Two-Decoding-Option Image Sharing Method - Visual Cryptography and Secret Image Sharing - page 460

with m=2. Recently, Lin and Lin proposed a TiOISSS [9] based on the VCS
and PISSS to reduce the pixel expansion. A halftone secret image is encrypted
into n shadows by (k;n)-VCS with the pixel expansion m, which every row
contains b "1" and w "0" and m = b + w. It is obvious that every m-subpixel

m
w

m
w

has combinations, and it can be used to represent about log 2

bits. Notice that in the conventional VCS, we can randomly permute all m

m
w

columns in matrices. However, when using the combinations to rep-

resent the information and simultaneously satisfy the security condition, we
could only randomly choose the combination for one shadow and the remaining
(n1) shadows are then determined according to the base matrices. Therefore,
in a shadow, only (jI 0 j/n) digits can be used to share log 2

m
w

bits. On the

other hand, we need (8 jIj/k) bits to share the gray-level secret image I by
(k;n)-PISSS. To assure we have enough space to hide the secret, the gray-level
secret image is compressed by Jpeg or other compression techniques to reduce
the information as (8 jIj/(kR)) bits where R is the compression ratio. In
[9], the authors consider the case in which the halftone secret image and the
gray-level secret image have the same size, i.e., jIj = jI 0 j.
As a result, (jI 0 j/n)log 2

m
w

(8 jIj/(kR)), and thus the com-

pression ration R should satisfy the following requirement to hide all informa-
tion of a gray-level secret image.

m
w

R 8n k log 2 (17.5)

Since jIj = jI 0 j, nally, the pixel expansion of Lin and Lin's (k;n)-TiOISSS

is

m (C)

LIN = m:

(17.6)

For example, the pixel expansion of Lin and Lin's (2, 2)-TiOISSS when
using (2, 2)-VCS with m = 2 is m (C)

LIN = 2 less than m JIN = 18. However, the
gray-level secret image can be perfectly reconstructed in Jin and Lin's scheme,
while Lin and Lin's scheme only recovers the compressed image. The greater
compression ratio will degrade the visual quality of the secret image.
Example 2. Construct Lin and Lin's (2, 4)-TiOISSS and Jin and Lin's

2 3 2 3

1100
0110
0011
1001

1100
1100
1100
1100

4 5 and B 0 = 4 5 .

(2, 4)-TiOISSS using B 1 =

m
w

4
2

Since = = 6 (there are six combinations: (1100), (0011),

m
w

(1010), (0101), (1001), (0110)), log 2 = log 2 6 = 2:585 bits. Suppose