Applications of Visual Cryptography - Visual Cryptography and Secret Image Sharing - page 334

FIGURE 12.11
Superimposing two encrypted images for the same key-slide shows the differ-
ence of the original picture.
images depict messages using a Font F consisting of f = jFj small symbols
(symbol-pictures) having q pixels.
Assume furthermore the symbols are placed on fixed positions, then Eve
can identify the pairs of symbols on corresponding positions as long as
f 2 =2 << 2 q . Then Eve can use, for example, the redundancy of natural lan-
guages to decipher the text. One measure to complicate this attack is to shift
the picture by a random number of pixels to the left or the right. Then Eve
will have to try out the position of the rst symbol and consider xy f 2 =2
combinations, where x and y are the differences of the shifts but smaller than
the width and the height of the symbols. Further complications can be caused
by filling the space around the text by partially random patterns, which Bob
can easily distinguish from the symbols, but Eve will have to start analyzing
parts in the middle of the image. Here she can only assume that about a quar-
ter of the surface of the letters overlap, which means this method of attacking
can be expected to be successfull if xyf 2 =2 << 2 q=4 .
Furthermore, the partially random patterns can compensate the statistical
imbalance of the correlation of neighboring points. For example, Eve could
look at pairs of pixels, where one is in some small distance above the other.
If both are on a position having a 0 on the slide, then, given many encrypted
images of texts, Eve could detect that they have the same color with a higher