Information Technology Reference
In-Depth Information
proposed. This format was intended for thrifty representation of a digital image des-
tined for hiding in a cover one. Use of SVD transform for data hiding was originally
proposed in [10].
Let cover image be represented in a 24 bit (
RGB
) format. Assume that it is seg-
mented into small blocks of size
l
k
pixels, and
A
is the matrix of an arbitrary block
corresponding to one of
Red
,
Green
or
Blue
color layer. Let bit
b
be embedded into
block
A
. The algorithm of the
embedding procedure
is as follows:
×
V
λ
1. Compute SVD of matrix
A
. Let
] be the vector composed of
singular values of matrix
A
ordered
in decreasing mode,
=[
λ
,
λ
,...,
λ
1
2
r
Y
are singular
X
and
vectors of matrix
A
,
i=1,2,…,r
,
and
r
is the rank of matrix
A
.
2. Compute Euclidean norm of vector
V
∑
=
λ
r
i
,
Norm
(
V
λ
)=
(
v
λ
)
2
, where
i
v
,
1
i=1,2,…,r ,
are the components of the vector
V
.
3. Select the value of the step of quantization of the Euclidean norm of the vector
V
,
Delta
[10].
4. Compute the integer
N=[Norm(
V
)/Delta]*,
where
*
symbolizes
the integer part
of the quotient of the above division.
5. Embed bit
b
according to the following algorithm:
If b=1 then
{if N is
odd
then
~
=N+1 else
~
=N}
else (if b=0)
{if N is
even
then
~
=N else
~
=N+1}}
6. Compute the modified norm of the vector of the singular values:
)
=
~
V
λ
Norm (
×
Delta+(Delta/2).
7. Compute the
modified vector of the singular values:
V
~
V
~
V
V
λ
λ
λ
λ
=
×
(Norm
(
)/
Norm
(
)).
8
.
Compute the modified matrix of the block in which bit
b
is embedded:
~
=
∑
=1
~
r
i
λ
X
Y
T
.
i
i
i
9. End of the single bit embedding procedure.
The described algorithm must be applied to each block of the cover image in which
a bit of data is to be embedded.
The
extraction
procedure is
blind
. Let
~
be the matrix of a block containing hid-
den bit
b
of data, which must be extracted.