Method of speech signal scrambling based on matched wavelet filters ⋆ Oleksandr Lavrynenko1,*,† 1 National Aviation University, 1 Lubomyr Huzar ave., 03058 Kyiv, Ukraine Abstract 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. Keywords speech signal, wavelet transform, packet wavelet transform, matched wavelet filter, speech scrambling, speech information protection, speech intelligibility, masking noise 1 1. Introduction change in the signal bandwidth and very low residual intelligibility of the signal in the communication channel Information protection is an integral part of communication [6]. When using fast transformations increases the degree systems. Nowadays, more and more attention is paid to the of information closure, but also increases the computational protection of speech information, which is associated with the complexity of the processing algorithm, there is a delay in growth of speech communication in the modern information the signal [7, 8]. Orthogonal scramblers are not deprived of environment [1]. the common disadvantages of scramblers and introduce With the development of digital communication in radio distortions in the recovered speech signal determined by the engineering, gaming methods, and cryptographic dispersion in the channel and synchronization error [9]. algorithms have become widespread. Initially, the analog Thus, the problem of developing new fast algorithms for the speech signal is converted into digital form [2]. An protection of speech information operating under noise encryption algorithm is applied to the coefficients or signal conditions is urgent. parameters obtained after encoding [3]. Such systems have a high level of protection and require computational 2. Literature review and problem resources. Under interference conditions such algorithms do not work efficiently. A wide range of tasks requires statement algorithms that are applicable in the presence of sufficiently Ukraine adheres to the following classification by the level strong interference [4]. of complexity of devices: maskers (simple), dynamic Along with mathematical methods of speech scramblers (medium complexity), and encryptors (high information protection, methods using digital signal complexity) [10]. The maskers providing the tactical level of processing (DSP) algorithms are widely demanded. information protection include spectrum inverters, and Scrambling algorithms using fast linear orthogonal static scramblers [11]. The proposed speech masking transforms (fast Fourier transform, fast wavelet transform) algorithm also belongs to this class. and discrete filter banks are of considerable interest [5]. As Scramblers using filter banks are widely used among a rule, they are based on manipulations with spectral tactical closure systems [12]. In general, the traditional coefficients of linear transformation of signals. Such scheme contains M-channel analysis-synthesis filter banks, algorithms, when scrambling, cause a relatively small and forward and backward permutation blocks (Fig. 1) [13]. CPITS-II 2024: Workshop on Cybersecurity Providing in Information 0000-0002-7738-161X (O. Lavrynenko) and Telecommunication Systems II, October 26, 2024, Kyiv, Ukraine © 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). ∗ Corresponding author. † These authors contributed equally. oleksandrlavrynenko@gmail.com (O. Lavrynenko) CEUR Workshop ceur-ws.org ISSN 1613-0073 229 Proceedings Mixing of signal segments according to a certain unlike other masking methods, the proposed method of permutation rule takes place in the block 𝑃. Reverse speech signal scrambling based on matched wavelet filters permutation occurs at the input of the decoder in the block has a high degree of information closure, high quality of 𝑃 . The permutation rule is the key to the system. They reconstructed speech, and a sufficiently large number of have very low residual intelligibility of the scrambled signal keys. in the communication channel, but introduce time delay and distortion in the reconstructed signal [14]. For its class, x(n) H0(z) ↓M ↑M G0(z) H1(z) ↓M ↑M G1(z) P(z) P(z)-1 ... ... ... ... y(n) HM-1(z) ↓M ↑M GM-1(z) Encoder Decoder Figure 1: Scrambler circuit as an M-channel filter bank This allows to use of its advantages for modernization of the 3. Proposed method existing fleet of radio stations. For example, the use of such a task on more complex devices with guaranteed In this section, a speech information protection algorithm information closure encryptors [15], is unjustified and, as a using digital wavelet filter banks is proposed [16]. To build rule, requires radical technical solutions affecting the design the protection system, an inverse scheme of single-level of devices. When modernizing radios, the reliability of the discrete wavelet transform is used. It includes digital protection system is important its simple design, and the synthesis and analysis filter banks (Fig. 2). The filters used insignificance of material costs. are synthesized using a key sequence. The key identifies the sender and receiver of information and is used only at the filter synthesis stage [17]. Masking Reconstructed ↑2 H H' ↓2 noise 1 3 noise Communication channel Useful Reconstructed ↑2 G G' ↓2 signal 2 4 signal Synthesis Bank Analysis Bank Figure 2: Block diagram of the information protection system The useful signal is input to input 2 of the synthesis bank, The additive mixture of interference and useful signal then to the sampling frequency expander and filter- images can be easily separated based on the orthogonality interpolator 𝐺. This shifts the frequency range of speech to of the approximating and wavelet functions. The choice of the high-frequency region, which is positive for its closure. the key initially determines the shape of these functions and For other types of data, the useful signal can be fed to any the frequency properties of the corresponding wavelet input of the synthesis bank. A masking additive white filters. To ensure reliable information protection, the key is Gaussian noise (AWGN) of higher power is fed to input 1, chosen to be noise-like and can be generated using a then to the sampling rate expander and filter interpolator 𝐻. pseudo-random number generator [20]. The signal images transformed by the filters are mixed to Such an information protection system can be realized form a noise-like mixture [18]. The extraction of a useful only due to the orthogonality properties of matched wavelet signal from such a mixture occurs after it passes through the filters (MWFs) [21]. Unknown basis functions must be used filter-decimator 𝐺 And the sampling frequency compressor for mixing with signal samples. A similar protection system in the analysis bank. The transform over the signal changes can be built on the well-known Daubechies, and Haar the bandwidth of the signal as a result of interpolation. The wavelet filters, but it will be easy to crack. frequency of the signal in the channel is increased by a To build a robust system, quadrature-mirror wavelet factor of 2 compared to the input signal. The system has the filters (QWFs) with unique frequency responses are property of exact recovery [19]. required [22]. Such filters can be matched with wavelet 230 filters. They must satisfy the conditions imposed on wavelet This will immediately satisfy one of the constraints placed filters: orthogonality of the wavelet basis, and presence of on filters: zero moments. 𝐺(𝜔 + 𝜋) ⋅ 𝐺(𝜔) + 𝐻(𝜔 + 𝜋) ⋅ 𝐻(𝜔) = 0, The zero moments of the frequency response of the where 𝐺(𝜔), 𝐻(𝜔) are the FRs of the corresponding approximating filter 𝐻 can be introduced a priori to solve the synthesis problem. If the filter has zero moments, the recovery filters, with 𝐺(𝜔) = 𝐺 ∗ (𝜔) and 𝐻(𝜔) = 𝐻 ∗ (𝜔). expression for 𝐻(𝜔) can be written in the form: 𝐻(𝜔) = Another important property, the orthogonality property of the wavelet basis for filters in the frequency 1+𝑒 𝑄(𝜔), where 𝑄(𝜔) is some function [23]. domain is written in the form: Let us present the developed method of synthesizing the |𝐻(𝜔)| + |𝐻(𝜔 + 𝜋)| = 2. (3) MWF. The theory of MWF is developed from the following Solving the system (1) under the assumption problem. It is required to construct for 𝑓(𝑛) a set of that𝐷(𝜔) = 0, and using the relation (2), we get orthogonal quadrature-mirror wavelet filters in such a way ( )⋅ ∗ ( ) that at its wavelet decomposition, the output of the detailing 𝐻(𝜔) = | ( )| | ( )| . filter is zero, i.e. all detailing coefficients of the wavelet The filter 𝐻(𝜔) is almost built, it remains to find the domain should be equal to zero (Fig. 3). condition on 𝐴(𝜔). This can be done using (3), given that 𝐴(𝜔) = 𝐴(𝜔 + 𝜋). As a result, we obtain a(n) |𝐴(𝜔)| = 2 ⋅ (|𝐹(𝜔)| + |𝐹(𝜔 + 𝜋)| ). HMWF ↓2 Let 𝐴(𝜔) be a real analytic function, then f(n) 𝐴(𝜔) = √2 ⋅ |𝐹(𝜔)| + |𝐹(𝜔 + 𝜋)| . The final result is represented as: {0} GMWF √ ⋅ ∗( ) ↓2 𝐻(𝜔) = . (4) | ( )| | ( )| As a result of solving the problem, digital wavelet filters Figure 3: MWF synthesis problem matched to the input sequence have been found. Such filters are called matched wavelet filters [25] since their impulse The procedure of wavelet transform of the signal 𝑓(𝑛) in response is formed taking into account the properties of the the frequency domain can be written in the following form: processed signal. In our case, it is a key sequence. Thus, the 𝐻(𝜔)𝐹(𝜔) + 𝐻(𝜔 + 𝜋)𝐹(𝜔 + 𝜋) = 𝐴(𝜔) (1) information about the key is embedded in the filters 𝐺(𝜔)𝐹(𝜔) + 𝐺(𝜔 + 𝜋)𝐹(𝜔 + 𝜋) = 𝐷(𝜔), themselves. where 𝐹(𝜔), 𝐴(𝜔), 𝐷(𝜔) are the Fourier images of the Thus, we can present a speech protection algorithm that sequence 𝑓(𝑛), interpolated approximating and detailing relies on the dual use of masking noise. The difference wavelet transform coefficients, respectively, and 𝐻(𝜔) and between the proposed system and its first variant is the 𝐺(𝜔) are the frequency response (FR) of the decomposition addition of masking noise to the signal at the input (before filters [24]. the transmultiplexer) and the inverse transformation at the In order to prevent elision, we can assume that the output. For this purpose, in addition to the transmultiplexer, relationship between the 𝐻 and 𝐺 filters is set to be fair for including expanders and compressors of the sampling the QWF: frequency, analysis, and synthesis filters, adders are 𝐺(𝜔) = 𝑒 ⋅ 𝐻 ∗ (𝜔 + 𝜋). (2) introduced into the system. Fig. 4 shows a detailed block diagram of the second variant of the scheme. Masking Reconstructed noise 1 ↑2 H H' ↓2 noise 3 Communication channel Useful Reconstructed signal 2 + ↑2 G G' ↓2 ‒ signal 4 Synthesis Bank Analysis Bank Figure 4: Block diagram of a speech protection system with double masking The masking noise [26] is fed to input 1, then to the A generalized speech information protection scheme can sampling rate expander and filter-interpolator 𝐻. At the also be proposed to close the conversations of several users. same time, it is also fed to the adder. The useful signal is fed It is known [27] that wavelet decomposition over both to input 2, mixed in the adder with the higher power subbands yields a complete balanced tree (Fig. 5). If the masking noise. The mixture then goes to the sampling rate initial block of wavelet filters is orthogonal, then the scheme expander and filter interpolator 𝐺. The signal images corresponding to any level of the full tree decomposition is transformed by the filters are mixed to form a noise-like orthogonal. Such a scheme as a whole, as well as its separate mixture. The reconstruction of the signal in the analysis block, has the property of accurate signal recovery. An bank is done in reverse order. The system has the property inverse scheme consisting of separate blocks can also be of accurate recovery. The key point is the uniqueness of the constructed for the full wavelet tree [28]. analysis and synthesis filter banks. Wavelet filters are synthesized in the previously described way. 231 4. Results and discussion H' ↓2 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 G' ↓2 recursive (IIR filters) systems. The case of operation of the protection algorithm in the conditions of application of the Analysis Bank ITU-T G.711 standard for coding signals in the channel with 8, 16, and 32 bits is considered [31]. The operating parameter of the system is the masking noise power. To analyze the influence of masking noise, the parameter 𝑀 is the ratio of signal and masking noise power in dB is introduced. To study the noise immunity of the system, the parameter 𝑁 is the ratio of signal and external noise power in the communication channel in dB was introduced: 𝑀 = 10 ⋅ 𝑙𝑔 ; 𝑁 = 10 ⋅ 𝑙𝑔 . Figure 5: Two-level decomposition of the frequency-time Estimates of speech parameters used in the paper are plane using wavelet packets discussed. PESQ (Perceptual Evaluation of Speech Quality) is used In this paper, an inverse scheme for two levels of to automatically evaluate the quality of speech transmitted decomposition is considered. It consists of 3 pairs of analysis in telecommunication environments. To obtain the and synthesis banks and has 4 inputs (Fig. 6). The circuit can evaluation, the source signal and the signal at the system be used to protect speech information in several ways: (1) output are compared. The evaluation is graded on the MOS masking noise is fed to one of the inputs, the other inputs scale (mean opinion score, ITU-T recommendation P.800), have useful signal; (2) useful signal is fed to one of the which covers the range from 1 (poor) to 5 (excellent). The inputs, the other inputs have masking noise. In the first case, acceptable quality of the reconstructed signal corresponds the number of users using a common channel for secure to a PESQ score greater than 2.5 points. transmission of speech information increases to 3. In the Expert evaluation of speech intelligibility 𝑄 is second case, due to the imposition of several noises introduced to determine speech intelligibility in the channel increases the security of the system. Along with this two- and at the system output. Based on the results of listening, level discrete wavelet transform scheme [29] complicates the experts evaluate the intelligibility of the signal. The the speech protection system. Only the first case is traditional 5-point scale was used, where the best sound considered in this paper. 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 ↑2 H the assessment 𝑄 > 3 [32]. The 𝑄 score agrees well with the PESQ speech quality score. ≡ It is considered what requirements the protection system should meet. ↑2 G The main purpose of the system is reliable closure of speech information with the possibility of its full recovery. Synthesis Bank 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 𝑀. The lower limit of the parameter 𝑀 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 𝑄. The upper limit is determined from the conditions when Figure 6: Frequency-time plane partitioning using wavelet the useful signal in the channel becomes completely packets in a multi-user scheme unintelligible and is based on the evaluation of 𝑄. The The circuit uses MWFs synthesized by key sequence. For masking noise power satisfying these conditions is selected synthesizing each pair of filter banks a common key for all from the interval formed by the intersection of the shaded pairs is used. Masking noise is fed to one of the inputs of the regions in Figs. 7 and 8. The value of the PESQ score, which system, the other inputs are approximately equal in power is chosen to be greater than 2.5, is also considered. useful signals. This principle is used to close the conversations of three users at once. As a masking noise is used AWGN [30] of higher power. 232 Figure 9: Dependence of 𝑃𝐸𝑆𝑄 on 𝑁 Figure 7: Dependence of speech intelligibility estimation in the communication channel on 𝑀 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 𝑀 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. Figure 8: Dependence of the system output speech intelligibility estimate on 𝑀 Thus, the selection interval for the parameter 𝑀 is: (a) −34 < 𝑀, дБ < −15 for FIR filters. (b) −20 < 𝑀, 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 𝑃𝐸𝑆𝑄 > 2.5 points (Fig. 9), it follows that acceptable quality of the transmitted signal is achievable at 𝑁 > 25 dB. It is established that the algorithm is robust to external Figure 10: Dependence of PESQ on the key dimension noise. The dependence of the signal-to-noise ratio (SNR) at the system output on the SNR in the channel is linear. To ensure reliable protection of information, the key is The resilience of the system, i.e., the extent to which it chosen to be noise-like and can be generated using a is secure against the tampering of the contents of the pseudo-random number generator. When the key length negotiation, is the most important and challenging issue. increases, the frequency response of filters becomes more The technical unrealizability of the cracking system is complicated, and the degree of information closure confirmed by the results of a direct search of key increases. It is found that it is inefficient to use very long combinations, which did not yield any results for a limited keys because the algorithm performance decreases as a time interval (a week). The search was conducted on a test result of long convolutions. The method of key distribution computer (Windows 11 operating system; 11th Gen Intel (R) is a separate non-trivial task. Most often participants agree Core (TM) i7-11370H 3.3 GHz processor; 16 GB memory) on the key to be used beforehand. 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 5. Conclusions with dimensionality 𝑏 from 150 to 250 bits (20 samples). Based on the research conducted on the speech information Accordingly, there are 2 variants of the key sequence. protection system, the following results are obtained in this paper: 233 (1) A method for synthesizing matched wavelet Future research requires analyzing the system behavior filters satisfying the property of orthogonality of depending on the type of masking noise, i.e., investigating the wavelet basis, the presence of zero moments is noise, structural, and combined interference. To find out presented. The important requirements on the which noise interference of white noise type, a mixture of filters are the conditions of complete signal white and pink noise, and structural interference of “speech recovery and elimination of overlapping spectra. chorus” type are the most suitable for the proposed The results of the studies show the effectiveness information protection system. of synthesized wavelet filters in solving the problem of information protection. 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