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Maria Calagna and Luigi V. Mancini
Table 11.4. Extract is the core function of the Extraction application. The digital map may
be extracted from the stego-map by applying the public-key of the Embedder that every user
knows. Also, if users own the right secret-key, then they will be authorized to have access to
the sensitive content that was hidden in the stego-map
Procedure Extract
Input:
S M, PK E , S K m , PK i ;
Extract DM (S M, PK E ) = dm;
if (S K m , PK i ) ∈ K GEN then
Extract HC (S M) S K m = HC;
hc = HC;
else
Extract HC (S M) S K m = ∅;
hc = ∅;
end
Output: dm, hc
the embedded sensitive content. The Extract() function releases dm and eventually the hidden content hc. The application of the Extract HC is transparent to the
users, so the knowledge of the class of users that are authorized to have access
to the sensitive hidden content is not revealed to those users that do not belong
to that class. These users will simply notice that no hidden content is available
to them.
11.7 Related Work on Information Hiding
In this section, due to the space limits, we chose to describe only a related work on
information hiding, though it was not designed specifically for the watermarking or
steganography purpose. Among different data hiding proposals [10] [26], a recent
work [3] shows that the SVD is a powerful tool to be used for information hiding.
According to the scheme that is introduced in [3], the orthogonal matrices U and
V are used as vessels for the secret message. While the singular value matrix Σ is
uniquely determined by the original matrix, the orthogonal matrices are not univocally determined [12]. In fact, an important requirement of the algorithm is that the
original matrix has a uniquely determined SVD decomposition that is assured if its
singular values are pair-wise distinct and non-zero. The secret message bits p k are
embedded in some elements u i j of the U matrix according to the formula:
u i j
= p k |u i j |
(11.8)
The updated orthogonal matrix U
, whose elements are u
i j , replaces U in the SVD
decomposition of the original matrix and the resulting stego is:
A
= U
ΣV
T
(11.9)
Maria Calagna and Luigi V. Mancini
Table 11.4. Extract is the core function of the Extraction application. The digital map may
be extracted from the stego-map by applying the public-key of the Embedder that every user
knows. Also, if users own the right secret-key, then they will be authorized to have access to
the sensitive content that was hidden in the stego-map
Procedure Extract
Input:
S M, PK E , S K m , PK i ;
Extract DM (S M, PK E ) = dm;
if (S K m , PK i ) ∈ K GEN then
Extract HC (S M) S K m = HC;
hc = HC;
else
Extract HC (S M) S K m = ∅;
hc = ∅;
end
Output: dm, hc
the embedded sensitive content. The Extract() function releases dm and eventually the hidden content hc. The application of the Extract HC is transparent to the
users, so the knowledge of the class of users that are authorized to have access
to the sensitive hidden content is not revealed to those users that do not belong
to that class. These users will simply notice that no hidden content is available
to them.
11.7 Related Work on Information Hiding
In this section, due to the space limits, we chose to describe only a related work on
information hiding, though it was not designed specifically for the watermarking or
steganography purpose. Among different data hiding proposals [10] [26], a recent
work [3] shows that the SVD is a powerful tool to be used for information hiding.
According to the scheme that is introduced in [3], the orthogonal matrices U and
V are used as vessels for the secret message. While the singular value matrix Σ is
uniquely determined by the original matrix, the orthogonal matrices are not univocally determined [12]. In fact, an important requirement of the algorithm is that the
original matrix has a uniquely determined SVD decomposition that is assured if its
singular values are pair-wise distinct and non-zero. The secret message bits p k are
embedded in some elements u i j of the U matrix according to the formula:
u i j
= p k |u i j |
(11.8)
The updated orthogonal matrix U
, whose elements are u
i j , replaces U in the SVD
decomposition of the original matrix and the resulting stego is:
A
= U
ΣV
T
(11.9)