TWO ALGORITHMS IN DIGITAL AUDIO STEGANOGRAPHY USING QUANTIZED FREQUENCY DOMAIN EMBEDDING AND REVERSIBLE INTEGER TRANSFORMS
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1 TWO ALGORITHMS IN DIGITAL AUDIO STEGANOGRAPHY USING QUANTIZED FREQUENCY DOMAIN EMBEDDING AND REVERSIBLE INTEGER TRANSFORMS Sos S. Agaian 1, David Akopian 1 and Sunil A. D Souza 1 1Non-linear Signal Processing Lab, University of Texas at San Antonio, 69 North Loop 164 West, San Antonio, Texas 78249, USA. sagaian@utsa.edu, dakopian@utsa.edu, sdsouza@lonestar.utsa.edu ABSTRACT Steganography is the art of hiding secret messages within another innocuous message or carrier. Steganography in digital audio has received considerable interest and in this paper we present two algorithms for secure digital audio steganography. In the first algorithm we use classical unitary transforms with quantization in the transform domain to embed the secure data. The secure data is embedded in the transform domain coefficients. In the second algorithm we use a reversible integer transform to obtain the transform domain coefficients. In the integer domain we look at the binary representation of the integer coefficients and embed the secure information as an extra bit. We also introduce a capacity measure to select audio carriers that will introduce minimum distortion after embedding. Keywords reversible, steganography, data hiding 1. INTRODUCTION In the last few years the infrastructure for distribution of digital media has grown rapidly. The distribution of such digital media provides an excellent opportunity for transmission of hidden information. Recently, digital steganography has received considerable interest and is used to hide information in carriers such as digital audio, images or video so that only the intended recipient is capable of retrieving the hidden information. Typically, algorithms in steganography can be broadly classified into two classes: 1) a spread spectrum based approach wherein a pseudo-noise sequence added to the carrier, 2) quantize the carrier and replace some of the quantized data with steganographic information [2]. Each of these classes include techniques that can applied in time and transform domains. In [1], Cox et al require the embedded information to be constructed as an independent and identically distributed (i.i.d.) Gaussian random vector that is inserted in spread spectrum like fashion into the carrier. A common example of second class is the manipulation of the least significant bit to represent the embedded information. Steganography in digital audio has invited considerable research interests and many techniques [3-5] have been proposed based on the characteristics of digital audio signals and the human auditory system (HAS). The effects of HAS relative to steganography are temporal masking and frequency masking. In temporal masking a weaker audible signal on either side (pre and post) of a strong masker becomes imperceptible. Similarly, in frequency masking, if two signals occurring simultaneously are close together in frequency, the stronger masking signal may make the weaker signal inaudible [5]. Wang et al [3], propose an audio watermarking algorithm based on HAS principles. The procedure involves selecting an audio clip immediately after a loud sound. The clip is transformed to the frequency domain and spectral components adjacent to high peaks are selected. A combination of a pn-sequence and secure data is embedded in a frequency band. Detection is achieved by autocorrelation properties of pn-sequences. High embedding capacity is achieved by QAM modulation techniques. In [1], Tian proposes an integer wavelet transform based watermarking algorithm. The algorithm uses the integer wavelet transform to obtain the integer coefficients in the transform domain. The binary representation of the coefficient is looked at and an additional bit representing secure information is added, thereby expanding the coefficient. A location map is embedded that identifies the pixels that are changed. Tilki and Beex [4], propose an algorithm for encoding a 35 bit digital signature onto the audio component of a television signal. The digital signature is encoded using 167 sinusoids in the 2.4 to 6.4 KHz range, specifically chosen as human sensitivity declines compared to its peak at 1 KHz. The 167 frequencies are chosen to correspond to the bin frequencies of the 496 point FFT of the original audio segment. The digital signature is then added to the audio component. The signature is detected by comparing the magnitude of adjacent FFT bins to a threshold and making a decision. Swanson et al [5] propose a robust audio watermarking algorithm in which the power spectrum of an audio block is calculated and tonal components below the absolute hearing threshold are removed. A frequency-masking threshold for each block is calculated
2 and used to weight a noise-like watermark. A temporal mask is used to further shape the time domain representation of the watermark. Adding the two signals creates the watermarked segment of audio. Detection requires the original signal and is accomplished by hypothesis testing. In this paper, we present two algorithms for secure digital audio steganography. Both algorithms do not require the original signal or information about the secure content for detection. Only a few parameters are necessary for detection and extraction of the steganographic data. Both algorithms feature a small pseudonoise sequence added to the carrier for detection purposes. The framework of both steganography algorithms includes characteristics of the human auditory system. While the frequency domain based steganography algorithm includes temporal and frequency-masking characteristics, the integer transform based algorithm includes temporal characteristics. We also introduce a simple capacity measure for selecting the cover audio clip that has the least distortion after the embedding process, based on the capacity measure formula developed in [7]. Experimental results show that the changes in the embedded audio section are imperceptible. The remainder of the paper is organized as follows: Section 2 introduces the block diagram and steps for encoding and decoding process of the proposed algorithm. Section 3 deals with the simulation results and section 4 provides the conclusion. 2. PROPOSED ALGORITHMS In this section, we present two algorithms for secure digital audio steganography. The first algorithm is called Quantized-frequency Secure Audio Steganography algorithm (QSAS). It is based on classical unitary transforms and quantization in the transform domain and is an extension of the work on watermarking presented in [3]. The differences are that our algorithm is developed for steganography wherein higher embedding capacity is relatively more important than the robustness requirements of watermarking. We also present a simple capacity measure to select an audio with the best embedding capacity. In the QSAS algorithm, we select the Fourier transform as we are dealing with audio signals and its properties in the frequency domain are well known. The DFT of an N-point discrete-time signal x(n) is defined by N 1 kn X(k) = x(n)w, for k =,1,,N-1 (1) N n= j2 π / N where WN = e. Similarly, the IDFT can be given by x(n) N 1 -kn =, for n =,1,,N-1 (2) k = N The coefficients appearing in FFT and IFFT structures are complex numbers with magnitude one and their inverses are complex conjugates of each other. The bin frequencies for an N point FFT are given by fs/n where fs is the sampling frequency. Among the N bins only N/4 bins are modified and the embedded information includes the pseudo random sequence and secure data. Our goal in the development of the second algorithm was to have a simple and robust integer based reversible audio steganography algorithm. The algorithm is a variation of the watermarking algorithm presented in [1]. The key differences are as follows: 1. The algorithm in [1] was implemented for watermarking images, while our algorithm is developed for audio steganography in which higher embedding capacity is relatively more important than the robustness requirements of watermarking. 2. Unlike images, audio samples are not represented by integer values and preprocessing of the audio signal plays a significant role. 3. We use a pseudo-random sequence to detect the location of the secure data and do not require a location map to identify the samples that have been modified by the algorithm. 4. Our algorithm uses the temporal characteristic of HAS to select the location at which we embed the secure data. We term this algorithm as Integer based Secure Audio Steganography algorithm (ITSAS). The output of an analog-to-digital converter (ADC) is a quantized Q bit integer value that typically represents the range of the input analog signal. For example, audio files in the Microsoft.wav format this range is mapped to (-1, 1). For processing these signals using integer transforms, each value must be converted to integer format. Computers typically process real numbers using floating-point representation. Converting from floating point to integer values is often very slow. An alternative representation is the fixed-point format in which a Q bit number is represented as M: N, where M=Q is the total number of bits that determine the range; N is number of bits that determine the precision. In some articles, the fixed-point format is referred to as the Q-format and is given as Q-15, Q-3, etc. implying that the precision (fractional part) is represented by 15 or 3 bits, respectively. A number represented in fixed-point format can be converted to an integer by multiplying the number by 2 N. The original Q format can be obtained by reversing the process. The reversible integer transform [1] for adjacent sample pair (x, y) is given as x+ y l =, h= x y 2 (3) where the symbol. is the floor function meaning, the greatest integer less than or equal to. The l coefficient is just the average of two adjacent samples while the h is the difference. Note, for audio signals the difference coefficient is typically very small compared to
3 the average coefficient of the signals. The inverse transform of (3) is given as h+ 1 h x= l+, y = l 2 2 (4) 2.1. Quantized Frequency Secure Audio Steganography In this section, we give a system description of the quantized frequency domain audio steganography algorithm Encoding block A system block diagram of the encoding process is given in Figure 1. The basic encoding steps are as follows: Inputs: cover audio segment, secured data. Step 1: Find all potential embedding blocks in the time domain of the audio signal based on temporal masking characteristics. Step 2: Generate the frequency spectrum of the selected block. Step 3: Generate an m-sequence of suitable length. Step 4: Combine the m-sequence and the secure data create a new sequence. Step 5: the best block in which we wish to embed the secured data. The frequency range of the band lies between parameters P and Q, based on frequency masking characteristics Decoding block The system block diagram for the decoding block is given in Figure 2. The block size, temporal threshold value as a percentage of maximum amplitude, order of the m-sequence and the quantization step are fixed values and are available to the decoding block. The basic decoding steps are as follows: Input: Audio signal with secure information. Step 1: Locate all potential blocks in the time domain of the audio signal based on threshold value. Obviously, these blocks are the same as the blocks located in the encoding process. Step 2: Generate an m-sequence of given order. The generator polynomial is the same in the encoding and decoding block. Identify Potential s Frame M- Sequence Generator FFT Frequency Band Quantize Correlate Extract Data Figure 2: diagram of decoding block - Frequency Domain based Algorithm Identify Potential s Frame M- Sequence Generator Secured Data FFT Frequency Band Quantize Embed Mixer ifft Step 3: Generate the frequency spectrum of the selected block. Step 4: Quantize the block with the same quantization step. Step 5: Correlate the block and the m-sequence obtained in step 2 to locate the starting point of the embedded band. Step 6: Extract the embedded information. Step 7: Repeat steps 3-6 for the each of the other blocks. Output: Secure information. Figure1. diagram of Encoding - Frequency Domain based Algorithm Step 6: Quantize the spectral content of the band. Step 7: Quantize the new sequence and additively embed it into the cover. Step 8: Take the inverse Fourier transform of the block. Step 9: Replace the time domain block in the original audio segment with the encoded block. Step 1: Repeat steps 3-9 for all blocks. Output: Audio signal with secure information Integer based Secure Audio Steganography Encoding block In this section, we give a system description of the integer transform based secure audio steganography algorithm. The system block diagram for the embedding block is given in Figure 3. Inputs: cover audio segment, secured data.
4 Step 1: Find all blocks where data can be embedded based on temporal masking characteristics of the audio signal. Step 2: The pre- process block is used to convert audio signal in each block to integer domain. Step 3: Compute the forward integer transform and obtain the transform domain coefficients as per (3). Step 4: Generate an m-sequence of suitable length (m). This the pilot sequence. Step 5: Combine the pilot with the secure data to form a new sequence. Step 6: Look at the binary representation of each h or difference coefficient. If the addition of a bit does not cause overflow or underflow, unlikely due to small difference values, then embed a bit of secure data from the sequence created in step 4 at the MSB+1 position. This creates a new value for the difference coefficient h. Step 3: Compute the forward integer transform of the frame and obtain the transform domain coefficients as per (3). Step 4: Generate an m-sequence of length (m). Step 5: Look at the MSB+1 of the binary representation of the difference coefficient for a block size of m. Step 6: Correlate the bit stream obtained in step 5 with the m-seq. Repeat step 5 till the sequence is located in the frame. Step 7: Extract the MSB+1 bit from the difference coefficients to obtain new values for the coefficient h = h. s Pre Process F. Integer s Pre Process F. Integer M-seq. Correlate M-seq. Secure Data Figure 3. diagram of Encoding - Integer. Step 7: Compute the reverse integer transform as per (4). Step 8: Replace the audio frame into the original audio stream. Step 9: Repeat steps 2-8 for each of the blocks. Output: Audio Signal with secure information Decoding block Embed R. Integer Post Process Mixer The system block diagram for the decoding block of the integer-based transform is given in Figure 4. The length of the m-sequence and the block size are available to the decoding block. The basic decoding steps are as follows: Inputs: Audio signal with secure information. Step 1: all blocks based on temporal masking characteristics of the audio signal. Step 2: The pre-process block is used to convert the audio signal in each block to integer domain. Extract R. Integer Figure 4. diagram of Decoding - Integer. Step 8: Compute the inverse integer transform as per (4) and replace the audio frame into the original audio stream. Step 9: Repeat steps 2-8 for all blocks. Output: Extracted information and original audio signal. 3. COMPUTER SIMULATION Post Process Mixer In this section we introduce a capacity measure formula for selecting the audio that would introduce the least distortion after the embedding process. The formula is given as: No.of samplesintheemdedding band M audio = MSE x No.of bitsinthesecuredata The capacity measure is calculated by multiplying the mean square error times the bit ratio of the embedding band in the cover audio and the secure message. For computer simulations we tested the algorithms over many audio pieces from classical, pop, country and speech. All cover audio signals are about 3 seconds long and are sampled at 441 KHz with 16 bits resolution. The classical pieces are Beethoven s Symphony No.4
5 in B flat, Adagio - Allegro vivace and Walter Piston s Turnbridge Fair, respectively. The country songs are Lyle Lovett s Long Tall Texan and Nanci Griffith s If I had a Hammer. The pop pieces are by Paul Simon called That was your mother and the Christmas classic Away in a manger recorded by Peter Jacobs. In the frequency domain based algorithm the range of the embedding band is chosen as P = 5.5 KHz and Q = 11 KHz (BW/4 BW/2) and the block size is chosen as 512 samples. As noted earlier, only N/4 = 128 frequencies are modified. As the Fourier coefficients are complex conjugates we actually embed information in half these coefficients. The time domain plot of the original signal is shown in Figure 5. As can be seen in the plot, the potential embedding blocks based on HAS characteristics are identified. The threshold is chosen to be 55 % of the maximum amplitude of the chosen cover audio signal. Figure 6 shows additional time domain plots of the cover audio signals. The embedding capacity is different for different audio cover signals based on the availability of embedding blocks that satisfy the HAS criteria. Waveform of the audio signal: beethoven ym4.wav - Length = 512/ s = 21 s.8 Threshold = x 1 4 Figure 5: Cover audio signals with potential blocks identified with threshold at 55% of maximum value of cover audio. Waveform of the audio signal: turnbrge air.wav - Length = 512/ s = 13 f 1.8 Threshold = x Waveform of the audio signal: paulsimon.wav - Length = 512/ s = 18 1 Threshold =.55 Waveform of the audio signal: nineseclyle.wav - Length = 512/ s = x Threshold = Waveform of the audio signal: myspeech.wav - Length = 512/ s = 23 1 Threshold =.55 The analysis of sample audio signals is provided in Table 1. As can be seen from the data the M audio measure is a simple method for selecting an audio clip that introduces the least distortion. Signal s / Payload (bits) SNR RMS M audio (1 4 ) Classical 21 / Classical 13 / Country 1 / Country 28 / Pop 18 / Pop 33 / Speech 23 / Table 1: SNR, RMS and M audio for audio signals embedded using quantization in frequency domain. The computer simulations for the integer-based algorithm were performed on the same set of audio signals. The block size is 512 and the number of bits that can be embedded per block is equal to 256. The analysis is provided in Table 2. Signal s / Payload (bits) SNR RMS M audio (1 4 ) Classical 21 / Classical 13 / Country 1 / Country 28 / Pop 18 / Pop 33 / Speech 23 / Table 2: SNR, RMS and M audio for audio signals embedded using reversible integer transform. 4. CONCLUSION In conclusion, we presented two algorithms for digital audio steganography with embedding in the frequency domain and the integer transform domain. Experimental results for both methods indicate that the changes in the embedded audio section are inaudible. The QSAS algorithm has lower embedding capacity but has much better SNR values. The ITSAS algorithm is preferred as it is reversible, simple, and efficient with acceptable SNR values. We also introduced a capacity measure that can be used to select an audio clip that introduces the least distortion after the embedding process x x 1 4 a b Figure 6 : Cover audio signals a) Classical 13 c d blocks, b) Country 1 blocks, c) Pop 18 blocks, d) Speech 23 blocks. 5. ACKNOWLEDGMENTS This research was partially funded by the Center for Infrastructure Assurance and Security.
6 6. REFERENCES [1] I. J. Cox, J. Kilian, F. T. Leighton and T. Shamoon, Secure Spread Spectrum Watermarking for Multimedia, IEEE Trans. Signal Processing, vol. 6, no. 12, pp , December [2] B. Chen and G. W. Wornell, Digital Watermarking and Information Embedding using Dither Modulation, Multimedia Signal Processing, 1998 IEEE Second Workshop, pp: , December [3] S. Wang, X. Zhang, and K. Zhang, Data Hiding in Digital Audio by Frequency Domain Dithering, MMM- ACNS, Springer-Verlag, Berlin Heidelberg, 23, pp [4] J.F. Tilki and A.A. Beex, Encoding a Hidden Digital Signature onto an Audio Signal Using Psychoacoustic Masking, in Proc. 7 th International Conference on Signal Processing Applications & Technology, Boston MA, October 1996, pp [5] M. D. Swanson, B. Zhu, A. H. Tewfik, L. Boney, Robust audio watermarking using perceptual masking, Signal Processing, vol.66, 1998, pp [6] S. Oraintara, Y. Chen, T. Nguyen, Integer Fast Fourier, IEEE Trans. Signal Processing. [7] Sos S. Agaian and Juan P. Perez, New Pixel Sorting Method for Palette Steganography and Steganographic Capacity Measure, GSteg Pacific Rim Workshop on Digital Steganography, November 17-18, 24, pp , ACROS Fukuoka 1-1 Tenjin 1-chome, Chuo-ku, Fukuoka, 81-1 Japan [8] Bassia, P., Pitas, I., and Nikolaidis, N, Robust Audio Watermarking in the Time Domain, IEEE Trans. Multimedia, vol. 3 (21) [9] Tilki, J.F., Encoding a Hidden Digital Signature Using Psychoacoustic Masking, Thesis submitted to the Faculty of the Bradley Department of Electrical and Computer Engineering,Virginia Polytechnic Institute and State University, June 9, [1] Tian, Jun, High Capacity Reversible Data Embedding and Content Authentication, IEEE Conference on Acoustics, Speech and Signal Processing, vol. 3, pp , 23.
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