} & **R** & **G** & **B** \\  & & **UACI** & **UACI** & **UACI** \\ \hline
55 & 5, 4, 2, 3, 2, 4 & 0.3559 & 0.3422 & 0.3417 \\
55 & 5, 4, 3, 3, 2, 4 & 0.3383 & 0.3394 & 0.3387 \\
56 & 5, 4, 2, 3, 2, 4 & & & \\ \hline
1200 & 3, 2, 4, 3, 5, 2 & 0.3336 & 0.3284 & 0.3177 \\
1200 & 3, 2, 4, 3, 5, 2 & 0.3380 & 0.3392 & 0.3385 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The optimized UACI. Figure 10: Histograms of original and encrypted images. (**a**) Histogram of the red channel of the original image before equalization; (**b**) Histogram of the green channel of the original image before equalization; (**c**) Histogram of the blue channel of the original image before equalization; (**d**) Histogram of the red channel of the decrypted image after equalization; (**e**) Histogram of the green channel of the decrypted image after equalization; (**f**) Histogram of the blue channel of the decrypted image after equalization. Figure 9: The optimized renderings. (**a**) Encrypted image before optimization; (**b**) Optimized encrypted image; (**c**) Decrypted image without optimization; (**d**) Optimized decrypted image. #### 4.2.4 Key Space Analysis

The size of the key space directly influences the quality of the encryption algorithm, and also determines the probability of its being successfully cracked. Generally, an encryption algorithm with a small key space is likely to be cracked by brute force without the use of any particular decryption skills. Research shows that the key space of the algorithm should be greater than \(2^{100}\) to prevent the possibility of being cracked [40; 41; 42]. When counting the key space, a 6-digit voice password is considered. The value range of \(f_{m}\) is 50-2000 Hz and the value interval is 1 Hz. The value range of \(k1\), \(k2\), \(k3\) and \(k6\) is 20-1000 and the value interval is \(10^{-7}\). The value range of \(K7\) and \(k8\) is \(10^{3}\)-\(10^{10}\), the value interval is 1, and the calculated key space is \(2^{232}\). If the number of voice cipher bits is increased, the capacity of the key space can be further increased.