WO2012049659A2 - High payload data-hiding method in audio signals based on a modified ofdm approach - Google Patents

Abstract

Abstract. This invention relates to a high-capacity data hiding method for audio signals following the OFDM concept. It is based on changing the phase component of the audio signal via an M-order Phase Shift Keying (MPSK) modulator on selected frequency samples of the audio signal. This approach allows the data hiding capacity and perceptual distortion to be controlled by the number of altered frequency components of the audio signal and the severity of this alteration. The data hiding capacity can be estimated a priori independently of the audio signal features. In addition, due to the relation of the proposed scheme with the traditional use of MPSK modulation, the BER of the encoded data is analytically derived, therefore, it is known in advance, allowing the integration of channel encoders. Results obtained with representative test cases show that the proposed algorithm provides an increase of one order of magnitude in data payload compared with state-of-the-art works.

Description

High payload data-hiding method in audio signals based on a modified OFDM approach

Field of the invention.

The present invention relates generally to a steganographic application using audio signals where high payload and low perceptual distortion are pursued. More particularly, the invention relates to a data hiding method for audio signals following the Orthogonal Frequency-Division Multiplexing (OFDM) concept. Background of the invention.

The expansion of the Internet together with a rapid advance in high capacity storage systems such as the Compact Disc (CD) and Digital Versatile Disc (DVD) has facilitated the fast and perfect copying of digital content. However, this has led to unauthorized copying and distribution of digital materials. Digital watermarking, also called data hiding in this patent application, has been considered a solution for this problem. It is a technique that embeds an imperceptible and statistically undetectable signal in digital content. Watermarking algorithms must be imperceptible, robust to common intentional or non-intentional attacks, and have a high data embedding rate. These requirements make high performance audio watermarking algorithms hard to develop because the human auditory system is sensitive to small changes in audio signals, as shown in Arnold, M. (2002)¹.

Within data hiding technique, digital watermarking and steganography are the main concepts devoted to exploit the hidden data for different purposes. In one hand, watermarking has been considered as one of the techniques with capacity to solve problems such as unauthorized copying and distribution of digital materials². In order to be considered suitable for practical applications, watermarking algorithms must satisfy among others the robustness requirement, which limits the payload to a few bits of hidden data. On the other hand, steganography is a kind of secret communication using digital multimedia as the communication channel, therefore, the main demand is for both a high payload and high perceptual transparency. Contrary to watermarking algorithms, in steganographic systems the robustness is not an issue³. An ideal steganographic scheme should have a large embedding capacity and excellent perceptual transparency⁴. Among the variety of data where information can be hidden, digital images and audio signals are preferred, where a lot of work has been carried out using digital images as cover signals^5,6,7 and to a lower extent using audio signals. During the last decade, several audio data hiding algorithms have been proposed in the literature^{1 ,8,9,10,1 1 , 12}. Within the main approaches, it can be cited the method of echo hiding as one of the most successful temporal domain methods^8,9,10. It embeds data bits using echo signals with different delays with the property of being highly imperceptible, but the payload is low. Other method is based on spread-spectrum data hiding methods embed a pseudo-random sequence generated using a secret owner's key into some frequency bands of the audio signal^{11 ,13, 14}. In spread-spectrum method, an audio signal is transformed by Discrete Cosine Transform (DCT), Discrete Fourier Transform (DFT), or Discrete Wavelet Transform (DWT) and a pseudo-random sequence is embedded considering the imperceptibility requirements. Implementation of this method is generally simple, however, the achieved payload is very low, and therefore, it is more appropriated for watermarking scenarios. Other algorithm, recently proposed, is based on spline interpolation and has shown one of the highest bitrates and human transparencies reported to date¹⁵. Modifying the phase of several frequency components is another approach used to hide data in media^16,17. When the frequency components are obtained using an orthogonal base, these data hiding schemes can be analyzed as Orthogonal Frequency-Division Multiplexing (OFDM) systems that use M-Phase Shift Keying (MPSK) constellations. OFDM is a scheme utilized as a digital multi-carrier modulation method where a large number of orthogonal sub-carriers are used to carry data. The data are divided into several parallel data streams or channels, one for each sub-carrier. Each sub-carrier is modulated with a conventional modulation scheme such as quadrature amplitude modulation (QAM) or phase-shift keying (PSK). In Tie-sheng et al., 2008¹⁸, the OFDM approach was used in combination with Quantization Index Modulation (QIM) in order to hide a secret image into a host image reporting a payload of 1 bit/pixel.

In Lin et al., 2006¹⁹, the data are hidden into the physical layer of OFDM-based wireless networks. This scheme is not appropriate for steganographic purposes due to the data are not hidden in the media signal but in the OFDM carriers of the wireless networks. The OFDM approach using frequency components of audio signals as carriers was presented as Acoustic OFDM in Matsouka et al., 2009²⁰. That scheme is focused on applications to transmit short messages to mobile handheld devices over aerial audio links. Acoustic OFDM uses Differential Binary Phase Shift Keying (D-BPSK) modulation. Although the robustness in analog scenarios is satisfactory, the payload reported by Acoustic OFDM is low and inappropriate for steganographic applications. The bitrate of the schemes based in OFDM concept are dependent on the audio clip used as host signal, in addition, the Objective Difference Grade (ODG) estimation is carried out after the data hiding process. These characteristics limit the flexibility of the data hiding process in the sense that it is not possible to know a priori the embedding capacity of the medium, therefore, in view of the deficiencies of the methods described above, improved methods of data hiding scheme for audio signals are needed.

In the prior art, there are many other examples of data hiding method like the one described in the USPat 7,289,961 where said method comprises: dividing the audio signal into a plurality of time frames and, in each time frame a plurality of frequency components; in each of at least some of the plurality of time frames selecting a fundamental tone and at least one overtone; and altering a phase of at least one of the plurality of frequency components in accordance with the data to be embedded, quantizing a phase difference of the at least one overtone relative to the fundamental tone to embed at least one bit of the data to be embedded.

Another example of the above is described in the USPat 2009/0076826 which discuss a method for watermarking data embedded in an audio signal by using modifications of the phase of said audio signal, said method comprising the steps: controlling by the value of a current bit of said watermark data the selection of the generation of a corresponding reference data sequence; modifying according to said corresponding reference data sequence, phase values in a current time to frequency domain converted block of said audio signal, whereby within said current block the allowable frequency range or ranges for said phase value modification by a predetermined maximum amount are determined by psyco-acoustic related calculations; frequency to time domain converting the modified version of said current block of said audio signal; outputting the corresponding section of the watermarked audio signal. At the light of the aforementioned, it is evident that several particular watermarking techniques have been developed. The reader is presumed to be familiar with the literature in this field. Particular techniques for embedding and detecting imperceptible watermarks in media signals are detailed in USPat 7,062,069, USPat 7,1 13,614, USPat 7,391 ,881 and USPat 7,454,033.

Brief summary of the invention.

This invention proposes a generalization of a data-hiding method for audio signals that uses the concept of OFDM and results in a method with the highest payload capacity when compared with previous commented studies. In addition, the proposed method allows the hiding capacity and perceptual distortion to be controlled by the number of altered frequency components of the audio signal and the severity of this alteration, in contrast to the previous OFDM-based data hiding schemes where the payload is a function of the audio signal being used. Few parameters are defined which control, using linear equations, the number of channels per second available for transmission and the space available for the used constellation. The border values for these parameters are obtained in order to keep the perceptual transparency at an acceptable range. Due to the constellation order does not affect the perceptual distortion for a set of, previously defined, algorithm parameters, the hiding capacity can be estimated a priori independently of the audio signal features with the achieved bit error rate (BER) known in advance, in contrast to previous approaches.

In this data hiding method for digital audio signals based on the OFDM concept, two parameters are defined in order to regulate the capacity and the perceptual transparency, said parameters represent the number of samples to be modified and the severity of the modification. In order to guarantee the perceptual transparency, after experiments it was possible to determine the border values for modification such that ODG is kept within the acceptable range [0,-1 ]. Moreover, an ODG equation depending of the important parameters is provided by using the multiple regression strategy. That equation lets the user know the perceptual distortion independently of the audio clip. In the same form, the order of the utilized MPSK modulator in the scheme affects the perceptual transparency. The bitrate can be estimated a priori and does not depend of the audio signal. The proposed data hiding method shows a payload about 10x higher that the highest payload in an audio data hiding scheme reported to date. Further features will become apparent with reference to the following detailed description and accompanying drawings.

Brief description of the drawings.

Figure 1. Shows a block diagram of an OFDM transmitter.

Figure 2. Shows a block diagram of an OFDM receiver.

Figure 3. Shows a 8-PSK signal constellation.

Figure 4. Shows a block diagram of a general insertion process of the present invention.

Figure 5. Brings together two graphics related to the meaning of the jump parameter, which represents the separation, in number of samples of the phase, between two consecutive samples to be modified.

Figure 6. Shows a graphical meaning of the definition of the arch parameter, which represents the available space, in degrees, to be used by the M-PSK constellation.

Figure 7. Shows a block diagram of a general extraction process.

Figure 8. Shows a graphic relating to the ODG plot for several jump values according to the method of the present invention.

Figure 9. Shows a graphic relating to the BER versus SNR for jump = 30, arch = 89 and B-PSK constellation.

Detailed description of the invention.

Orthogonal Frequency Division Multiplexing (OFDM) is one of the most recently used modulation techniques used to combat the frequency-selective fading of the multi-path channels, permitting high data rates by reducing intersymbol interference (ISI). In a conventional data transmission system, the symbols are transmitted sequentially, one by one, with the frequency spectrum of each data symbol allowed to occupy the entire available bandwidth. A high rate data transmission supposes very short symbol duration, implying large bandwidth requirement of the modulation symbol. There is a high likelihood that the frequency selective channel response affects in a very distinctive manner the different spectral components of the data symbol, hence introducing the ISI. It is possible to assume that the frequency selectivity of the channel can be mitigated if, instead of transmitting a single high rate data stream, the data are transmitted simultaneously, on several narrowband subchannels (with a different carrier corresponding to each subchannel). Hence, for a given overall data rate, increasing the number of carriers reduces the data rate that each individual carrier must convey, therefore lengthening the symbol duration on each subcarrier. Slow data rate (and long symbol duration) on each subchannel merely means that the effects of ISI are greatly reduced. This is in fact the basic idea that lies behind OFDM: transmitting the data among a large number of closely spaced subcarriers. The orthogonality allows for efficient modulator and demodulator implementation using the DFT algorithm on the receiver side, and inverse DFT on the transmitter side. Although the principles and some of the benefits have been known since the 60s, OFDM is popular for wideband communications today by way of low-cost digital signal processing components that can efficiently calculate the Fast Fourier Transform (FFT), which is a DFT implementation.

Figures 1 and 2 show a simplified scheme of an OFDM transmitter 10 and receiver 20, respectively, using the FFT algorithm. In the transmitter, s[n] is a serial stream of binary data, these are demultiplexed into N parallel streams 15 (Xo, Xi, XN-I), and mapped to a symbol stream (usually complex, in the figures 1 and 2, Re and Im are the real and imaginary components of the FFT samples respectively) using a modulation constellation. An inverse FFT 16 is computed on each set of symbols and then quadrature-mixed to passband in the standard way. The resulting s(t) signal is transmitted over the air as electromagnetic waves.

The receiver 20 picks up the signal r(t) and subsequently downconverts it via a quadrature receiver by using cosine and sine waves at the carrier frequency 25 followed by low-pass filters 26. After Analog-to-Digital Conversion (ADC) 27, an FFT 28 is performed to obtain the orthogonal components. This returns N parallel streams 29 (Yo, Yi, YN-I), each of them is converted to a binary stream using the appropriate symbol detector. These streams are then re-ordered into a serial stream, s[n] which is an estimate of the original binary stream sent by the transmitter 10. The data to be transmitted in an OFDM scheme must be modulated using a given constellation. For audio signals, the human auditory is less sensitive to changes in the phase components that change in the magnitude components. Due that, in the present invention, MPSK modulation is used, which produces high perceptual transparency in the stego audio, instead of other modulation schemes such as QAM that modifies the magnitude components.

Figure 3 shows an 8-PSK constellation that is typically used in OFDM systems. M-order Phase Shift Keying (MPSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal. A convenient way to represent MPSK modulations is by using a constellation diagram 30. In MPSK, the defined constellation points 31 are usually positioned with uniform angular spacing around a circle. This gives maximum phase-separation between adjacent points and thus the best noise immunity. MPSK symbols are positioned on a circle so that they can all be transmitted with the same energy.

The proposed method utilizes the OFDM concept in the sense that each frequency component of the audio signal can be interpreted as each of the carriers in the multi- carrier system. Besides, the information of each carrier is modulated using a MPSK modulation but with each subcarrier (frequency component) being phase modulated, i.e. the original audio signal has not been eliminated, but just changed with the modulated scheme. In addition, by limiting the modifiable phase-space, the transparency of digital media can be controlled. These choices give raise to a modified version of an OFDM system, and the strength of the proposed method over previous approaches. The method is explained in two parts: insertion and extraction process.

The insertion process of the proposed data hiding method consists of an orthogonal transformation, and an inverse orthogonal transformation. The audio signals are transformed in orthogonal components using a DFT 40 and those components are modified according to the MPSK-modulated data. In order to obtain the stego audio signal, the modified components are transformed back to the time domain using an inverse DFT 50. Figure 4 shows the general insertion process; by comparing this figure with figure 2 it is clear that the insertion algorithm can be interpreted as an OFDM-kind modulator, due to the parallelized data is hidden into a set of orthogonal components (the DFT components of the audio signal). This has been one of the main motivations of this invention. Each MPSK constellation point 55 is added to the original phase values, Pn, in an offset fashion. In a non-blind scheme, the original phase values are required in the extraction process. On the other hand, in a blind scheme, the original phases can be approximated by using an interpolator. Previous to the insertion process, it is necessary to define which and how many frequency values of the digital audio signal are modified in order to maintain acceptable values of the perceptual transparency in terms of the ODG. An ODG value between 0 and -1 is considered a good perceptual transparency²¹. To define these Phase values, two parameters are required: jump and arch. The jump parameter represents the separation, in number of phase samples, between two consecutive phase samples to be modified. For example, if jump = 3 and the first modified phase sample starts at the one hundred sample, denoted as Phase[100], the next modified phase samples will be Phase[103], Phase[106], Phase[109], etc., until the whole frequency spectrum is covered. Figure 5 shows a graphical meaning of the jump parameter.

The arch parameter represents the available space, in terms of arc degrees, to be used by the MPSK constellation. For example, if arch = 5 it means that the available space for the constellation is between -5° and 5°, a 10° arc. In the proposed method the MPSK constellation is mapped only to the space defined by arch instead of using the whole phase space (2π radians) as in communications systems, because the perceptual transparency is kept at acceptable ranges when no drastic changes are carried out on the phase components.

Figure 6 shows a graphical meaning of the arch parameter. As it will be shown ahead, the order of the MPSK constellation does not affect the ODG value for previously defined jump and arch values. Therefore, it is possible to transmit high bitrates, only limited by the allowable error probability associated with the used MPSK constellation and the target application. The number of channels per second available for data hiding is a function of the jump parameter as follows: fi .5 n _ samp - ini _ samp (1 ) n chan =

n _ samp jump J where, n_chan is the number of channels per second available for data hiding, fs is the sampling frequency of the digitalized audio signal, n_samp is the number of audio samples to be transformed by the DFT, and ini_samp is the first phase sample to be modified. In this invention a CD-quality audio signal is considered, therefore, fs = 44100Hz, and n_samp = 4096. The rest of the parameters are obtained using experimental results.

With these values equation (1 ) becomes:

ump

The bitrate is calculated as follows:

bit _ rate = n _ chan log ₂ M , (3) where bit_rate is the bitrate in bits per second (bps) and M is the order of the used MPSK constellation. From equations (2) and (3) it can be seen that for a fixed jump value (ini_samp is a constant as it will be shown in the next section) the amount of data to be hidden is only a function of the MPSK order. That conclusion suggests that the proposed method is very flexible in terms of the payload desired to be inserted in the data.

Figure 7 shows the general extraction process. The extraction process is conformed by an orthogonal transformation, the same used in the insertion process, and an MPSK demodulation.

The audio signals are transformed in orthogonal components using a DFT 60 and those components are used to recover the MPSK-modulated data by subtracting them from the original (where the data detection process requires the original audio clip. It is useful for applications such as copyright disputes) phase components or from the approximated (where the original signal is not available to the detector. It is useful for applications such as broadcast monitoring) (usually by interpolation) phase components. After that, the symbol extraction is carried out by using the appropriate MPSK demodulator. In what follows, the BER of the proposed method will be analyzed, while lines below describe the experiments carried out to obtain the border values for jump (separation between two close phase components to be modified, measured in number of phase samples) and arch (available phase space for the MPSK constellation used for the data hiding process) parameters in order to keep the human transparency in an acceptable range.

One of the main strengths of the proposed method lies in its ability to predefine the bit error rate (BER) achieved in the hidden data after it is decoded. This permits the design of the associated channel coder to guarantee that what is extracted from the hidden signal are reliable data. This is opposed to previous approaches, where medium payloads are pursued without considering if hidden data are worthy to be detected, therefore, there is an uncertainty about the true performance and innplennentability of those schemes.

The following analysis considers the estimation of BER for the proposed OFDM data hiding scheme and models the quantization error as additive white gaussian noise (AWGN), a consideration commonly employed.

Firstly, one parameter, a (Radian units are used instead arc degrees), is defined as:

The a parameter represents the percentage of circumference being used in MPSK modulation. Let us first recall the well-known formula for symbol-error probability in MPSK modulation systems, P_e,_symboi, defined as Proakis²²:

P_e, symbol ⁼ Σ ^Qi') MPKS ' (5) M m=\

where Q(.)MPSK is the BER produced by each of the M MPSK symbols and Q(.) is the Q- function defined as:

J

Q{x) = -f= f exp(-i² / 2)dt (6) For Gray coding the bit-error probability, P_e,bit, is related to P_e,_Sym/3o/with: p e,bit = -¹ P e,symbol ' (7) where k = log₂M. For a symetric MPSK modulation, the M terms in equation (5) are equal, and the P_e,M is readily reduced to²²:

P_e,bit where SNRE/_J is the Signal-to-Noise Ratio per bit.

The BER of the proposed method can be calculated from the previous equations by noticing from Figure 6 that the a parameter has the effect of shrinking the original MPSK constellation, and therefore, the constellation symbols get closer, with the exception of the symbols near π. Hence, equation (5) should be divided into two components, one with two gaussian tails and the other with M-1 gaussian tails. Under the commented considerations and after simple manipulations, result in equation (8) the P_e,/3 _f Of the proposed method as:

Q\ πα

+ - 2kS.\R_t sin (\ - α)π +

Mk M where the inequality is required due to the fact that the considerations for deriving equation (8) have been stressed. Nevertheless, this approximation is valid and good enough when M > 4. When M gets bigger, it is possible to dismiss the second component and to simplify equation (9) as follow:

From equation (10) it is possible to see that if a goes smaller and/or M goes bigger then, it is necessary to rise the SNR_Eb value in order to keep BERs small enough, in other words, if the percentage of circumference used by MPSK modulation is smaller. Nevertheless, due to the high Signal-to-Quantization-Noise-Ratio (SQNR) in audio digital signals, the resulting BER is significantly low, as will be discussed below.

In order to determinate the best values for ini_samp, jump and arch parameters, several experiments were carried out. Due to one of the aims of the proposed method is to keep the perceptual transparency at an acceptable range, only medium and high frequencies are modified and the low frequencies are kept unaltered, as the human hearing sensitivity is higher in low frequency bands than in medium and high frequency bands, according to the human auditory system (HAS)²³. The cut-frequency for the data hiding process is represented by the ini_samp parameter and was estimated via the following simulation settings:

- For 10000 repetitions, an audio signal was divided in blocks of 4096 samples (that block size provides enough resolution for audio processing purposes). Each block was transformed to the frequency domain by the FFT algorithm. From the 2048 frequency components 64 phase samples (preliminary experiments shown that a lower or higher number of components being modified does not significantly vary the ini_samp estimation.) were modified, with ini_samp, jump and arch parameters being random numbers in order to simulate different configurations of available constellation space and amount of phase samples being modified.

- Due to the ODG value is the unique perceptual transparency indicator, for each repetition the ODG was calculated and registered. - For ODG values within the range [0,-1 ], the highest ini_samp value was selected because that range guarantees perceptual transparency.

From this procedure, the ini_samp value obtained was 120, which corresponds to the 1 .3 KHz component. This means that the frequency components below of 1 .3 KHz will not be modified during the data hiding process.

In order to know the combinations of jump and arch parameters that guarantee the perceptual transparency determined for the ODG value, the next experiment was carried out: - The ini_samp parameter was set to 120 as it was obtained from the last experimentation.

- The arch parameter was varied in a random fashion (simulating the points of an MPSK constellation) from ±1 to ±178 degrees for each jump value from 1 to 30. Note that if the number of unmodified phase samples between two samples being modified is higher that 30, the number of available channels for data hiding is not attractive for steganography applications because it would be too low, therefore the bitrate will also be too low.

- The ODG value was calculated for each pair, and recorded in a matrix ODG [arc, jump].

- The procedure was repeated for 5 different songs and the ODG matrices were averaged in order to merge the characteristics of each song in the general estimation. Each song belongs to different sorts of music such as pop, classic, latin, bing band and rock music in order to stress the performance of the proposed method and validate its suitability for real applications. The border values for jump and arch parameters are defined in function of ODG values in the range [0,-1 ] because that range of the ODG values is the acceptable in terms of perceptual transparency. This means that only the combinations of available constellation space and amount of phase samples that guarantee perceptual transparency will be used.

Figure 8 shows the ODG values obtained after performing the experiments, described previously, for several amounts of separation between two samples to be modified. As it is expected, for high separation between modified samples the ODG improves because a smaller number of phase samples are modified in comparison with a low separation according to equation (2). This happens because when a low number of phase samples are modified the introduced distortion is minor than when a higher number of phase samples is altered. Table 1 shows the jump and arch useful values (those that produce ODG values within the acceptable range [0,-1]) and their n_chan and ODG associated values. From this table, it can be seen that for jump = 2, the highest arch value for ODG in the range [0,-1] is 25°. On the other hand, for jump = 30, the highest arch value for ODG in the range [0,-1 ] is 89°.

Table . jump and arch useful values (ODG in the range [0,-1]) jump arch C) Available space (°) n_chan ODG

2 25 50 10314.8 -0.97335

3 31 62 6869.4 -0.99343

4 36 72 5157.4 -0.98230

5 40 80 41 19.5 -0.99798

6 44 88 3434.7 -0.99825

7 46 92 2942.5 -0.99072

8 49 98 2578.7 -0.99869

9 51 102 2289.8 -0.97790

10 53 106 2054.4 -0.97532

1 1 55 1 10 1872.5 -0.97306

12 57 1 14 1712.0 -0.99522

13 59 1 18 1583.6 -0.98800

14 61 122 1465.9 -0.96209

15 60 120 1369.6 -0.96558

16 64 128 1284.0 -0.98832

17 64 128 1209.1 -0.98328

18 69 138 1 144.9 -0.97832

19 69 138 1080.7 -0.99054

20 72 144 1027.2 -0.98291

21 75 150 973.7 -0.99706

22 76 152 930.9 -0.99426

23 77 154 888.1 -0.99413

24 80 160 856.0 -0.99337

25 80 160 823.9 -0.99960

26 83 166 791 .8 -0.97762

27 83 166 759.7 -0.99201

28 87 174 727.6 -0.99507

29 86 172 706.2 -0.95715 From figure 8 it is possible to appreciate that each ODG curve (for each jump value) could be approximated by a linear equation. A frequently used technique for approximating a phenomena by a linear equation is using the multiple regression method²⁴. In order to obtain an ODG equation, an online multiple regression computer²⁵ was used. The resulting ODG equation is:

ODG [arch , jump ] = 0.30592979 - 0.00601405 jump

- 0.02242764 arch + 0.00030866 (jump )(arch ). (1 1 ) Equation (1 1 ) allows to determine the ODG value that will be obtained for a pair of defined jump and arch values. Moreover, it is possible to define ODG= -1 and to select the arch and jump values according to a specific application. For example, in an steganographic application where the goal, is to transmit at high bitrates, the separation between two samples to be modified Gump value) must be low in order to use a high number of channels for transmission. State-of-the-art data hiding schemes such as Fallahpour & Megias, 2009¹⁵, 2010b²⁶, transmit about 3 and 5 kbps, respectively without being able to declare which is the BER so obtained. In the proposed method, if jump = 2 and the modulator is 256-PSK it is possible to transmit about 82.5 kbps with a good perceptual transparency. Moreover, in a CD-quality audio signal, the BER is ~ 0 due to the audio signal' SQNR is about 93 dB. Theoretically, if the precision used in the implementation of the proposed method is equal to infinite, it would be possible to hide bit streams using a MPSK constellation of order equal to infinite. However, utilizing double precision arithmetic in the implementation, the maximum order of the MPSK constellation used is 256, which result in up to 8 bits per channel. Under those conditions the minimum payload achieved is 684 bps (jump = 30, arch = 89 and B-PSK constellation) and the maximum one is 82.5 kbps (jump = 2, arch = 25 and 256-PSK constellation).

Table 2 shows a comparison with several state-of-the-art data hiding schemes in audio signals. From these results, it is possible to see that the proposed method, with the values used in this paper (jump = 2, arch = 25 and 256-PSK constellation), can hide about 9.4 times more bits than the highest payload of a data hiding method reported to date. Table 2. Comparison of different data hiding schemes.

At this point, for the purposes of testing the validity of the theoretical analysis for the presence of AWGN through experimentations. Figure 9 shows, in BER terms, the behavior of the proposed method with jump = 30, arch = 89 and B-PSK constellation. The label Analytical corresponds to the plot obtained using equation (10). It can be noted that the match between the analytical results and the experimental ones is very close.

Finally, it is worth noting that the proposed method was devoted to the steganographic application. However, due to its high payload, it could be possible to apply the proposed OFDM-based data hiding approach in watermarking applications where robustness is a major concern. In watermarking systems, robustness means to keep BER low in a noisy channel. By using Error Correcting Codes (ECC) it is possible to mitigate BER at bitrate cost. In order to find out which class of ECC is the adequate for achieving a satisfactory robustness for a given scenario, it is necessary to carry out further research and it constitutes an open research issue. However, because the high payloads achieved by the proposed method, it is possible to expect that, despite bitrate reduction by ECC, the payload will be high and still attractive for both watermarking and steganographic applications. While preferred embodiments have been shown and described, modifications thereof can be made by one skilled in the art without departing from the scope or teachings herein. The embodiments described herein are exemplary only and are not limiting. Many variations and modifications of the method described herein are possible and are within the scope of the invention, for example, variations in the kind of Analog-to-Digital Converters used, or the implementation of specific arrays for calculating the Discrete Fourier Transform and inverse DFT, or using other signals as carriers instead of audio signals. In addition, several other blocks can be added to the said invention that may improve the performance of the stego signal. For example, to include channel coders before inserting the data in the audio or video signals.

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Claims

Claims.

1 . A method for high payload data-hiding in audio signals based on a modified OFDM approach, the method comprising the steps:

a) defining frequency values of a digital audio signal to be modified in order to maintain acceptable values of the perceptual transparency in terms of the

Objective Difference Grade,

b) transforming the audio signal in orthogonal components using a Discrete Fourier Transform,

c) modifying the orthogonal components obtained in (b) according to a M-order Phase Shift Keying-modulated data within a small angular space, to get a stego audio signal, and

d) transforming back the modified orthogonal components obtained in (c) to the time domain using an inverse Discrete Fourier Transform.

2. The method of claim 1 , wherein an Objective Difference Grade value comprised between 0 and -1 is considered a good perceptual transparency.

3. The method of claim 2, wherein to define the Phase values, the parameters jump and arch are required.

4. The method of claim 1 , wherein each M-order Phase Shift Keying constellation point is added to the original phase values, Pn, in an offset fashion.

5. The method of claim 1 , wherein the M-order Phase Shift Keying constellation is mapped only to the space defined by arch instead of using the whole phase space.

6. The method of claim 1 , wherein the number of channels per second available for data hiding is a function of the jump parameter as follows:

n _samp V jump

where, n_chan is the number of channels per second available for data hiding, fs is the sampling frequency of the digitalized audio signal, n_samp is the number of audio samples to be transformed by the DFT, and ini_samp is the first phase sample to be modified.

The method of claim 1 , where high payload is achieved by means of choosing a low jump value.

The method of claim 1 , wherein the bitrate is calculated as follows: bit _ rate = n _ chan log ₂ M ,

where bit_ te is the bitrate in bits per second (bps) and M is the order of the used M- order Phase Shift Keying constellation.

The method of claim 1 , further comprising:

e) transforming the stego audio signal obtained in (d) in orthogonal components using a Discrete Fourier Transform,

f) recovering from those components the M-order Phase Shift Keying-modulated data by subtracting them from the original phase components or from the approximated phase components, and

g) extracting the symbol by using the appropriate M-order Phase Shift Keying demodulator.

The method of claim 9, wherein said time-to-frequency conversion is a Discrete Fourier Transform and said frequency-to-time domain conversion is an inverse Discrete Fourier Transform.