# Direct Spread Spectrum Technology for Data Hiding in Audio +
## 3 Materials and Methods
### Direct Spread Spectrum in Steganography  
Direct spread spectrum technology has long been used in steganography. In the first works [20; 21; 40], a general scheme of a steganosystem with the direct spreading of the spectrum was proposed. The authors used cover images, but all their reasoning can be extended to other multimedia data. The general idea of such a stegosystem is as follows (Figure 1). In order to hide the data, the following steps are performed:  
1. The information message is presented in polar form \(m_{i}\);
2. \(m_{i}\) multiplied bit by bit by the spreading sequence as in (3);
3. Multimedia data (images, audio, video, etc.) are interpreted as noise in the communication channel. Using our notation, this is \(N\) in (4). 4. Further, these data are hidden in the cover data according to rule (4). However, we currently denote: 1. \(N\)--multimedia data (container, cover), inside which the message is hidden;
2. \(Mix\)--modified multimedia data (filled container) after hiding messages in them. Figure 1: Block diagram of concealment and recovery. In order to restore the data, the following steps are performed:  
1. Correlation is calculated. * The product is calculated \(s_{i}Mix\); * The sum is calculated \(\rho(s_{i},Mix)=\sum\limits_{v=0}^{n-1}s_{i,v}Mix_{v}\);
2. If Equations (6) and (7) are true, then the value of the recovered bit is calculated by the Equation (8). 3. The recovered message is presented in a custom view. It should be noted that even in the first works, the authors encountered significant difficulties. For example, in [53] was shown that the error rate in the extracted messages is very high (see, for example, Table 2 on page 12 of [53]). BER can be reduced in different ways, for example, by using filtering, correction codes, etc. The simplest is to increase the power of chip codes. For this, Equation (4) can be rewritten as  
\[Mix=N+P\sum\limits_{j=1}^{k}M_{j}=N+\sum\limits_{j=1}^{k}m_{j}(Ps_{j}) \tag{9}\]  
where the value \(P\) specifies the power amplification factor of the chip codes \(s_{j}=(s_{j,0},s_{j,1},\ldots,s_{j,n-1})\). By increasing the power, \(P\), it is actually possible to achieve a decrease in BER. However, this inevitably leads to distortion of the container \(N\). For example, for \(k=10\) and \(P=10\), each value of the cover file \(N\) may be skewed by \(\pm kP=100\). This may present a real problem because BER is still high. For example, in [53], it is shown that even with \(P=100\) an error rate is more than 10% (see Table 2 from [53]). We carried out detailed studies of this problem in [23; 24]. In particular, we repeated the experiments with images from [21; 40; 53; 54]. We studied the effect of different ways of forming spreading sequences on the BER value. The general conclusions about the high BER were confirmed, and the explanation for this phenomenon is, in our opinion, the following. The first term in (4) presents a certain implementation of random additive white noise \(N\). This is indeed the case for spread spectrum communications systems. Those assumption (6) is fulfilled, which gives an almost error-free recovery of the message according to rule (8). However, in the stagnosystem, in (4), multimedia data are meant. This is usually highly redundant, highly correlated data. This is not a random realization of Gaussian noise, and assumption (6) is often not met. Obviously, this leads to errors in the recovered bits according to rule (8). In works [55; 56], an effective way to combat this phenomenon was proposed. We proposed to form chip sequences in a special, adaptive way. Indeed, if we take into account the statistical properties of multimedia data (in [55; 56], we used cover images), then it is possible to form chip codes \(s_{1},s_{2},\ldots,s_{k}\), in such a way that condition (6) is guaranteed to be satisfied. In this case, it is possible to ensure an almost error-free extraction of information messages according to rule (8). In this article, we continued our experiments.