**1. Introduction**

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The increased interest in analog speech scrambling techniques are due to the increased visibility and publicity given to the vulnerability of communication systems to eavesdropping of unauthorized remote access (Gersho & Steele, 1984). In wireless communications, including High Frequency (H.F) and satellite communications, it is almost impossible to prevent unauthorized people from eavesdropping unless speech scramblers may be used to protect privacy. Among speech scramblers, analog scramblers are attractive and wide applicable. The conventional analog scramblers manipulate speech signal in the frequency or time domain or both. A typical frequency domain scrambler is the band splitting scrambler, which breaks the speech signal into several sub bands and permutes them. A typical time domain scrambler is the time division scrambler, which breaks the speech signal into short time segments and permutes them within a block of several segments(Sakurai et al., 1984). These conventional analog scramblers cannot provide sufficient security against cryptanalysis because the number of permutable elements in these scramblers is not large enough to provide an adequate number of different permutations due to hardware limitation and processing delays.

To strengthen security, a two-dimensional scrambler which manipulates the speech signal both in the frequency domain and in the time domain was proposed. Regarding other types of scramblers, which can attain a high degree of security, the transform domain scrambler was proposed.

In 1979, Wyner proposed a method, in which the orthogonal transform called a Prolate Spheroidal transform (PSD) was executed on a set of the sampled speech signal. A mathematical basis for using both band splitting and time division, at the same time was presented by F. Pichler in 1983. He showed how an operation which realizes band splitting and time division can be designed, and pointed out that such an operation can be realized by a fast algorithm. The mathematical background is the theory of group-character for finite Abelian Groups and the theory of the General Fast Fourier Transform (GFFT) (Pichler, 1983). Also in 1984 Lin-Shan et. al., presented frequency domain scrambling algorithm, which is an extension of the Discrete Fourier Transform (DFT) scrambler previously proposed. The use of short-time Fourier analysis and filter bank techniques lead to the special feature that the original speech could be correctly recovered while the frame synchronization is completely

Speech Scrambling Based on Wavelet Transform 43

scrambling efficiency through the calculation of distance measures, and takes the effect of the channel noise into consideration (Sadkhan, et al., 2005). In 2007, A Parallel Structure of different wavelet transforms were applied for speech scrambling. The proposed structure provided a good results in comparison with the system implemented in 2005 (Sadkhan,

Speech Scrambling seeks to perform a completely reversible operation on a portion of speech, that it is totally unintelligible to unauthorized listener. The most important criteria

 The scrambler's ability to produce encrypted speech with low residual intelligibility. The extent to which the encryption and decryption processes affect the quality of the

Cryptographers face the problem of designing scrambling systems which distort the very redundant speech signal to the extent that useful information is unable to be recovered. The encryption process must remain secure when subject to the powerful information processing structures of the human auditory system and knowledge-base automated cryptanalytic processes. There are two fundamentally distinct approaches to achieve voice security in speech communication systems: digital ciphering and analog scrambling. In spite of significant progress in digital speech processing technology, analog speech scramblers continue to be important for achieving privacy in many types of voice communication (Gersho & Steele, 1984), due to the desire for secure communication over existing channels with standard telephone bandwidth at acceptable speech quality and reasonable cost. To make the distinction between analog and digital speech encryption devices, the following definitions can be considered. Analog scramblers produce scrambled speech which is analog signal occupying the same bandwidth as the original speech. Analog or digital signal processing may be used to generate this signal. Digital speech encryption systems digitize and compress the input speech in order to obtain a digital representation at a bit rate suitable for the communications channel to be used. The resulting bit stream is encrypted using well-know data encryption techniques. The ability of a digital encryption schemes to compete with the well-established analog scramblers is depend on the quality of the speech compression algorithms used. The speech quality resulting from contemporary compression

Analog speech scrambling experienced a metamorphosis as a result of the development and release of very high speed signal processing hardware. Analog scrambling algorithms which were impractical due to their complex nature are now being implemented in real time using

One family of analog scramblers that has shown a great deal of promise is the transform domain scrambler. These scramblers operate on speech which has been sampled and digitized. The sampled speech is portioned into frames of equal length, containing N speech samples. A chosen transformation is then performing on each frame to yield a transform vector with N components. Encryption is achieved by permuting these transform components within the vector before the inverse transform is applied to return the

Falah, 2007)

**2. Speech scrambling system** 

used to evaluate speech scramblers are:

speech recovered by intended reception; and The scrambler's immunity to cryptanalysis attack.

schemes is rapidly improving (Sakurai, et al., 1984).

this technology.

unnecessary. In 1990 Sridharan et. Al., presented a comparison among five discrete orthogonal transforms in speech encryption systems. The results of the research showed that the Discrete Cosine Transform (DCT) and the Discrete Prolate Spheroidal Transform (DPST) could be used in narrow band systems. The Karhunen Loeve Transform (KLT) and the Discrete Hadamard Transform (DHT) were more suitable where wider bandwidth was available. The DCT turned out to be the best transform with respect to residual intelligibility of the encryption speech and recovered speech quality. The DFT produced results which were inferior to the DCT. The DCT implementation would also offer speed advantage over the FFT (Sridharan et al., 1990).

Original BSS (Blind Source Separation) – based speech encryption system utilizes BSS to perform decryption, but the complexity of BSS algorithms limits the decryption speed and its real-time applications. In 2010 , fast decryption utilizing calculation for BSS-based speech encryption was proposed. The paper analyzed the correlation of speech signals with key signals, and then utilized the correlation calculation to achieve speech decryption. The experiment results showed that correlation calculation decryption nicely simplifies BSS-bsed speech encryption system, largely speeds up the speech decryption, and slightly improves the quality of decrypted speech signals (Guo & Lin, 2010). While Mermoul and Belouchhrani claimed that the interactability of the under-determined BSS problem has been used for the proposal of BSS-based speech encryption has some weakness from cryptographic point of view. In their paper they proposed new encryption method that bypass these weaknesses. Their proposed approach is based on the subspace concept together with the use of nonlinear function and key signals. An interesting feature of the proposed technique is that only a part of the secret key parameters used during encryption is necessary for decryption (Mermoul & Belouchrani, 2010)

(Mosa, et al., 2010) introduced a new speech cryptosystem, which is based on permutation and masking of speech segments using multiple secret keys in both time and transform domain.

In 2000, an automated method for cryptanalysis of DFT-based analog speech scramblers was presented by Wen-Whei and Heng-Iang, through statistical estimation treatments. In the proposed system, the cipher text only attack was formulated as a combinatorial optimization problem leading to a search for the most likely key estimate. For greater efficiency, they also explored the benefits of Genetic Algorithm to develop the method. Simulation results indicated that the global explorative properties of Genetic Algorithms make them very effective at estimating the most likely permutation and by using this estimate significant amount of the intelligibility could be recovered from the cipher text following the attack on DFT-based speech scramblers (Whei & Iang, 2000)

A time-frequency scrambling algorithm based on wavelet packets was proposed by Ajit S. B. Bopardikar (1995) by using different wavelet packet filter banks, they added an extra level of security since the eavesdropper had to choose the correct analysis filter bank, correctly rearrange the time-frequency segments, and choose the correct synthesis bank to get back the original speech signal. Simulations performed with this algorithm give distance measures comparable to those obtained for the uniform filter bank based algorithm( Bopardikar, 1995). In 2005, an analog speech scrambler which is based on Wavelet Transformation and Permutation was proposed by Sattar B. Sadkhan and evaluating the

unnecessary. In 1990 Sridharan et. Al., presented a comparison among five discrete orthogonal transforms in speech encryption systems. The results of the research showed that the Discrete Cosine Transform (DCT) and the Discrete Prolate Spheroidal Transform (DPST) could be used in narrow band systems. The Karhunen Loeve Transform (KLT) and the Discrete Hadamard Transform (DHT) were more suitable where wider bandwidth was available. The DCT turned out to be the best transform with respect to residual intelligibility of the encryption speech and recovered speech quality. The DFT produced results which were inferior to the DCT. The DCT implementation would also offer speed advantage over

Original BSS (Blind Source Separation) – based speech encryption system utilizes BSS to perform decryption, but the complexity of BSS algorithms limits the decryption speed and its real-time applications. In 2010 , fast decryption utilizing calculation for BSS-based speech encryption was proposed. The paper analyzed the correlation of speech signals with key signals, and then utilized the correlation calculation to achieve speech decryption. The experiment results showed that correlation calculation decryption nicely simplifies BSS-bsed speech encryption system, largely speeds up the speech decryption, and slightly improves the quality of decrypted speech signals (Guo & Lin, 2010). While Mermoul and Belouchhrani claimed that the interactability of the under-determined BSS problem has been used for the proposal of BSS-based speech encryption has some weakness from cryptographic point of view. In their paper they proposed new encryption method that bypass these weaknesses. Their proposed approach is based on the subspace concept together with the use of nonlinear function and key signals. An interesting feature of the proposed technique is that only a part of the secret key parameters used during encryption is necessary for decryption

(Mosa, et al., 2010) introduced a new speech cryptosystem, which is based on permutation and masking of speech segments using multiple secret keys in both time and transform

In 2000, an automated method for cryptanalysis of DFT-based analog speech scramblers was presented by Wen-Whei and Heng-Iang, through statistical estimation treatments. In the proposed system, the cipher text only attack was formulated as a combinatorial optimization problem leading to a search for the most likely key estimate. For greater efficiency, they also explored the benefits of Genetic Algorithm to develop the method. Simulation results indicated that the global explorative properties of Genetic Algorithms make them very effective at estimating the most likely permutation and by using this estimate significant amount of the intelligibility could be recovered from the cipher text

A time-frequency scrambling algorithm based on wavelet packets was proposed by Ajit S. B. Bopardikar (1995) by using different wavelet packet filter banks, they added an extra level of security since the eavesdropper had to choose the correct analysis filter bank, correctly rearrange the time-frequency segments, and choose the correct synthesis bank to get back the original speech signal. Simulations performed with this algorithm give distance measures comparable to those obtained for the uniform filter bank based algorithm( Bopardikar, 1995). In 2005, an analog speech scrambler which is based on Wavelet Transformation and Permutation was proposed by Sattar B. Sadkhan and evaluating the

following the attack on DFT-based speech scramblers (Whei & Iang, 2000)

the FFT (Sridharan et al., 1990).

(Mermoul & Belouchrani, 2010)

domain.

scrambling efficiency through the calculation of distance measures, and takes the effect of the channel noise into consideration (Sadkhan, et al., 2005). In 2007, A Parallel Structure of different wavelet transforms were applied for speech scrambling. The proposed structure provided a good results in comparison with the system implemented in 2005 (Sadkhan, Falah, 2007)
