Cryptography Reference
In-Depth Information
To ensure the validity of the map data, it must simultaneously satisfy
′
−x
1
′
−x
2
x
1
x
2
≤τ . Substitute Eqn. (6.7) and (6.8) into the
condition, and an equivalent condition is obtained
⎧
⎨
≤τ and
(
2d
x
+w
i
+1
2
d
x
+1
2
floor
−floor
≤τ,
(6.9)
(
2d
x
+w
i
2
d
x
2
⎩
floor
−floor
≤τ.
According to the parity of d
i
x
and the value of w
i
(0 or 1), the two sub-
conditions in Eqn. (6.9) can be simplified. Their intersection is taken to be
the final condition (Eqn. (6.10)) which determines whether the vertex pair
(v
1
,v
2
) is suitable for difference expansion:
−2τ +1≤d
i
x
≤2τ−2.
(6.10)
Eqn. (6.10) is then used to check the suitability of all N vertex pairs. A N -
length flag F is generated to record the results. Here F =f
i
∈0, 1,
i =1,,N. When f
i
=1theith vertex pair (v
1
,v
2
) meets the embedding
condition. A hidden bit will then be embedded by expanding the difference
d
i
x
. Accordingly, f
i
= 0 means that
f
i
v
1
,v
2
does not meet the embedding
condition. In this scheme, a hidden bit will also be embedded in such
v
1
,v
2
by replacing the LSB of d
i
x
. The original LSB of d
i
x
should not be discarded
for the sake of ensuring the reversibility of the scheme. A bit sequence L is
generated to record all replaced LSBs to avoid information loss. Both F and L
are necessary information which will be needed later for data recovery. They
are embedded in the cover map as a part of the hidden data.
Data Embedding and Extraction
1. Structure of Hidden Data
To ensure reversibility and to improve the capacity, the hidden data (denoted
as W ) should be composed as follows:
W = H + comp(F ) + comp(L)+P,
where comp() is the lossless compression algorithm. The meaning of each
component is listed below.
H: The header information recording the lengths of the other three compo-
nents. It is useful for reliably separating each data component from W
during the procedure of data extraction.
comp(F ): Lossless compressed flag F . The flag is necessary for recovering
the original data because we must know the embedding method of each
vertex pair. That is, by the difference expansion or by LSB replacement.
F is compressed to save space for the payload.
