Cryptography Reference
In-Depth Information
also called (t, n)-secret sharing. The total number of participants sharing the
secret key is n, and we need to have at least t of the shadows to reconstruct
the secret key [5].
In 1995, Naor and Shamir introduced a new application, Visual Secret
Sharing (VSS), for secret sharing. The basic problem with VSS is to share
a secret image with several participants. For a general (t, n)-VSS scheme,
the secret image is divided into n shadows, and each shadow is dispatched to
different participants. The participant cannot find out any information from
the shadow; because each shadow has only part of the secret information,
and t or more shadows are needed to recover the secret image. They only
become visible by stacking t shadows together. It is not necessary to use any
complicated computation and other advanced cryptographic mechanisms to
reveal the image.
Naor and Shamirs scheme is only suitable for a binary image composed
of black and white pixels, but not for gray-scale or color images. Hence, the
practical application of the scheme is limited. Some researchers converted the
gray-scale image into halftone images as the secret data needed to replace
the binary image. For example, Lin and Tsai [6] used dithering techniques to
convert a gray-scale image into a binary image. Firstly, they divided a gray-
scale image into several blocks. Secondly, they used a space-filling curve dither
array to mix the order of the pixels in each block. Thirdly, they computed
the score for each pixel in the block. If the score of the pixel is smaller than
a dithering threshold, then the pixel is represented by a black bit. Otherwise,
the pixel is represented by a white bit. After being converted, the binary image
is obtained as the secret image. Then, they applied the general VSS scheme
on the secret image to generate some shadows for the latter use.
Nevertheless, the quality of the recovered image is low when using this
scheme on the binary images. From the human visual systems, we see that
the revealed image is not clear when compared to the original. Therefore,
many researchers reconsidered the physical properties of contrast, resolution,
and color, of the image to improve the performance of VSS schemes [7, 8, 9].
In 2005, Lukac and Plataniotis [10] proposed a bit-level based VSS scheme
operated directly on the bit planes of the secret image. That is, they de-
composed the secret image into several bit planes and took each bit plane
as a binary image. Their scheme could completely recover the original secret
image. In this scheme, n participants could share one secret image.
However, for a company which owns a large number of secret images,
each participant needs to maintain many secret shadows to recover the secret
images as each shadow only can be used to recover one secret image. In order
to broaden the utility of the shadow, Droste [11] introduced a new method for
the VSS scheme. In Drostes VSS scheme, a shadow can contain several secret
messages. That is, any t participants can recover a different secret image by
using Drostes VSS scheme. Nevertheless, Drostes scheme is ine
cient.
This chapter proposes an e
cient VSS scheme that adopts Lukac and
Plataniotis bit-level concept to represent the secret image. The recovered
