Polynomial-Based Image Sharing - Visual Cryptography and Secret Image Sharing - page 396

15.1 Introduction
The concept of secret sharing comes from the method of secret key manage-
ment and was rst seen in the following works [1, 7]. The secret's owner wants
to share the secret with other participants, but no participants can obtain the
secret alone. When some of the participants work together, the secret is then
revealed. From a technical viewpoint, this secret sharing scheme may also be
referred to as the (t;n)-threshold, where t denotes the threshold value that
will reveal the secret and n is the total number of holding shadows. In this
method, when a secret is given, it must be divided into n shadows and it is
then reconstructed by t or more shadows, possessed by the shadow holders;
no information can be conjectured by fewer than t shadows. In the wake of
this cryptographic application proposal, many related methods were further
proposed to enrich secret sharing diversity in both theoretical and practical
arenas [4, 6, 8, 12].
Visual security was proposed by Naor and Shamir [6] in 1994, where an
image could be reconstructed by superimposing two shares. The shares issued
in this scheme are made up of random binary patterns. The target secret, rec-
ognized by the human visual system, is nally stacked by the (t;n)-threshold
scheme. One of the main advantages, in this scheme, is that it does not require
complicated computations, which traditional numeric cipher-text in secret de-
cryption does, while the sizes of the enlarged shares, and target secrets are left
the same. Thien and Lin [8] proposed an applied secret image scheme for im-
age embedding to improve upon Naor and Shamir's method. The concealment
of a secret image avoids cipher-based attacks on the basis of stego-image im-
perceptibility. In 2006, Horng et al. uncovered another way to cheat the (t;n)-
threshold under visual cryptography (VC) applications [3]. In their proposal,
a scenario was successfully put forward showing that shareholders were able
to collaborate with each other by sending fake shares to other shareholders.
Accordingly, the final target secret image was different from the genuine one,
corrupting the secret sharing system.
Steganography is a kind of data hiding technique that provides another
method of security protection for digital image data. The purpose of steganog-
raphy is to embed secret data in preselected meaningful images, called cover
images, with people being visually unaware of the secret's existence. Numer-
ous schemes have been developed to achieve successful data hiding [2, 5]. To
prevent the fake stego-image from the dishonest participants, Lin and Tsai
[4] authored an authentication-based steganography study, where their detec-
tion technique tested whether the offered shares were genuine or not. In their
scheme, parity checks were applied to prevent the modified shares from mali-
cious attacks. Later on, in 2007, Yang et al. [12] enhanced the mechanism of
Lin and Tsai by proposing a revised scheme in which more detailed fake shares