Cryptography Reference
In-Depth Information
17.4.2 The Lossless TiOISSS
We construct a (k;n)-TiOISSS based on a (k;n)-PISSS and a (k;n;m;g)-
GVCS to share a gray-level secret image I. For the lossless version, we first
determine (8 jIj/k) bits by PISSS. So, jIj=k gray supixels in each shadow of
(k;n;m;g)-GVCS are required to hide (8 jIj/k) bits. Since there are g gray
subpixels in every m subpixels of (k;n;m;g)-GVCS, the halftone secret image
I
0
for GVCS should be jI
0
j = jIj=(kg). So, the shadow size is mjI
0
j. For
the lossless version, the pixel expansion of our (k;n)-TiOISSS m
(L)
PRO
is
m
(L)
PRO
= m=(kg):
(17.8)
The formal encoding and decoding algorithms are described as follows.
Some notations are defined first.
Notation Used
P() encryption of (k;n)-PISSS.
P
-1
() decryption of (k;n)-PISS.
I the gray-level secret image with the size jIj, which is used as the input
of P().
P
i
the output shadows of P(I ), i 2 [1;n], with the size (jIj=k).
G() encryption of (k;n;m;g)-GVCS with B
0
1
and B
0
0
, and the values
of gray subpixels are chosen according to the gray pixels in Pi.
i
.
G
-1
() decryption of (k;n;m;g)-GVCS (stack shadows and visually de-
code the secret by HVS).
H() halftoning function, transform and resize a gray-level image to a
halftone image.
I
0
a halftone secret image with the size jI
0
j = jIj=(kw) obtained from
I
0
=H(I ).
G
i
the
G(I
0
), i 2 [1;n],
output
shadows
of
with
the
size
((mjIj)/(kg)).
Encryption Algorithm of the Lossless Version of Our (k;n)-
TiOISSS
Input: the gray-level secret image I ; the parameters k;n;m;g; matrices
B
0
1
and B
0
0
.
Output: n shadows G
i
;i 2 [1;n].
1-1) Encrypt the secret image to obtain Pi=
i
= P(I ), i 2 [1;n].
1-2) Obtain I
0
from I
0
=H(I ) .
1-3) Output n shadows G
i
=G(I
0
), i 2 [1;n].
Decryption Algorithm of the Lossless Version of Our (k;n)-
TiOISSS
Input: any k out of n shadows Gi2
i
1
;G
i
2
;:::;G
i
k
.
Output: the halftone secret image I
0
(Phase 1); the gray-level secret image
I (Phase 2).
Search WWH ::
Custom Search