## 3 Reversible Watermarking Based on intDCT
### Extracting Embedded Information and Reconstructing Original Data
The work in [40] proposed a blind audio watermarking algorithm by discrete wavelet transform, which has a capacity of around 100 bps when \(SNR=21\) [dB], and the work in [41] proposed a robust audio watermarking scheme based on fractional Charlier moment transform, achieving SNR = 32 [dB], with capacity around 500 bps. As a popular criterion, MOS-LQO scores are used in [42], which refers to a reversible watermarking method based on variable error expansion of linear prediction applied to G711 \(\upmu\)-law-coded speech signals. The MOS-LQO is 4.13 for a capacity of 711 bps, 3.44 for 1253 bps, and 2.84 for 1995 bps. Additionally, as a reference of evaluation criteria, [PERSON] [43] et al. and [44; 45; 46] used perceptual evaluation of objective difference grades (ODGs), and log spectrum detection (LSD, the smaller, the better) as the criteria to evaluate the objective audio quality. LSD evaluates signals in short-term Fourier transforms of the original and watermarked signals. Typically, the LSD criterion for speech watermarking is less than or equal to 1 [dB]. The work in [46] proposed a watermarking scheme for tampering detection by modifying the line spectral frequencies (LSFs). The results showed scores for LSD \(\leqq\) 1 [dB] and ODGs \(\geqq\) 3.0 (slightly annoying). The work in [44] also achieved a similar result to [46]. The work in [45] proposed a blind method with spread spectrum using linear prediction residue, with MOS results located between 3 and 4, and LSD around 1 [dB], with a bit rate of 16 bps. The works in [44; 45] aimed for irreversible watermarking. ### Computational Cost of Embedding

Since the matrix calculation exists in intDCT, we calculated the computational cost for embedding. Even though calculation time depends on the computer's performance and the programming language for implementation, as a reference, we calculated the computational cost for embedding 112 data with expanded [9 th,16 th] blocks and the system configuration listed in Table 3. The average processing time is approximately 4.884 [s] for speech with an average length of 10 [s]. This result shows that real-time embedding is possible. ### Evaluation of Reversibility

We performed experiments to verify the reversibility of the proposed method by computing the differences between the reconstructed and original data. Data are read in the time domain as a matrix in GNU Octave version 3.4.2, and subtraction is applied. Different from the conventional works with semi-reversible or irreversible algorithms, the algorithm proposed in this work guarantees reversibility by rounding calculation; no data loss occurs by applying the proposed algorithm if there is no overflow. To examine the reversibility, we conducted an experiment to calculate the difference between the reconstructed data and the original data with 112 data. The results indicate that all 112 data resulted in differences of 0, which verified the proposed work's reversibility. ### Overflow Analysis with Controllable Location Map When Embedding Data into Music Signals

As shown in Figure 3, using the highest eight blocks as the payload did not cause overflow in any of the speech materials. Here, the music signal is another target of tampering detection [47; 48; 49]. Music signals have more variation than speech signals, which may cause \begin{table}
\begin{tabular}{c c} \hline \hline
**Configuration** & **Value** \\ \hline OS & Windows Vista Business \\ \hline CPU & Intel Core 2 Quad CPU Q9650 \\  & @ 3.00 GHz (\(\copyright\)Intel Corporation, Santa Clara, CA, USA) \\ \hline Memory(RAM) & 2 GB \\ \hline Programming language & Matlab \\ \hline Average time & 4.884 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: System configuration and computational cost. overflow when all eight blocks are used for the payload [12]. Therefore, we experimented with embedding data into one to eight blocks at the highest frequency bands and calculated the probability of overflow of one frame.