Today it is practically impossible to calculate the presence of a hidden message in an audio signal if it is not known by what steganographic method this message was hidden. During the analysis of audio signals, the authors hypothesized that the audio signal is a statistically homogeneous signal that has constant probabilistic characteristics. If the signal is heterogeneous, then it should be broken into some statistically homogeneous chunks, i.e., find the signal breakdown points and study the signal in the intervals of the breakdown point. In this paper, the method of finding the hidden message in audio signal is proposed by partitioning the signal into intervals with the help of breakdown points. Later, for each individual interval, statistical studies of the first two moments of the signal are performed and the presence or absence of hidden message is concluded.
Due to Russia's full-scale invasion of Ukraine, martial law was introduced. At the same time, the Russian military is carrying out aggression against Ukraine not only on the ‘physical’ battlefield, but also in cyberspace. According to the State Service for Special Communications and Information Protection, the number of cyberattacks on state information systems and critical infrastructure has tripled. It should be noted that a large number of domestic and foreign scientists are working on the issue of protecting information and communication systems from outside interference. But at the same time, not many people think that attackers can covertly transmit the personal data of users through protected information and communication systems. For example, a text message may be embedded in a transmitted media file, which does not pose a threat to information from the cyber incident response side, but has great value to attackers, in particular hackers from the Russian Federation.
The issue of steganography and stegoanalysis in general is being studied by many scientists. However, the vast majority of works deal specifically with hiding information in an image. However, given the rapid development of information transmission through audio and video files, it is worth paying more attention to the methods of steganography and steganalysis of media files.
The vast majority of known studies are based on the improvement of already known methods of
audio signal steganography [
In view of the above, and given Russia's full-scale war against our country, the issue of creating modern methods of protecting the confidentiality and integrity of media data is more acute than ever, as there are no universal methods of protection that would take into account various factors, such as the quality and length of the communication channel, the level of access restriction, computing resources, etc.
As mentioned above, it is difficult to detect the fact that a message has been hidden in an audio file if the steganography algorithm used to do so is unknown. In this regard, the authors assumed that the audio signal can be investigated under conditions of uncertainty. As one of the hypotheses, the assumption was made that the audio signal can be considered as a signal with homogeneous statistical characteristics.
The hypothesis is as follows. All statistical processing of any sample (in this case audio signal) for the purpose of model building, parameter estimation, etc. is based on the assumption that the sample has not changed during data collection. Therefore, the preliminary stage of any statistical processing should be the stage of verification of such homogeneity. Thus, the question here is: is the sample presented statistically homogeneous in the sense of invariability of its probability characteristics? If the answer to this question is yes, then the usual statistical processing should be carried out, depending on the aims of the researcher. If the answer is no, then the task of detecting moments of change in probability characteristics and splitting the original sample into several statistically homogeneous pieces arises.
The authors decided to consider the audio signal as a stationary signal. However, by treating stationary signals as time series and applying the stationarity test criteria to them, we can conclude that most of them are non-stationary. Consequently, in practice, various information signals from the physical point of view, as a rule, cannot be directly described by stationary models. Therefore, it is necessary to solve the problem of searching for such ways of information signals preprocessing that would allow to allocate intervals at which signals can be considered as conditionally stationary.
To analyse such signals, we propose to investigate the detection of instantaneous time moments of signal breakdown, provided that a non-stationary signal can be considered as piecewise stationary at different intervals of stationarity.
Under a breakdown is usually understood any changes in the system parameters, processes
occurring instantly or very quickly compared to the characteristic period of measurements [
The following classification of breakdown types can be presented [
According to the above classification of breakdown types, it can be concluded that such classification can be reduced to a simpler one: • • • ‘mean bias’; ‘variance bias’; ‘trend’.
However, it should be noted that this classification applies more to random signals. Audio signals mostly lack a monotonic component, so the concept of ‘trend’ is generally not taken into account.
Based on the simplified classification of breakdown types, an algorithm for detecting instantaneous breakdowns of audio signals was developed, the structural and logic diagram of which is shown in Figure 1.
1. Scan the time series of the audio signal sˆr [ j] with a sliding window of length WS1=0.02J and determine the sliding characteristics of the sample mathematical expectation Mˆ [ j] and standard deviation σˆ [ j].
2. Check the nature of the distribution law of the obtained characteristics Mˆ [ j] and σˆ [ j]. If there
is a breakdown of the ‘variance bias’ or ‘mean bias’ type, the corresponding characteristics have
multimodal distribution laws (Figure 2 and Figure 3). In the study, the Hartigan criterion [
3. Once a breakdown has been detected and its type identified, a sliding analysis of the corresponding characteristic ( Mˆ [ j] or σˆ [ j] according to Figures 2 and 3) is used to determine the breakdown moments.
To do this, scan the corresponding characteristic with a sliding window of length WS2=0.05J and determine the sliding characteristic of the standard deviation σˆ S [ j]. The sections of the characteristic σˆ S [ j], exceeding the limit value L =σˆS [ j] +1,1σ [σˆS [ j]] are considered to be those that indicate the beginning and end of breakdown (Figure 4).
A song with a duration of 1 minute 50 seconds was taken as the investigated signal. Using DeepSound software, a 10,675-symbol text message was added to this song using some unknown steganography method.
During the experiment, the authors implemented the above algorithm for finding breakdown points for a time series of 500,000 samples in Matlab software. For this signal, the results shown in Table 1 were obtained.
The signal decomposition by breakdown intervals is shown in Figure 5.
As can be seen from Table 1 and Figure 5, the taken time series has 3 breakdown points, 2 of which show the presence of variance shift, and 1 point shows the presence of mean bias. After finding these intervals, we can evaluate the statistical characteristics of the time series at each interval separately and compare them with the characteristics of the reference signal.
Determination of moving characteristics of sample mathematical expectation and standard deviation
Breakdown type identification Splitting the signal into intervals by breakdown points Calculate the mean and standard deviation at each breakdown interval
Division of the original aduiosignal into intervals according to the breakdown points of the signal under test Calculate the mean and standard deviation of original signal at each breakdown interval Comparing the results of the original audio signal and the audio signal under test Coordinates of Mean of breakdown points test signal [0:240939] -2.0458e-05 [240940:476050] -1.7131e-06 [476051:482347] -0.0039
The paper proposes a new method for finding hidden containers in multimedia messages, which, unlike the known ones, will cope with the task of detecting noise audio signal by dividing the signal into intervals of homogeneity and conducting statistical evaluation of each interval separately. Homogeneity intervals are selected by the breakdown points of the signal.
The authors have developed algorithmic-software for detecting the fact of presence of a hidden message. Unlike the known methods of steganalysis, this algorithm will make it possible to detect a hidden container in media files regardless of what steganographic method it was embedded with.