# A Hybrid Domain Color Image Watermarking Scheme Based on Hyperchaotic Mapping
## 3 The Proposed Watermarking Scheme
### Security Analysis  
The security of the image watermark is a key point that the watermark algorithm needs to consider. A robust algorithm needs to ensure that illegal personnel cannot extract the watermark image from the cover image. In this paper, we use Lorenz hyperchaotic map encryption to protect the watermark. Even if the attacker extracts the watermark, only the encrypted image is obtained. Lorenz chaotic map has good chaotic properties, including sensitivity dependence on initial conditions, long-term unpredictability, etc. A small change in initial conditions can cause a significant deviation from the system trajectory, making it form a complex trajectory in the phase space. These characteristics ensure that the generated chaotic sequence has a high degree of randomness and improve the strength of watermark encryption. In addition, the scheme has good robustness. In the face of some attacks, the watermark image can be completely extracted, which greatly improves the security of the watermark.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Type of Attack** & **Airplane** & **Baboon** & **Goldhill** & **House** & **Lake** & **Peppers** \\ \hline No attack & 0 & 0 & 0 & 0 & 0 \\ Salt and pepper noise (m = 0, v = 0.05) & 0.0891 & 0.0926 & 0.0722 & 0.0765 & 0.0704 & 0.0836 \\ Gaussian noise (m = 0, v = 0.05) & 0.1713 & 0.1787 & 0.1598 & 0.1564 & 0.1627 & 0.1733 \\ Speckle noise (m = 0, v = 0.05) & 0.1389 & 0.1300 & 0.0710 & 0.1108 & 0.0947 & 0.1128 \\ Sharpening & 0.1473 & 0.2576 & 0.2059 & 0.1855 & 0.1754 & 0.1623 \\ Gaussian filter & 0.0743 & 0.2280 & 0.1116 & 0.1121 & 0.0808 & 0.0640 \\ Mean filtering (3 \(\times\) 3) & 0.0907 & 0.2664 & 0.1356 & 0.1389 & 0.0994 & 0.0772 \\ Rotation (10\({}^{\circ}\)) & 0.3067 & 0.2979 & 0.3538 & 0.3336 & 0.2471 & 0.2872 \\ Flip vertical & 0 & 0 & 0 & 0 & 0 & 0 \\ Cropping (20\%) & 0.3148 & 0.3278 & 0.1644 & 0.3471 & 0.2956 & 0.2659 \\ JPEG (QF = 90) & 0.0075 & 0.0661 & 0.0371 & 0.0165 & 0.0347 & 0.0056 \\ JPEG2000 (QF = 90) & 0.0407 & 0.1236 & 0.1381 & 0.0790 & 0.0549 & 0.0432 \\ \hline \hline \end{tabular}
\end{table}
Table 6: BER of watermark images extracted from different attacks.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Type of Attack** & **Proposed** & [27] & [28] & [21] & [29] & [30] \\ \hline No attack & 1 & 1 & 0.9992 & 1 & 0.9967 & 0.9976 \\ Salt and pepper noise (m = 0, v = 0.05) & 0.9971 & 0.9780 & 0.9583 & - & 0.8693 & - \\ Gaussian noise (m = 0, v = 0.05) & 0.9242 & 0.9072 & 0.9294 & - & 0.7996 & 0.8339 \\ Speckle noise (m = 0, v = 0.05) & 0.9947 & 0.9046 & 0.9625 & 0.9194 & 0.9276 & - \\ Sharpening & 0.8958 & - & 0.9385 & 0.9596 & - & 0.8560 \\ Gaussian filter & 0.9575 & - & - & 1 & - & 0.8186 \\ Mean filtering (3 \(\times\) 3) & 0.9435 & 0.9420 & 0.9796 & - & 0.9269 & 0.8271 \\ Rotation (10\({}^{\circ}\)) & 0.8715 & - & - & - & 0.9569 & - & - \\ Cropping (20\%) & 0.9636 & 0.9997 & - & 0.9438 & - & - \\ JPEG (QF = 90) & 0.9966 & 0.9921 & - & 0.9979 & 0.9948 & 0.94779 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of NCC with other schemes under different attacks.