Visual Cryptography for Multiple Secrets - Visual Cryptography and Secret Image Sharing - page 90

can be shared by more than two shares is also an interesting topic. Potentially,
sharing multiple secrets may have more flexibilities and applications than
sharing only one secret. Visual identification and visual authentication are
some typical applications in visual cryptography [6]. It would be of much
significance to reexamine these topics from a viewpoint of sharing multiple
secrets.
As a matter of fact, the sharing of multiple secrets visually brings forth new
problems to be considered. For instance, with regard to the \starting position
for encoding" in A or/and B in Experiment 2, we may design such a concern
to be some kind of private key, which is only accessible between the dealer and
authorized participant(s). Without the correct starting positions in A or/and
B, the alignment of A and B cannot recover the secret yet. In addition, the
second secret of the three secrets in Experiment 1 might be designed to be
fake for the purpose of diffusion. That is to say whether the whole secret
message is \Help is never on its way"or \Help is on its way"may be treated
to be another private key between the dealer and authorized participant(s).
Mainly, the number of secrets, the degree of the starting position for encoding,
the combination of the true or fake reconstructed secrets, and so on, can be
designed as private keys to increase the level of security in the visual multi-
secret sharing system.
3.5 Concluding Remarks
By adopting circle or cylinder shares, we discuss general visual secret sharing
schemes for x 1 (indeed, these schemes work well for x = 1) secrets in
two shares in this chapter. The previous studies considered sharing only two
secrets in two shares [12, 13]. Shyu et al.'s scheme can be implemented easily
and it takes only some constant working space. All encoding information can
be determined in run time. By introducing an independent random permu-
tation (i.e., j , see formulae (3.1) and (3.4)) when encoding each pair of the
corresponding blocks (i.e., a j and b j , see Step 3.2.1 and 3.2.4 in Algorithm
1), the scheme ensures the maximum randomness that the subpixels in an en-
coded block may possibly provide. For the transmitter, one machine capable of
running the encoding scheme is needed, while for the receivers, no computing
device is required and the decryption process is simply by the human visual
system. The proposed scheme can be easily extended to gray-level images by
adopting the halftone technology [4] or even color images by exploiting color
decomposition [4] or color composition [9].
In traditional visual secret-sharing schemes, rectangle shares are encoded
to conceal one shared secret. They are easily superimposed by aligning the
rectangular corners. As compared to the rectangle shares, the circle or cylinder
shares are relatively hard to superimpose since there are no reference points