Visual Cryptography for Multiple Secrets - Visual Cryptography and Secret Image Sharing - page 58

secrets in visual cryptography for any x 2 secrets in two shares. Their pixel
expansion is 2x, which is the best result so far in the model that each pixel
would be expanded.
Based on a different set of encoding patterns, Feng et al. [3] developed
another scheme to achieve the same goal using two cylinder shares. The pixel
expansion needed is 3x.
In this chapter, we introduce these interesting algorithms. The rest of the
paper is organized as follows. In Section 3.2, we briefly review the visual one-
secret sharing scheme in two shares proposed by Naor and Shamir [7]. The
visual two-secret sharing scheme by Wu and Chen [12] and Wu and Chang [13]
are discussed in Sections 3.3.1 and 3.3.2, respectively. The schemes for visual
multisecret are examined in Section 3.4 in which the experimental results and
discussions are also presented. Section 3.5 g ives some concluding remarks.
3.2 Naor and Shamir's Basic Visual Secret Sharing
Scheme
The basic idea of Naor and Shamir's encoding scheme [7] for sharing a single
pixel, say p, in a binary image P into two shares s 1 and s 2 is illustrated in
Table 3.1. If p is white, the dealer randomly chooses one of the first two rows
of Table 3.1 to encode s 1 and s 2 . If p is black, the dealer randomly chooses
one of the last two rows in Table 3.1 to encode s 1 and s 2 . The possibilities of
the two encoding cases are equally likely to occur, independently of whether
the original pixel is black or white. Thus, neither s 1 nor s 2 exposes any clue
about the binary color of p. When these two shares are stacked together, i.e.,
s 1 s 2 , two black subpixels appear if p is black, while one black subpixel and
one white subpixel appear if p is white as indicated in the rightmost column in
Table 3.1. Based upon the contrast between these two kinds of reconstructed
pixels, our visual system can tell whether p is black or white by observing
s 1 s 2 .
Note that s 1 (or s 2 ) in Table 3.1 is not a single pixel, but two subpixels. We
call s 1 (or s 2 ) an extended block and the pair (s 1 , s 2 ) the pair of two extended
blocks with respect to p. The number of the subpixels in each of the two
extended blocks (s 1 , s 2 ) for encoding p is referred to as the pixel expansion.
In Table 3.1, the pixel expansion is 2. In realistic implementations, it may be
chosen as 4 (= 2 2) in order to retain the aspect ratio of the original secret
image. Since there are six possible patterns for a 2 2 extended block, all
pairs of two extended blocks (s 1 , s 2 )'s for encoding a specic binary pixel p
(visual one-secret sharing) are summarized in Table 3.2.
When p is white (black), the dealer randomly chooses one of the first (last)
six rows of Table 3.2 to encode p into s 1 and s 2 . It is seen from the last column
of Table 3.2 that the reconstructed pixel r = s 1 s 2 may contain two white