Hiding: '
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Information Steganography & Steganalysis
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Steganography (covered writing)
From Herodotus to Thatcher. Messages should be undetectable. Messages concealed in media les. Perceptually insignicant data is common in media representations.
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Steganalysis
Detecting the presence of a message. Statistically based. Extraction of message itself is secondary.
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Steganography: Denition
Simmons 1983: Prisoners problem USA USSR non-proliferation treaty compliance checking Alice and Bob are prisoners, Wendy is a warden. Alice and Bob are allowed to exchange messages, say images, but Wendy checks all messages. Alice and Bob try to hide information in their messages so that Wendy cannot detect it. Wendy cannot arbitrarily suppress all messages; the prisoners human rights cannot be violated without some proof of illegal activity. &
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Hiding by Matching Input
LSB sequence c1 , c2 , c3 , . . . , cn . Message bits m1 , m2 , m3 , . . . , mk , k < n. Look for a good approximate match. Theorem: If the the number of matching bits should exceed chance then the cover should be exponentially longer that the message. Hiding by matching is very wasteful (you can hide very few bits this way)
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LSB Methods (least signicant bit)
The given cover is an image. Image represented by pixel values raw images: each pixel is a byte (gray value) raw images: each pixel is a byte (color index in a palette) raw images: each pixel is three bytes (r,g,b values) Image represented by a sequence of JPEG coefcients. LSBs of pixel values or JPEG coefcients can be altered freely. There are many LSBs in an image. &
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Original Image
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80% JPEG
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JPEG Inserted into the Original Image
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Image File Formats
An image is a two-dimensional array of image points or pixels. Gray-level images: each pixel is described by one number corresponding to its brightness. Color images: each pixel is described by three numbers corresponding to the brightnesses of the three primary colorse.g., red, green, and blue. A typical image le has two parts, the header and the raster data. The header contains the magic number identifying the format, the image dimensions, and other format-specic information that describes how the raster data relates to image points or pixels. The raster data is a sequence of numbers that contains specic information about colors and brightnesses of image points. &
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Raw Image File Formats (e.g. BMP and PGM, TIFF)
The header contains the magic number and image dimensions. The raster data is a sequence of numbers corresponding to either one or three color values at each pixel. Raw (uncompressed) images are quite large and require a lot of storage space. Some space saving can be obtained by compressing the raster data by using loss-less compression (e.g. TIFF and PNG formats).
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Pallete Images
Frequently, raw images contain much more information than required. In images saved for human viewing the reduction of the number of possible colors. In some formats (e.g. GIF and PNG) the image is saved using a reduced color set. Each pixel value is represented by a single number corresponding to an index in the color palette that is stored in the image header. The palette contains the information needed to restore colors of all image pixels. The image le can be made even smaller by using loss-less compression of the raster datae.g., run-length encoding represents a sequence of several pixels of the same color by just two numbers, the length and the color of the sequence (run). &
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Lossy Compression: JPEG
Removes some image details to obtain considerable saving of storage space without much loss of image quality. The savings are based on the fact that humans are more sensitive to changes in lower spatial frequencies than in than the higher ones. In addition, it is believed that humans perceive brightness more accurately than chromaticity. JPEG uses Y CrCb format to save brightness information (Y ) in full resolution and chromaticity information (Cr and Cb) in half resolution. At the encoder side each channel is divided into 8 8 blocks and transformed using the two-dimensional discrete cosine transform (DCT). &
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JPEG: DCT Transform
Let f (i, j), i, j 0, = . . . , N 1 be an N N image block in any of the channels and let F (u, v), u, v = 0, . . . , N 1 be its DCT transform. The relationship between f (i, j) and F (u, v) is given by
2 F (u, v) = C(u)C(v) N 2 f (i, j) = N
N 1 N 1 N 1 N 1
f (i, j) cos
i=0 j=0
u(2i + 1) 2N u(2i + 1) 2N
cos
v(2j + 1) 2N v(2j + 1) 2N
C(u)C(v)F (u, v) cos
u=0 v=0
cos
where C(u) = 1/ 2 for u = 0 and C(u) = 1 otherwise.
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JPEG: Quantization
A DCT of an 8 8 block of integers is an 8 8 block of real numbers. The coefcient F (0, 0) is the DC coefcient and all others are called the AC coefcients. JPEG divides the coefcients by values from a quantization table to replace the real number values by integers. It is expected that many coefcients for higher values of u + v become zero and that only a fraction of all coefcients will remain nonzero. The coefcients are reordered into a linear array by placing higher frequency coefcients (higher values of u + v) at the end of the array; those coefcients are most likely to be zeroes. Huffman codding is applied to all coefcients from all blocks in the image; zero valued coefcients are encoded separately using special markers and their count for additional saving. &
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A header consists of image type and dimensions, compression parameters, and the quantization table. It is combined with the Huffman encoded coefcients packed as a sequence of bits to form a JPEG encoded image. On the decoder side the integer valued coefcients are restored by Huffman decoding. The quantization is reversed and the inverse DCT is applied to obtain the image. Huffman coding is loss-less; the losses occur in quantization process.
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JPEG: Quantization Table
(u,v) 0 1 2 3 4 5 6 7 0 16 12 14 14 18 24 49 72 1 11 12 13 17 22 35 64 92 2 10 14 16 22 37 55 78 95 3 16 19 24 29 56 64 87 98 4 24 26 40 51 68 81 103 112 5 40 58 57 87 109 104 121 100 6 51 60 69 80 103 113 120 103 7 61 55 56 62 77 92 101 99
Default JPEG quantization table. The coefcients are divided by their corresponding values and then rounded to the nearest integer. &
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Secret Key Based Steganography
If system depends on the secrecy of the method there is no key involvedpure steganography. Not desirable Kerkhoffs principle Compression + Encryption of the message Secret Key based staganography Public/Private Key Steganography
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Lossy vs. Lossless Steganography
Lossless steganography: modify lossless compression methods. An example would be modifying run length encoding process to embed messages. During the encoding process the method checks all run lengths lon...