Cryptography Reference
In-Depth Information
Table 13.1.
Embedding on difference values.
Category
Original
Original Location Map New Value New Set
Set
Set
Value
Changeable
EZ
or EN
1
h
1
2h + b
CH
EN
2
or CN
h
0
2⌊
2
⌋+ b
Non-Changeable NC
h
0
h
NC
The data embedding by replacement is illustrated in Table 13.1. After all
bits in B are embedded, they then apply the inverse transform in Eq. (13.13)
to obtain the embedded image.
The extraction process starts by calculating the average value l and the
difference value h of pixel pairs (x, y) by scanning the watermarked image in
the same order used during embedding. Referring to Table 13.1, they divide
pixel pairs into two sets
CH
(changeable) and
NC
(not changeable) using the
condition given in Eq. (13.15). They extracts all LSBs of h for each pair in
CH
to form a bitstream B which is identical to that formed during embedding. The
extracted bitstream B is decompressed to restore the location map by a JBIG2
decoder. Hence, all expanded pixel pairs after the DE in
CH
are identified.
By identifying an end of message symbol at its end for a JBIG2, bitstream C
including the original LSBs of the changeable difference in
EN
2
∪
CN
and the
payload is retrieved. The original values of differences are restored as follows.
For
h in
EZ
∪
EN
1
, they restore the original values of
h as follows:
h
2
h =
.
(13.16)
For h in
EN
2
∪
CN
, they restore the original values of according to the
following Eq. (13.17).
h
2
h =2
+ b
1
,
1
∈C.
(13.17)
Finally, they apply the inverse transform given in Eq. (13.13) to retrieve
the original image. They then compare the retrieved authentication hash with
the hash function of the restored image. If the two hash functions match
exactly, the image content is authentic and the restored image is exactly the
same as the original image.
Tian implemented the DE method and tested the method on various stan-
dard grayscale images. Tian also implemented the RS lossless data-embedding
method in [7] and the lossless G-LSB data-embedding method in [8] in order
to compare the results among the three methods using 512512, 8 bpp
grayscale Lena. From the comparison results described in [11], Tian achieves
the highest embedding capacity, while keeping the lowest distortion. Except
