In this research study, a method of speech information protection using digital wavelet filter banks is proposed. An inverse scheme of single-level discrete wavelet transform is used to build the protection system. It includes digital synthesis and analysis filter banks. The filters used are synthesized using a key sequence. The key identifies the sender and receiver of the information and is used only in the filter synthesis stage. Also presented is a method for synthesizing matched wavelet filters satisfying the property of orthogonality of the wavelet basis, the presence of zero moments. The important requirements of the filters are the conditions of complete signal recovery and elimination of overlapping spectra. The results of the research show the effectiveness of synthesized wavelet filters in solving the problem of information protection. A speech protection algorithm is developed, which uses matched wavelet filters at the stage of building a bank of analysis-synthesis filters matched to the key. The algorithm has a simple implementation, and fast algorithms of digital signal processing (convolution, decimation, interpolation), allowing encrypting of the signal in real-time. The proposed algorithm is noise-resistant and can be used in channels with intensive interference. The algorithm is robust to time delays and hiccups, as well as distortions in the communication channel.
Information protection is an integral part of communication
systems. Nowadays, more and more attention is paid to the
protection of speech information, which is associated with the
growth of speech communication in the modern information
environment [
With the development of digital communication in radio
engineering, gaming methods, and cryptographic
algorithms have become widespread. Initially, the analog
speech signal is converted into digital form [
Along with mathematical methods of speech
information protection, methods using digital signal
processing (DSP) algorithms are widely demanded.
Scrambling algorithms using fast linear orthogonal
transforms (fast Fourier transform, fast wavelet transform)
and discrete filter banks are of considerable interest [
Ukraine adheres to the following classification by the level
of complexity of devices: maskers (simple), dynamic
scramblers (medium complexity), and encryptors (high
complexity) [
Scramblers using filter banks are widely used among
tactical closure systems [
. The permutation rule is the key to the system. They
have very low residual intelligibility of the scrambled signal
in the communication channel, but introduce time delay and
distortion in the reconstructed signal [
H0(z) H1(z)
HM-1(z) . . .
. . .
↓M ↓M ↓M
rule, requires radical technical solutions affecting the design of devices. When modernizing radios, the reliability of the protection system is important its simple design, and the insignificance of material costs.
P(z)
P(z)-1 ↑M ↑M ↑M
In this section, a speech information protection algorithm
using digital wavelet filter banks is proposed [
H' G' ↓2 ↓2 3 4
noise 1
signal 2 ↑2 ↑2 H G
filters. They must satisfy the conditions imposed on wavelet filters: orthogonality of the wavelet basis, and presence of zero moments.
The zero moments of the frequency response of the
approximating filter can be introduced a priori to solve
the synthesis problem. If the filter has zero moments, the
expression for ( ) can be written in the form: ( ) =
1 + ( ), where ( ) is some function [
Let us present the developed method of synthesizing the MWF. The theory of MWF is developed from the following problem. It is required to construct for ( ) a set of orthogonal quadrature-mirror wavelet filters in such a way that at its wavelet decomposition, the output of the detailing filter is zero, i.e. all detailing coefficients of the wavelet domain should be equal to zero (Fig. 3).
↓2
↓2
a(n)
{0}
The procedure of wavelet transform of the signal ( ) in
the frequency domain can be written in the following form:
( ) ( ) + ( + ) ( + ) = ( ) (1)
( ) ( ) + ( + ) ( + ) = ( ),
where ( ), ( ), ( ) are the Fourier images of the
sequence ( ), interpolated approximating and detailing
wavelet transform coefficients, respectively, and ( ) and
( ) are the frequency response (FR) of the decomposition
filters [
In order to prevent elision, we can assume that the relationship between the and filters is set to be fair for the QWF: ( ) = ⋅ ∗( + ).
(2)
This will immediately satisfy one of the constraints placed on filters:
( + ) ⋅ ( ) + ( + ) ⋅ ( ) = 0, where ( ), ( ) are the FRs of the corresponding recovery filters, with ( ) = ∗( ) and ( ) = ∗( ).
Another important property, the orthogonality property of the wavelet basis for filters in the frequency domain is written in the form:
| ( )| + | ( + )| = 2. (3)
Solving the system (1) under the assumption that ( ) = 0, and using the relation (2), we get ( ) = | ( )(| )⋅| ∗(( ) )| .
The filter ( ) is almost built, it remains to find the condition on ( ). This can be done using (3), given that ( ) = ( + ). As a result, we obtain
| ( )| = 2 ⋅ (| ( )| + | ( + )| ).
Let ( ) be a real analytic function, then
( ) = √2 ⋅ | ( )| + | ( + )| .
The final result is represented as:
( ) = | ( √)| ⋅ |∗( ( ) )| . (4)
As a result of solving the problem, digital wavelet filters
matched to the input sequence have been found. Such filters
are called matched wavelet filters [
Thus, we can present a speech protection algorithm that relies on the dual use of masking noise. The difference between the proposed system and its first variant is the addition of masking noise to the signal at the input (before the transmultiplexer) and the inverse transformation at the output. For this purpose, in addition to the transmultiplexer, including expanders and compressors of the sampling frequency, analysis, and synthesis filters, adders are introduced into the system. Fig. 4 shows a detailed block diagram of the second variant of the scheme.
H' G' ↓2 ↓2
Reconstructed
noise 3 4 ‒
Reconstructed
signal
A generalized speech information protection scheme can
also be proposed to close the conversations of several users.
It is known [
Masking noise 1 Useful signal 2 + ↑2 ↑2
H G
Communication
channel
Synthesis Bank
Analysis Bank
The masking noise [
H'
G'
The research on the system of speech information
protection using MWF was carried out on speech signals.
The system was analyzed for non-recursive (FIR filters) and
recursive (IIR filters) systems. The case of operation of the
protection algorithm in the conditions of application of the
ITU-T G.711 standard for coding signals in the channel with
8, 16, and 32 bits is considered [
Estimates of speech parameters used in the paper are discussed.
PESQ (Perceptual Evaluation of Speech Quality) is used to automatically evaluate the quality of speech transmitted in telecommunication environments.
To obtain the evaluation, the source signal and the signal at the system output are compared. The evaluation is graded on the MOS scale (mean opinion score, ITU-T recommendation P.800), which covers the range from 1 (poor) to 5 (excellent). The acceptable quality of the reconstructed signal corresponds to a PESQ score greater than 2.5 points.
Expert evaluation of speech intelligibility is introduced to determine speech intelligibility in the channel and at the system output. Based on the results of listening, the experts evaluate the intelligibility of the signal. The traditional 5-point scale was used, where the best sound quality corresponds to the highest score. At one point of the scale, the useful signal is completely unintelligible.
Acceptable quality of the recovered signal corresponds to the assessment
> 3 [
It is considered what requirements the protection system should meet.
The main purpose of the system is reliable closure of speech information with the possibility of its full recovery. Based on the purpose, for the proposed speech protection system the recovered signal should have good intelligibility. The signal in the channel on the contrary should be completely unintelligible. Such conditions are fulfilled for a certain interval of values of the parameter . The lower limit of the parameter is determined from the conditions when distortions of the reconstructed signal become unacceptable for perception. It is estimated by the PESQ criterion and the expert evaluation of speech intelligibility . The upper limit is determined from the conditions when the useful signal in the channel becomes completely unintelligible and is based on the evaluation of . The masking noise power satisfying these conditions is selected from the interval formed by the intersection of the shaded regions in Figs. 7 and 8. The value of the PESQ score, which is chosen to be greater than 2.5, is also considered. Thus, the selection interval for the parameter is: (a) −34 < , дБ < −15 for FIR filters. (b) −20 < , дБ < −15 for IIR filters.
The noise immunity of the system is considered as the performance of the system under information distortion in the presence of noise. Generalized, as an external noise is used AWGN, modeling data distortion. Based on the values of > 2.5 points (Fig. 9), it follows that acceptable quality of the transmitted signal is achievable at > 25 dB.
It is established that the algorithm is robust to external noise. The dependence of the signal-to-noise ratio (SNR) at the system output on the SNR in the channel is linear.
The resilience of the system, i.e., the extent to which it is secure against the tampering of the contents of the negotiation, is the most important and challenging issue.
The technical unrealizability of the cracking system is confirmed by the results of a direct search of key combinations, which did not yield any results for a limited time interval (a week). The search was conducted on a test computer (Windows 11 operating system; 11th Gen Intel (R) Core (TM) i7-11370H 3.3 GHz processor; 16 GB memory) and the algorithm was simplified. As in most modern defense systems, the system persistence is determined by the amount of key information. In this work, we used keys with dimensionality from 150 to 250 bits (20 samples). Accordingly, there are 2 variants of the key sequence. There is a dependence on the key length in the system (Fig. 10). With its increase the quality of the reconstructed signal deteriorates from excellent to good (at 150 samples and further). This behavior of the system can be explained by the accumulation of errors as a result of convolution with a filter with a long impulse response. It is acceptable to use a key with a dimensionality of 20–30 samples.
The physical unrealizability of the hacking system is based on the fact that to date there are no systems that allow to distinguish the signal against the background of noise at the values of the parameter used in this work. The application of known methods of noise suppression did not give a positive result. It is technically very difficult to isolate a useful signal. To ensure reliable protection of information, the key is chosen to be noise-like and can be generated using a pseudo-random number generator. When the key length increases, the frequency response of filters becomes more complicated, and the degree of information closure increases. It is found that it is inefficient to use very long keys because the algorithm performance decreases as a result of long convolutions. The method of key distribution is a separate non-trivial task. Most often participants agree on the key to be used beforehand.
Based on the research conducted on the speech information protection system, the following results are obtained in this paper: (1) A method for synthesizing matched wavelet filters satisfying the property of orthogonality of the wavelet basis, the presence of zero moments is presented. The important requirements on the filters are the conditions of complete signal recovery and elimination of overlapping spectra. The results of the studies show the effectiveness of synthesized wavelet filters in solving the problem of information protection. (2) A speech protection algorithm is developed that uses MWF at the stage of building a bank of analysis-synthesis filters consistent with the key. The algorithm has a simple implementation, and fast algorithms of digital signal processing (convolution, decimation, interpolation), allowing encrypting of the signal in real-time. The proposed algorithm is noise-resistant and can be used in channels with intense interference, with the value of the parameter > 25 dB. The algorithm is robust to time delays and hiccups, distortions in the communication channel. (3) Operating parameters of the protection system are obtained, satisfying the high degree of system closure and acceptable quality of the recovered signal. Operating parameters are calculated based on PESQ estimation, and expert estimation . Such estimations allow us to qualitatively describe the processes occurring in the speech protection system. The parameter setting interval : −34 < , дБ < −15 for FIR filters and −20 < , дБ < −15 for IIR filters is obtained. (4) The system is analyzed for FIR and IIR filters. The quality of the decoded signal is lower when using FIR filters, because of the error amplification in recursive systems. (5) The case of operation of the protection algorithm in conditions of application of ITU-T G.711 standard for signal coding is considered. The results are obtained taking into account the quantization of the signal in channels 8, 16, and 32 bits. It is found that 8 and 16-bit quantization of encrypted signal in the channel provides necessary conditions for correct protected transmission of speech information. There is no need to increase the number of quantization levels (for example, up to 32 bits). (6) The estimation of the degree of speech information closure, determined mainly by the ratio of masking noise and useful signal levels, is carried out. From the analysis of signal spectrograms in the channel, it follows that it is very difficult to distinguish a useful signal from the mixture. The amount of key information, which determines the number of tests required for key selection, has been estimated. In this work, we used keys of dimension from 150 to 250 bits, and the number of key combinations is 2 . Direct search of key combinations for the allotted time did not give results. The information can be decrypted only by knowing the key on the receiving side with which it was encrypted.
Future research requires analyzing the system behavior depending on the type of masking noise, i.e., investigating noise, structural, and combined interference. To find out which noise interference of white noise type, a mixture of white and pink noise, and structural interference of “speech chorus” type are the most suitable for the proposed information protection system.