Digital Image and Audio

Many common digital steganography techniques employ graphical images or audio files as the carrier medium. It is instructive, then, to review image and audio encoding before discussing how steganography and steganalysis works with these carriers.

Figure 1 shows the RGB color cube, a common means with which to represent a given color by the relative intensity of its three component colors—red, green, and blue—each with their own axis (more Crayons 2003). The absence of all colors yields black, shown as the intersection of the zero point of the three-color axes. The mixture of 100 percent red, 100 percent blue, and the absence of green form magenta; cyan is 100 percent green and 100 percent blue without any red; and 100 percent green and 100 percent red with no blue combine to form yellow. White is the presence of all three colors.

Figure 1. The RGB Color Cube

Most digital image applications today support 24-bit true color, where each picture element (pixel) is encoded in 24 bits, comprising the three RGB bytes as described above. Other applications encode color using eight bits/pix. These schemes also use 24-bit true color but employ a palette that specifies which colors are used in the image. Each pix is encoded in eight bits, where the value points to a 24-bit color entry in the palette. This method limits the unique number of colors in a given image to 256 (2^8).

The choice color encoding obviously affects image size. A 640 X 480 pixel image using eight-bit color would occupy approximately 307 KB (640 X 480 = 307,200 bytes), whereas a 1400 X 1050 pix image using 24-bit true color would require 4.4 MB (1400 X 1050 X 3 = 4,410,000 bytes).

Color palettes and eight-bit color are commonly used with Graphics Interchange Format (GIF) and Bitmap (BMP) image formats. GIF and BMP are generally considered to offer lossless compression because the image recovered after encoding and compression is bit-for-bit identical to the original image.

The Joint Photographic Experts Group (JPEG) image format uses discrete cosine transforms rather than a pix-by-pix encoding. In JPEG, the image is divided into 8 X 8 blocks for each separate color component. The goal is to find blocks where the amount of change in the pixel values (the energy) is low. If the energy level is too high, the block is subdivided into 8 X 8 subblocks until the energy level is low enough. Each 8 X 8 block (or subblock) is transformed into 64 discrete cosine transforms coefficients that approximate the luminance (brightness, darkness, and contrast) and chrominance (color) of that portion of the image. JPEG is generally considered to be lossy compression because the image recovered from the compressed JPEG file is a close approximation of, but not identical to, the original.

Audio encoding involves converting an analog signal to a bit stream. Analog sound—voice and music—is represented by sine waves of different frequencies. The human ear can hear frequencies nominally in the range of 20-20,000 cycles/second (Hertz or Hz). Sound is analog, meaning that it is a continuous signal. Storing the sound digitally requires that the continuous sound wave be converted to a set of samples that can be represented by a sequence of zeros and ones.

Analog-to-digital conversion is accomplished by sampling the analog signal (with a microphone or other audio detector) and converting those samples to voltage levels. The voltage or signal level is then converted to a numeric value using a scheme called pulse code modulation. The device that performs this conversion is called a coder-decoder or codec.

Pulse code modulation provides only an approximation of the original analog signal, as shown in Figure 2. If the analog sound level is measured at a 4.86 level, for example, it would be converted to a five in pulse code modulation. This is called quantization error. Different audio applications define a different number of pulse code modulation levels so that this "error" is nearly undetectable by the human ear. The telephone network converts each voice sample to an eight-bit value (0-255), whereas music applications generally use 16-bit values (0-65,535).

Figure 2. Simple Pulse Code Modulation

Analog signals need to be sampled at a rate of twice the highest frequency component of the signal so that the original can be correctly reproduced from the samples alone. In the telephone network, the human voice is carried in a frequency band 0-4000 Hz; therefore, voice is sampled 8,000 times per second (an 8 kHz sampling rate). Music audio applications assume the full spectrum of the human ear and generally use a 44.1 kHz sampling rate.

The bit rate of uncompressed music can be easily calculated from the sampling rate (44.1 kHz), pulse code modulation resolution (16 bits), and number of sound channels (two) to be 1,411,200 bits per second. This would suggest that a one-minute audio file (uncompressed) would occupy 10.6 MB (1,411,200*60/8 = 10,584,000). Audio files are, in fact, made smaller by using a variety of compression techniques. One obvious method is to reduce the number of channels to one or to reduce the sampling rate. Other codecs use proprietary compression schemes. All of these solutions reduce the quality of the sound.

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