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Many implementation details need some care. For exam- ple, one might not wish to disturb a pixel in a large expanse of flat colour, or lying on a sharp edge; for this reason, a prototype digital camera designed to enable spies to hide encrypted reports in snapshots used a pseudo-random se- quence generator to select candidate pixels for embedding bits of cipher-text and then rejected those candidates where the local variance of luminosity was either too high or too low.

One scheme that uses bit-tweaking in a novel way is Chameleon. Ideally, all distributed copies of a copyright work should be fingerprinted, but in applications such as pay-TV or CD, the broadcast or mass production nature of the medium appears to preclude this. Chameleon al- lows a single ciphertext to be broadcast while subscribers are given slightly different deciphering keys, which produce slightly different plaintexts. The system can be tuned so that the deciphered signal is only marked in a sparse sub- set of its least significant bits, and this may produce an acceptably low level of distortion for digital audio. The precise mechanism involves modifying a stream cipher to reduce the diffusion of part of its key material [62].

Systems that involve bit-twiddling have a common vul- nerability, that even very simple digital filtering operations will disturb the value of many of the least significant bits of a digital object. This leads us to consider ways in which bit tweaking can be made robust against filtering.

D. Spreading the hidden information

The obvious solution is to consider filtering operations as the introduction of noise in the embedded data chan- nel [63], and to use suitable coding techniques to exploit the residual bandwidth. The simplest is the repetition code

  • one simply embeds a bit enough times in the cover object

that evidence of it will survive the filter. This is inefficient in coding theoretic terms but can be simple and robust in some applications.

Another way to spread the information is to embed it into the statistics of the luminance of the pixels, such as [64], [65]. Patchwork [64], for instance, uses a pseu- dorandom generator to select n pairs of pixels and slightly increases or decrease their luminosity contrast. Thus the contrast of this set is increased without any change in the average luminosity of the image. With suitable param- eters, Patchwork even survives compression using JPEG. However, it embeds only one bit of information. To embed more, one can first split the image into pieces and then apply the embedding to each of them [28], [66].

These statistical methods give a kind of primitive spread spectrum modulation. General spread spectrum systems encode data in the choice of a binary sequence that appears like noise to an outsider but which a legitimate receiver, furnished with an appropriate key, can recognise. Spread spectrum radio techniques have been developed for mili- tary applications since the mid-1940’s because of their anti- jamming and low-probability-of-intercept properties [67], [68], [69]; they allow the reception of radio signals that are over 100 times weaker than the atmospheric background


Tirkel et al. were the first to note that spread spectrum techniques could be applied to digital watermarking [70] and later a number of researchers have developed stegano- graphic techniques based on spread spectrum ideas which take advantage of the large bandwidth of the cover medium by matching the narrow bandwidth of the embedded data to it (e.g., [63], [71], [72], [47]).

In [16],

Cox et al. present an image watermarking

method in which the mark is embedded in the n most per- ceptually significant frequency components V = {vi} of an image’s discrete cosine transform to provide greater robustness to JPEG compression. The watermark is a s e q u e n c e o f r e a l n u m b e r s W = { w i } n i = 1 d r a w n f Gaussian distribution, and is inserted using the formula n i=1 r o m a

˜ ˜vi = vi(1+αwi). If I is the original image and I the water-

marked image, that is the image whose main components have been modified, the presence of the watermark is veri- fied by extracting the main components of I and those with

˜ same index from I and inverting the embedding formula to

g i v e a p o s s i b l y m o d i fi e d w a t e r m a r k W . T h e w a t e r m a r k

i s s a i d t o b e p r e s e n t i n ˜ I i f t h e r a t i o W · W / W · W i s

greater than a given threshold.

The authors claim that O( n/ ln n) similar watermarks must be added before they destroy the original mark. This method is very robust against rescaling, JPEG compres- sion, dithering, clipping, printing/scanning, and collusion attacks. However it has some drawbacks. Most seriously, the original image is needed to check for the presence of a watermark.

The second problem is the low information rate. Like Patchwork, this scheme hides a single bit and is thus suitable for watermarking rather than fingerprinting or steganographic communication. The information rate of such schemes can again be improved by placing separate marks in the image, but at a cost of reduced robustness.

Information hiding schemes that operate in a transform space are increasingly common, as this can aid robustness against compression, other common filtering operations, and noise. Actually one can observe that the use of a par- ticular transform gives good results against compression algorithms based on the same transform.

Some schemes operate directly on compressed objects (e.g., [72]). Some, steganographic tools, for example, hide information in gif [73] files by swapping the colours of selected pixels for colours that are adjacent in the current palette [74]. Another example is MP3Stego [75] which hides information in MPEG Audio Layer III bitstreams [51] dur- ing the compression process. However, most schemes op- erate directly on the components of some transform of the cover object like discrete cosine transform [16], [17], [18], [76], [77], [78], wavelet transforms [17], [79], and the dis- crete Fourier transform [47], [80].

A novel transform coding technique is echo hiding [81], which relies on the fact that we cannot perceive short echoes (of the order of a millisecond). It embeds data into a cover audio signal by introducing two types of short echo with different delays to encode zeros and ones. These bits


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