Two-Decoding-Option Image Sharing Method - Visual Cryptography and Secret Image Sharing - page 455

reconstruct a secret image by k or more shadows, while he cannot conjecture
any information from less than k shadows. There are two major categories
in ISSS: one is the visual cryptography scheme (VCS) and the other is the
polynomial-based ISSS (PISSS).
In the (k, n)-VCS, a secret image is encrypted into n shadows by expand-
ing each secret pixel into m (the pixel expansion) subpixels. Notice that the
dierence between the pixel and the subpixel is that the "pixel" denotes the
secret pixel located in the secret image, and the "subpixel" means the pixel
located in shadows. Actually, the size of a subpixel is the same as that of the
secret pixel. Therefore, shadows are, in general, expanded. Any k participants
may photocopy their shadows on transparencies and stack them on an over-
head projector to visually decode the secret through the human visual system
(HVS) without hardware and computation. However, stacking k 1 or fewer
shadows will not gain any information. The first VCS encrypted a halftone
(black-and-white) secret image into noise-like shadows [11]; subsequently, most
VCSs were dedicated to reducing the pixel expansion [5, 7, 16, 17, 18, 2].
Indeed the visual quality of the VCS is poor, which comes from its intrinsic
property using the OR-operation for decoding. Contrarily, the PISSS can re-
cover the secret image without any distortion, while it needs the computation.
By directly adopting Shamir's secret sharing scheme [12], a (k, n)-ISSS takes
the secret pixel as the constant term in (k1)-degree polynomials to share the
secret. To gain small shadows, Thien and Lin used all coecients in a (k1)-
degree polynomial to generate shadows with size 1=k times to the secret image
[13]. Afterwards, Wang and Su [15] further reduced the shadow size by using
the Huffman code. Shadows in [13, 15] are noise-like, which shadows are of-
ten suspect to censors. It would be better to design a (k, n)-ISSS with the
ability of steganography, i.e. shadows look like a cover image (a pre-selected
meaningful image). Actually, we can construct a (k, n)-ISSS being provided
with meaningful and meaningless shadows according to our need. Some (k,
n)-ISSSs with meaningful shadows were proposed [14, 21, 8, 19, 1, 4, 6]. For
example, two user-friendly (k, n)-ISSSs [14, 21] produced the shadow with a
shrunken secret image on it. However, the portrait on shadows had already
leaked the secret information, and thus this scheme is, strictly speaking, not
a secret sharing scheme. Other (k, n)-ISSSs [8, 19, 1, 4] can present any cover
images on shadows. Lin and Tsai's scheme [8] had the authentication capabil-
ity to detect the faked shadows. The schemes in [19, 1, 4] improved Lin and
Tsai's scheme to solve the dishonest participant problem of authentication,
enhance the detection ratio of manipulated shadows, and improve the visual
qualities of shadows.
A new type of ISSS with two decoding options was introduced recently,
where the secret image is revealed both by stacking the transparencies and
by computation. This scheme is referred to as two-in-one ISSS (TiOISSS).
TiOISSS can decode secret images for preview by the HVS when a computer
is temporarily unavailable. When the computer is available during the decod-
ing scene, we then spend more computation to obtain a high-quality image for