## 1 Introduction  
The rapid growth of big data facilities and communications services has democratized multimedia contents access. However, the ease of access has also caused problems, such as the illegal copying and distribution of copyrighted works. Digital watermarking has been used as a tool for copyright protection, data authentication, copy protection, traitor tracing, broadcast monitoring, and so on. Digital watermarking consists of embedding some information, known as a watermark, in an imperceptible and secure fashion in the original media, to show ownership, authenticate the multimedia, establish a secret communications channel, and so on. Watermark embedding is mainly carried out in two domains: the spatial/time domain (for images and video and audio, respectively) [1; 2; 3; 4] or the frequency domain [5; 6; 7]. In audio watermarking, one of the most simple but effective attacks is the gain attack, which consists of varying the original volume uniformly to confuse the watermark detection/extraction algorithm. Spread spectrum (SS) watermarking [7; 8] has shown robustness to volume attacks; however, this robustness is paid for by low embedding capacity and auditive transparency. On the other hand, quantization-based watermarking algorithms [9; 10] have high embedding capacities and low distortion, thus they fail under volume attack.  
An gain-invariant high-rate watermarking algorithm, known as Rational Dither Modulation (RDM), was proposed in [11]. RDM has been utilized for audio watermarking with good results [12]. Although RDM is one of the most relevant gain-invariant algorithms, the high peak-to-average power ratio of RDM is its main drawback [13]. Some studies have proposed improvements to RDM, which showed high-rate and gain-invariant properties [14; 15; 16]. Recently a gain-invariant watermarking algorithm was proposed in [13]; this algorithm showed high robustness against both uniform and variable gain attack. The algorithm in [13] was evaluated on digital images, showing robustness to gain attacks and typical digital signal processing operations, such as filtering, Gaussian noise addition, and lossy compression. However, despite its otherwise remarkable characteristics, this algorithm lacks key-based security. According to [PERSON]'s principle, the security of a cryptosystem must be guaranteed only with the knowledge of the key, even if everything about the system is public. Although a watermarking system is not a cryptosystem in the whole sense, [PERSON]'s principle is valid for the watermarking purposes.  
In this paper, two strategies to achieve key-based security for the algorithm in [13] are proposed and evaluated. The resulting algorithm is used for audio watermarking in the integer Cosine Discrete Transform (intDCT) domain, using the entropy of intDCT coefficients as an embedding suitability indicator. The embedding is carried out in the high-entropy sub-bands in order to achieve good perceptual transparency. Entropy has been used as a selection criterion for data embeddings in an adaptive fashion [17; 18; 19; 20; 21], but mostly in the wavelet domain; to the best of our knowledge, this is the first time that the entropy of intDCT coefficients has been used for data embedding.  
This paper is organized as follows. Section 2 introduces the related background. The security strategies for the algorithm in [13] are described in Section 3. Then, Section 4 introduces the proposed audio data-hiding algorithm. Experiments and results are presented in Section 5. Finally, Section 6 concludes the paper through a discussion.