# A Tweak-Cube Color Image Encryption Scheme Jointly Manipulated by Chaos and Hyper-Chaos
## 5 Performance Analysis
### Time and Computational Complexity Analysis  
Time and speed analysis is also a critical measurement feature for an encryption algorithm. Thus, the security of a scheme cannot be at the expense of increasing time consumption. The time costs of images with different sizes were measured separately, and the results are listed in Table 12. Obviously, the encryption time of our scheme is less than that of some recent encryption algorithms.  
Ulteriorly, we will discuss the computational complexity of our scheme. At the outset, the generation process of the key streams made the computational complexity become \(\Theta(4\times\mathrm{m}\times\mathrm{n})\). Afterwards, the rows and columns of the three components R, G, and B were simultaneously cyclically shifted twice so that the computational complexity changed to \(\Theta(16\times\mathrm{m}\times\mathrm{n})\). Besides, the bit-level operations do not affect the complexity, hence the computational complexity of this paper is \(\Theta(16\times\mathrm{m}\times\mathrm{n})\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multicolumn{3}{c}{**Calculated NPCR (\%)**} & \multicolumn{3}{c}{**Theoretical NPCR (\%)**} \\ \cline{2-7}  & **R** & **G** & **B** & \(\mathbf{N}_{0.05}^{*}\) & \(\mathbf{N}_{0.01}^{*}\) & \(\mathbf{N}_{0.001}^{*}\) \\ \hline Couple & 99.5956 & 99.6124 & 99.6185 & Passed & Passed & Passed \\ House & 99.6017 & 99.6268 & 99.5956 & Passed & Passed & Passed \\ Tree & 99.6094 & 99.6096 & 99.6129 & Passed & Passed & Passed \\ Lena & 99.6037 & 99.6128 & 99.5995 & Passed & Passed & Passed \\ Peppers & 99.5904 & 99.6246 & 99.6033 & Passed & Passed & Passed \\ [PERSON] & 99.5921 & 99.6109 & 99.6170 & Passed & Passed & Passed \\ [PERSON] in [35] & 99.6357 & 99.6416 & 99.6224 & - & - & - \\ [PERSON] in [37] & 99.6505 & 99.6444 & 99.6627 & - & - & - \\ [PERSON] in [42] & 99.6300 & 99.5900 & 99.6700 & - & - & - \\ [PERSON] in [43] & 99.6445 & 99.6353 & 99.6429 & - & - & - \\ [PERSON] in [35] & 99.5693 & 99.6435 & 99.6171 & - & - & - \\ [PERSON] in [37] & 99.6357 & 99.6158 & 99.6247 & - & - & - \\ [PERSON] in [35] & 99.6563 & 99.6428 & 99.6493 & - & - & - \\ [PERSON] in [37] & 99.6536 & 99.6078 & 99.6520 & - & - & - \\ [PERSON] in [43] & 99.6461 & 99.6628 & 99.6277 & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 10: The actual values of NPCR for different color images.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multicolumn{3}{c}{**Calculated UACI (\%)**} & \multicolumn{3}{c}{**Theoretical UACI (\%)**} \\ \cline{2-7}  & **R** & **G** & **B** & \((\mathbf{N}_{0.05}^{*}\mathbf{N}_{0.05}^{*+})\) & \((\mathbf{N}_{0.01}^{*-}\mathbf{N}_{0.01}^{*+})\) & \((\mathbf{N}_{0.001}^{*-}\mathbf{N}_{0.001}^{*+})\) \\ \hline Couple & 33.5911 & 33.4298 & 33.4019 & Passed & Passed & Passed \\ House & 33.5739 & 33.4600 & 33.4721 & Passed & Passed & Passed \\ Tree & 33.4029 & 33.4018 & 33.4793 & Passed & Passed & Passed \\ Lena & 33.5056 & 33.4533 & 33.4719 & Passed & Passed & Passed \\ Peppers & 33.4634 & 33.5485 & 33.4818 & Passed & Passed & Passed \\ Baboon & 33.5139 & 33.4682 & 33.5363 & Passed & Passed & Passed \\ Lena in [35] & 33.5839 & 33.3954 & 33.4687 & - & - & - \\ Lena in [37] & 33.4462 & 33.4131 & 33.4399 & - & - & - \\ Lena in [42] & 33.4300 & 33.3900 & 33.5100 & - & - & - \\ Lena in [43] & 33.1147 & 30.5298 & 27.7471 & - & - & - \\ Peppers in [35] & 33.4317 & 33.5392 & 33.6326 & - & - & - \\ Peppers in [37] & 33.4570 & 33.4705 & 33.4423 & - & - & - \\ [PERSON] in [35] & 33.3687 & 33.5956 & 33.4528 & - & - & - \\ [PERSON] in [37] & 33.4753 & 33.5090 & 33.4176 & - & - & - \\ [PERSON] in [43] & 29.8421 & 28.1446 & 30.7024 & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 11: The actual values of UACI for different color images.