Cryptography Reference
In-Depth Information
Suppose J() is a Jpeg-compression function, where I C =J(I ), and the com-
pression ratio is R = (the number of bits in I=the number of bits in I C ) 1.
At this time, the gray-level secret image I is compressed to I C such that the
information bits in I C can be embedded into the halftone secret image I 0 .
By replacing I with I C in our lossless TiOISSS, we could get the compress-
ible TiOISSS. The formal encoding/decoding algorithm of the compressible
version of our (k;n)-TiOISSS is omitted for brevity.
In the lossless version of the proposed TiOISSS, since jI 0 j = jIj=(k g),
k 2 and g 1, then jI 0 j < jIj. This observation implies that our TiOISSS
could embed all information bits of lossless I into I 0 , where jI 0 j < jIj, for any
values of (k;n;m;g). So, actually, our TiOISSS does not need compression on
I. However, to be fairly compared with the compressible version of Lin and
Lin's scheme, we use a compression ratio R = R LIN = (n=k)8=log 2
m
w
such that we have the same image quality of the reconstructed image (a Jpeg-
compressed version) as Lin and Lin's scheme; at this time the size of our
halftone secret image can be further reduced to jI 0 j = jIj=(kgR). Then,
the shadow size is mjI 0 j = (mjIj=(kgR)) and the pixel expansion
of the compressible version m (C)
PRO is
m (C)
PRO = m=(kgR):
(17.9)
17.5 Experimental Results and Comparisons
Example 5 shows three (2, 4)-TiOISSSs, Jin et al.'s scheme [6], Lin and Lin's
scheme [9] and our scheme [20], respectively; this example demonstrates the
lossless version. The compressible versions of Lin and Lin's (2, 4)-TiOISSS
and our (2, 4)-TiOISSS are given in Example 6, where a compression ratio
4
2
R = 6:5 > R LIN =(4=2) 8=log 2
=6.19 is used.
Example 5. Construct three lossless versions of (2, 4)-TiOISSSs: (1) Jin
et al.'s scheme (2) Lin and Lin's scheme (3) our scheme (the lossless version)
2
4
3
5 and B 0 =
2
4
3
5 .
1100
0110
0011
1001
1100
1100
1100
1100
using B 1 =
A 512512 gray-level Lena in Figure 17.3(a) i is used as a secret image. By
(2, 4)-PISSS, we rst obtain four 512 256 gray-level shadows P 1 P 4 . To
share all information bits in Pi, i , Jin et al's scheme and Lin and Lin's scheme
need the 12741274 halftone secret image and the 15361536 halftone image,
while our scheme needs the 256 256 halftone secret image (since k = g = 2,
so jI 0 j = jIj=(k g) = jIj=4). The shadow sizes of Jin et al.'s scheme, Lin
 
 
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