Visual Cryptography from Halftone Error Diffusion - Visual Cryptography and Secret Image Sharing - page 7

(a) Secret binary image (b) Share 1

(c) Share 2 (d) Decoded image

FIGURE 1.4
Example of 2-out-of-2 scheme. The secret image (a) is encoded into two shares
(b)-(c) showing random patterns. The decoded image (d) shows the secret
image with 50% contrast loss. (Reprinted with permission from IEEE Trans.
Inf. Forensics Security, vol. 4, no. 3, pp. 383{396, Sep. 2009 c IEEE 2009).

The participants in X are able to observe the secret image without perform-
ing any cryptographic computation. VSS is characterized by two parameters:
the pixels expansion , which is the number of subpixels on each share that
each pixel of the secret image is encoded into, and the contrast , which is
the measurement of the difference of a black pixel and a white pixel in the
reconstructed image [5].
For each secret binary pixel p that is encoded into subpixels in each of
the n shares, these subpixels can be described as an n Boolean matrix M,
where a value 0 corresponds to a white subpixel and a value 1 corresponds
to a black subpixel. The ith row of M, ri, i , contains the subpixel values to
be assigned to the ith share. The gray level of the reconstructed pixel p,
obtained by superimposing the transparencies in a participant subset X =
fi i ;i 2 ; ;i s g, is proportional to the Hamming weight w(v) of the vector
v = OR(r i 1 ; r i 2 ; ; r i s ), where r i 1 ; r i 2 ; ; r i s are the corresponding rows in
the matrix M [26, 25].

Definition 1 Let ( Qual ; Forb ) be an access structure on a set of n par-