## 6 Discussion and Conclusions  
In this paper, we have proposed a data-hiding scheme using sub-band entropy for embedding region selection. The insertion and extraction stages were based on a gain-invariant watermarking approach, previously proposed in [13]. The insertion domain, the intDCT coefficients, was shown be suitable for data-hiding, holding very good auditive transparency. Although the approach in [13] was robust to gain attack and other common (intentional and unintentional) attacks, it lacked key-based security. Two strategies for key-based security--the additive and the multiplicative strategies--were proposed and evaluated. It was shown that both strategies had the same auditive transparency as the proposed data-hiding scheme without key-based security. In the experiments, the PSNR mean and median were calculated as \(44.37\) and \(43.29\), respectively, and ODG mean and median were calculated as \(-0.9362\) and \(-0.6318\), respectively, for the unprotected scheme. Thus, additive strategy had PSNR mean and median as \(44.36\) and \(43.30\), respectively, and ODG mean and median as \(-1.0638\) and \(-0.6409\), respectively. In similar way, the multiplicative strategy achieved very close values, with PSNR mean and median as \(44.34\) and \(43.29\), respectively, and ODG mean and median as \(-0.9387\) and \(-0.6222\), respectively. These results are highly competitive against state-of-the-art schemes based on embedding-region selection by entropy, such as [20; 34], for which the best and average PSNR value were \(36.4\) dB and \(37.2\) dB, respectively. Table 1 shows a comparison between the proposed data-hiding scheme and the relevant entropy-based audio-watermarking approaches. Statistical tests have shown that there was no significant difference between the unprotected scheme and the key-based protected strategies, in terms of PSNR and ODG; thus, [PERSON]'s principle was achieved. However, key-based security strategies have differences between them after the Wilcoxon rank-sum test: The multiplicative strategy produced better BER results than the additive strategy when an incorrect key was used for data extraction; both BER mean and median were practically \(0.5\) for the multiplicative strategy, and were \(0.4591\) and \(0.4582\), respectively, for the additive strategy. As can be read in Table 1, only the approach proposed in [34] holds key-based security; however, the complexity of its solution is higher than the proposed strategy in this paper, as the approach in [34] encrypts the data to embed using chaotic mapping; thus, our proposed strategies require a key-generated sequence and addition or multiplication only. The steganographic capacities of the proposed data-hiding scheme were evaluated using the Kullback-Leibler divergence. Despite very few outliers having been measured in the audio dataset, the median value of KL divergence for both the additive and multiplicative strategies were calculated as \(3.7421\times 10^{-4}\) and \(2.0380\times 10^{-4}\), respectively; according to the authors of [32], the proposed data-hiding scheme is secure for steganographic applications. From Table 1, it can be observed that  
Figure 15: BER results after Advanced Audio Coding (AAC) compression at 256 kbps. (**a**) BER results. (**b**) BER distribution. only the proposed data-hiding scheme showed statistical transparency; thus, it is attractive for both watermarking and steganographic applications. On the other hand, payload evaluation results seemed to prove inconclusive, as payload did not follow a clear distribution for the utilized audio dataset, with high payload variance. This behavior may have been due to differences in musical genre or the spectral content of the audio clips; the audio dataset in this study [27] had no explicit music style classification, which makes it difficult to try correlate payload with music genre or spectral content; thus, more research is needed to clarify this behavior. Despite this, for some audio clips, the payload was higher than the average payload in [20].